Income Tax 2023-2024. Ira Distribution Tax Software Example.  First, a word from our sponsor. Actually, we're sponsoring ourselves on this one because apparently the merchandisers, they don't want to be seen with us. But that's okay, whatever.  Like our Accounting Rocks product line. If you're not crunching cords using Excel, you're doing it wrong. A must-have product because the fact as everyone knows of accounting being one of the highest forms of artistic expression means accountants have a requirement, the obligation, a duty to share the tools necessary to properly channel the creative muse. And the muse, she rarely speaks more clearly than through the beautiful symmetry of spreadsheets. So get the shirt because the creative muse, she could use a new pair of shoes. If you would like a commercial free experience consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com Here we are in our Form 1040 example problem using LASERT tax software. You don't need tax software to follow along, but if you have access to tax software it's a great tool to run scenarios with. You can also get access to the forms, schedules, instructions at the IRS website irs.gov, irs.gov, starting with our normal starting point. Adam, tax man, just trying to avoid the dang tax man living in Beverly Hills 90210. It's going to start off with a single file or no dependence W2 income at the 100,000. We have the standard deduction 13,850, getting us to taxable income 86,150. We can mirror that in our Excel worksheet with the tax formula. So we have the 100,000, 13,850, 86,150, and then the tax calculated by the software 14266 which is on page 2 of our 1040, 14266. Let's go back to page 1. We're focused on the income line item once again. This time we're looking at IRA distributions. So we're looking at line 4A and line 4B, page 1 of the Form 1040. The form typically used to express or give this information to us given by the financial institutions to both us and of course the IRS is going to be the 1099R which is distributions from pensions, annuities, retirement or profit sharing plans, IRAs, insurance contracts, etc. So normally you would be seeing these forms more when you're doing taxes for older individuals. In other words, when you do taxes for people in their working years you expect to see things like W2 forms and whatnot. When people are in their retirement years then you would expect to see more of their income expressed from the 1099R and these are going to be distributions that could be subject to tax because they were not subject to tax when they first put the money in oftentimes if it's a normal IRA situation or like a 401K or other type of retirement plan. Now here we're focused mainly just on the IRA. So if it's an IRA you might see a checkbox down here to indicate that it's going to be an IRA. We've got the gross distribution up top and the taxable amount. Those are going to be the key numbers as well as possibly you can have withholdings from these distributions noting that when you talk about people that are in their working years the primary source of income oftentimes is the W2 and therefore the employer is forced to withhold based on the W4 information provided by the employee to the employer that is then shown on the W2 form. In retirement oftentimes the primary income that people are getting are taking money out of their savings subject to taxes therefore it makes sense to do withholdings here box 4 on the 1099Rs. So that could come into play with tax planning as well. You might have to come up and ask the question of do you want to set up your distributions from your IRAs to have withholdings on them or possibly you can simply set up quarterly payments that somebody can make to try to cover the taxes that you're going to estimate that will be resulting from the withdrawals. Those are kind of some again planning questions that you have to basically take into consideration as opposed to the data input stuff which is usually fairly straightforward driven by the forms. Alright so then you could also have the state withholdings down below as well. So we'll keep it here and we'll say okay let's go to the first page and say we have income now we're going to say it's a pension or IRA income and let's just call it IRA distribution. Now also note that if they're a married couple then you could have, you want to keep it straight between the taxpayer and the spouse because sometimes that could have implications on the tax return even though they're a married couple. So we're single right now so not an issue if I select the dropdown here's going to be the codes that are in place. So number one early distribution no known exception versus early distribution if there is an exception and a normal distribution. If they're past retirement age these are the codes that you might expect to see and say box seven here then and if they're past retirement age you would expect normal distributions and that would comply with their age and that would mean that they're subject to tax but not basically to penalties. If they take the money out before retirement age then you're going to say is it an early distribution no known exceptions which means they'll be subject to tax but they'll also be hit with a penalty or is it going to be an early distribution in which an exception applies in which case that exception might be indicated on the form here which you would hope that it would be but then you could research further exceptions to make sure that you have the exception documented on the return so you cannot include it in income in that situation or possibly included in income but not be subject to the penalty for early withdrawal. Alright let's start off by saying they're over the age limit to pull the money out so let's say normal conditions that our taxpayer is let's say 2023 minus let's say like 67 let's do that again 2023 minus 67 so they're going to be like 67 something years old let's say so that's going to be 1956 so now let's say that they don't have any W-2 income they may still but let's say W-2 income no and they're pulling money out from their IRA so now we're going to say this is their primary source of income it's going to be seven normal distribution this is an IRA so I'll check it off as an IRA and then the gross distribution let's say is 70,000 the taxable amount 70,000 so it's not always the case that you're going to have one IRA of course or even a retirement plan if it was like a 401K plan that will be the only source of income in other words it used to be that people worked at the same company for their entire life and then they had a retirement plan with that company like a 401K plan and then in retirement you would expect most of their income would be coming out of the 401K plan so it would be fairly basic but more and more you have multiple people in a family working so you could have husband and wife and they're going to have multiple jobs throughout their life which means they might end up putting money into multiple IRAs, multiple retirement plans and so on and so forth so you might have a bunch of these documents so we'll take a look at that in a second but let's start with one so we're going to say alright what will that look like so now we're going to say nothing's in the W-2 income and then down here we have the IRA distributions and we're looking at just the taxable amount because we said all of it was taxable because we're imagining it was a normal distribution from an IRA which was not subject to tax when they put the money into the IRA is subject to tax when they take the money out of the IRA also note that they bounced me up to a 1040 SR I'm going to go back to the 1040 just so we can see like the normal form that we're used to and then you can kind of see the same construction on the 1040 SR so there's the 70,000, there's the 15,700 because they're over the age limit now so if I go back on over I'm going to say okay this 100,000 let's go to income and I'm going to say they don't have the job and let's add another category down here for the IRA distributions so I'll pull this down and I'm going to say let's say this is going to be IRA distributions and then we'll make this black and white, home tab, font group, let's make it black and white and then I'll make some of it blue for the data input up to here let's say making it blue and then this was going to go so IRA 1 let's just say 70,000 now if there was a non-taxable amount let's put that in our category on the right again and then we can put an explanation if there was any rationale for it being non-taxable but so then I'm going to say this is going to be the total IRA distribution equals the sum I need to put it in the outer column over here equals the sum of this stuff so my total income is now the W2 income I don't have any of that, don't have any of that and all I have is I'm just going to copy this down to here is that IRA so there's the 70,000, pulls over to page 1, there's the 70,000 now they're over the age limit so instead of being single at that number I have to add to it because they're single another 1850 for the standard deduction so now it's that 157 so that means that we're at 54,3 so there's the 54,3 page 2 calculating the tax 7259 and there's the 7259 so that would be the normal kind of process and of course then this number is being determined by how much money they're taking out of the IRA so you have to juggle the problem of what are the required distributions that they might have to take if they're over a certain limit like 72 and then and what do they need to live on and then how much taxes are you going to pay given the amount that you take out of this IRA now also note that if they had some other source of income or savings that they can pull money out of like it would be best if they can live off of 70,000 but pull less out of the IRA because they don't need to so that they can lower the amount of tax possibly so if I'm going to live on 70,000 but I want to pull out half of that 70,000 divided by 2 that would be great because maybe I have 35,000 in a Roth IRA which is not subject to tax possibly when I take it out or it's in another savings account then I can live off of 70,000 but I would only have to pull out of my IRA if I was able to do that 35,000 and then my tax would be of course significantly lower and my tax bracket would be lower because now I'd only be 10 so that's kind of like what you would like to do when you're thinking about how you're going to live in retirement some of the thought process would be well look all of this money is in a fund when I take it out I'm going to be subject to taxes anyway that I can spread that money out while still getting the maximum tax benefits that I could so that when I take the money out in retirement I could take money out so that I have a lower taxable income but you also have to keep in mind when they force you to take the money out which is going to happen after 72 or something okay so then let's say that he was not of age to take the money out and there might be a penalty on this let's go back to saying that his age here is let's say 1977 I was saying and then we're going to say okay well then he took the money out and he didn't have any good reason to take it out because it was under the threshold of a retirement account and 70,000 and so now we're going to say it was an early distribution no known exceptions uh-oh that's not the code we like to see we don't like to see that code in line 7 this often happens when people get a new job and they take the money out of or they quit a job and get a new job or not and then they take the money out of the retirement account and say well I need the money because I don't got a job right now which means it might not be an IRA in that case but similar situation it'd be like a retirement plan but if we go back on over now we've got the 70,000 again and we're still at and now we're at the 13,850 so if I go back on over here I have to change this back to the 13,850 brings us to taxable income 56,150 56,150 tax calculated on page 2 is going to be the 7666 here but then we have an added tax other taxes which is the penalty of the 7,000 so this is coming from schedule 2 so if I look at schedule 2 I can say okay what happened here K-PASO what happened additional tax on IRAs or other tax-favored accounts you can attach form 5329 if required so 5329 is additional taxes on qualified plans and so on and so here it's calculating basically you can see a 10% penalty calculated on it so that's really not good because now I had to pay taxes on it and a penalty of 10% which is fairly hefty penalty so you don't want to do that typically if you pull the money out you want to have a rationale a reason for it now if there's a natural disaster or something then there might be an exception to the rule and so on and you can look into those specific cases otherwise the general idea would be don't pull the money out if you don't have to pull the money out is the general idea now you might be saying okay but what if I want to what if I'm under the age to pull the money out but I noticed that all of my money is in like like Vanguard and BlackRock and they keep on doing this ESG stuff which is ruining the world with this woke craziness like they're paying people to lose money like they're paying Disney to make crappy movies and lose money and like I'm sick of it so I'm contributing to the problem by investing in this ESG stuff so we're like okay what if I roll the money over if it's a rollover then I can basically possibly roll it over to another account that's still under the umbrella without taking the money out this will also be important if one person is going from one job to another job in which case it might not be an IRA in that case but you might have a similar situation where you're trying to roll over what was under the umbrella of a retirement account so that you don't get hit with taxes on it so what you'd like to see in there is a code that says I think it's a G that says it's going to be a rollover direct rollover now that would be the easiest thing to do so in here again you don't want to see the code that's going to say it's an early distribution that you're going to be subject to penalty you'd like your thing to say like G or something which says that it's going to have a direct rollover and that means that you didn't even put your hands on it you just said I went to the new place and I said hey look my old place is doing this crazy SG stuff I just want to invest them they make me money I'm not trying to change the world to go crazy so I want you to and then if they contact the other company then hopefully they can roll over the money directly and properly give you the 1099R reflecting that it's a rollover so that it'll be nice and easily shown on your tax return so now we can see that we have an IRA here and it's going to be a rollover hold on a second still I still have it subject to tax that would mean the taxable amount hopefully would be zero right so now you would think what would this look like gross distribution taxable amount would have zero though and then possibly a code that would say it's a rollover which would be a code G maybe and then I can go back on over and say okay I'll tell the government yeah we had an IRA distribution but it was a rollover which is now being indicated by the software there's four zero over here and no impact on the taxable income in that case alright let's go back to saying that it's a legit distribution and just add some federal withholdings on it so let's say once again that our taxpayer Adam is going to be it's a two thousand twenty three minus like sixty seven so sixty seven years old it's going to be back to like nineteen fifty six and let's say that it's not wages but we go back to our plan here it's a normal distribution now code number seven normal distribution and seventy thousand and then he had taxes withheld of fifteen thousand let's say and so now you withheld taxes on it which is typical often of a ten ninety nine are given the fact that that's your primary source of income possibly so you might in keeping with what many people are used to of having withholdings instead of estimated payments set it up that way I'm going to go back to the ten forty so now of course you've got the the IRA hold on a second I messed up the data input I'm going to say it's all taxable seventy thousand but then we had withholding of fifteen thousand okay so then if we go back on over here's our seventy thousand that pulled over and then our our fifteen seven because they're over the threshold let's mirror that over here seventy thousand plus another of that comes to fifteen seven taxable income of fifty four three hundred so that makes sense fifty four three hundred page two tax seven two five nine so now we're going to say seven two five nine and then we withheld fifteen thousand so now it comes from the ten ninety nine I'm going to add that into my worksheet and say okay we had payments over here I'm going to add another payment so I'm going to let's put it under the w twos so I'm going to add some rows here I'll insert some rows and let's say this is going to be four this is going to be let's just call it well what did we call it over here it's form ten ninety nine we'll just say form ten ninety nine with holdings did it and then we'll add make that black and white black white put some blue stuff here and let's put it down to here bordered and blue and then we're going to say this is from ten ninety nine are was withholding fifteen thousand and then this is going to be the total total form ten ninety nine withholdings summing that up to the outer column and so that's going to be added down in our total and so that pulls into page one of our formula and so now that's the wrong thing here so there it is so there's the fifteen so now we've got the refund seven seven four one seven seven four one alright so that's the general idea now of course if there's any if you have any questions about what's included in some of these boxes like the distribution code you can go to the instructions which you can find on the back of the form or possibly go to the iris website and you can see instructions for box six and you see instructions for required continued and you have your your different items here which could then give you further guidance for more questions going forward that's for the data input side and then if you have people questioning whether they should take the money out or tax planning with regards to taking the money out or putting money into iris then of course you're going to have to drill down on more usually complex planning topics to see what the best strategies would be but at the minimum you probably want to help people to determine how much they're going to pull out next year how to minimize the amount that they would pull out that would be taxable as well as come up with strategies so they don't get hit hard with the mandatory distributions and then what are going to be the tax consequences and how are you going to pay them do you want to take the money out of out of the distributions in the form of withholdings or possibly maybe you can make estimated tax payments to cover that and then if I go back to the first tab you can also kind of if you look at this drop down you can see early distribution disability, death prohibition, transactions these codes can give you some insight as to some of the things that might be exceptions for the general rule and of course you can do more research if someone needs to take money out what would be some exceptions to the general rule whether it's going to be taxable or subject to penalty so those are two different things taxable it's going to be taxable most likely but it's subject to a penalty if you pull it out early and then you want to make sure that whatever you do if you're trying to pull money out that the financial institution is clear and puts the proper code on the 1099R so that the IRS has on their end from the financial institution which hopefully eliminates or indicates that you're not subject to a penalty


Hey, welcome back to Numbers Don't Lie.  I always, that's why I walk in, I see that every day and it reminds me of Think Big, okay?  We talk about how, I've said this a lot, okay? We talk about how there are more millionaires, okay? More millionaires in the insurance industry than any other industry in the world, true or false? Definitely freaking true, okay? Every time I'm around real estate guys, I'm like, hey, sorry, real estate, but insurance money, there are more millionaires in this industry, in the industry world, which is amazing, right? That's an opportunity. That's a massive opportunity, check, right? If also think about being a brand new agent. What is the easiest career, I would say not the easiest, but the most lucrative career to earn $100,000 your very first year in a new career. And it's this one, I'm telling you, it 100% is. Now, because of those things, okay? Because of those things, it shouldn't be the most easy career in the world, correct? Okay, and because of that, 92% actually fell, okay? Across general insurance. If we're just talking life insurance, the number's higher, right? It's not easy, but why should it be easy if there's more millionaires in this industry, in the industry in the world? And there's more people that are able to make $100,000 in their first year than any other industry in the world. It shouldn't be easy, right? It should be tougher. You can't have all the money in the world and the easiest career in the world, right Dylan? I mean, that'd be kind of silly, right? Okay, so what I wanna talk through really quick is as a new agent, how do you get to that mark? As fast as you possibly can.  And the way I think about it is, let's just say that, let's just say that you sell, ooh, ooh, okay. Let's just say that you sell, I'm gonna change it up on him, Dylan. In the middle of the show, I'm gonna totally change what we're gonna do. Okay, you ready? Okay, you guys ready? Okay, what we're gonna do is I'm gonna say, how do you get to where you're making $100,000 a year selling PNC, okay? Maybe you can't get there your first year. Maybe you can, you know, heck, I don't know. But let's just look at those numbers and think, okay. And let's just say that the average home, let's just say that for a household, let's just say you sell one household.  I'm gonna think about like Oklahoma, Missouri, New York, California. I'm gonna kind of merge some of these numbers. So stay with me, okay? Let's just say that a, Lauren, what do we pay for our house insurance every year? 1,400 a year? Perfect, okay? So you get a house, okay? Now these are real-life numbers. As you can see, okay? 1,400 bucks, what about for cars? Do you have a clue? We have three cars. Well, you're close enough, whatever. We're using it now, it's too late. 2,300 for a house? What? I don't know. It's okay, 2,400, okay? Way to go, Lauren. Messing up my show, okay? 2,400, we're going with it, okay? If it's off, it's Lauren's fault, okay? You can blame her, okay? You need to know your numbers. That's right, numbers don't lie, okay? Cars, let's think about cars. Let's think about, so an average household, let's just say you have two cars, okay? Obviously, there's three policies there. And let's just say that we pay about, I'm gonna look across the whole year, okay? I realize a lot of people pay semi-annually for vehicles, I'm with you, right? I'm actually going to train a PNC office tomorrow for two days. I'm gonna be in Oklahoma, if you're in Oklahoma. Let's look at, let's just say 1200 a year for two cars, okay? Does that sound close, babe? Yeah, she has no idea, you don't need her, so we're good, okay? So let's just say that, let's just say it's 3,600 per year per household, and let's just say that, let's just, I'm gonna use 10% commission. Just because 10% is pretty conservative, I know some people that are making 14, 50% when they sell a whole house insurance, okay? Maybe less with cars. I'm gonna use this as a general average, okay? I'm not saying, I didn't say everything was gonna be perfect, okay? The numbers don't lie, but I may, okay? And that's okay, all right? So 360 bucks in commission, that's like 30 bucks a month. Across the whole year, it's $360, okay? So let's take that, 100K divided by 360 bucks, okay? And this is all extremely on the fly. Babe, can you pull out your calculator? $100,000 divided by 360 bucks. We're looking at 250, 250 policy. 277, so you need 277 average households based on this crazy, sporadic, extremely random math, okay? 277 households, all right? So take that divided by 52 weeks, okay? And you really, you need about, what is that? Babe, 277 divided by 52, it's just over five, okay? What math, 5.34, okay? So you need 5.34 households per week. So you literally need one of these per week, or per day, okay? Per day, one of these per day, okay? So what we're doing some math, it's fun, what we're doing some math with a PNC office out in Oklahoma right now is they need, they need, based on all their money, they need to bring in enough revenue for their office, several staff, cover all the payroll, everything else, right? They need, this is real math, okay? They need 60, they need to write 60 policies per month. My first coaching call, we figured this out, okay? That's three per day. And I said, well, what happens? So I'm gonna use cold calling, for example, because anybody can cold call. So I can go to your office right now, jump on a phone and cold call and get home and auto quotes, right? Even though I don't sell home and auto insurance, that's not the point, right? And let's just say that three a day, okay? So we did some math and we figured out is, they need, they close, they close about 20%, okay? Independence can close higher, captives can close lower, that's pretty average, that's pretty consistent, okay? So that is, they need to give 15 quotes per day, okay? Supposedly, supposedly when they make 100 calls, they end up with about three quotes, okay? So to get to 15, you just need to take this times five. So they need to make 500 calls per day. And right now, they're typically not making 100. So you're never gonna write 60 if you don't figure out your numbers and put in the work, all right? So this is, if you wanna make some money in PNC, selling home and auto insurance, there's more millionaires in this international world, it's probably the most lucrative and fastest way to make 100K, but it ain't easy, okay? So if that's you, use these numbers, know your numbers, and go make some money.


Bought this calculator at an estate sale for $2 listed it the same day. I bought it sold almost immediately listed it for 799 dollars and took a best offer of 750 that is Almost unbelievable right at whoa whoa 235 dollars. Oh my goodness. Hey fellow buddies. Thanks for watching Amazing, right? All right, let's get started Hey, Bolo buddies. Thanks for watching. All right, I've got 40 Bolo's coming your way. Some of these are big money big money Bolo's I'm telling ya huge Some of them are just unexpected but these are items that sold in April These were sold by my Bolo buddies Facebook Members so what I did is I posted a screenshot that looks like this that says share your best April Bolo and then my Facebook people in my Facebook group put in the comments a Screenshot and they tell me where they got it what they paid for it and what it sold for and then I bring a video to You guys so the first item says I've got several big Bolo's I'll go with the most recent sale bought it at the Goodwill paid six dollars and sold it for two hundred and twenty nine dollars in one day and It is this mid-century modern Sunburst clock if you guys don't know about the Sunburst clocks They come in different styles, but they can definitely go for big money. This one is amazing So definitely be on the lookout and six bucks at the Goodwill is a fantastic price Unbelievable really pick this up for free from Craigslist took a best offer of a hundred and ninety five plus $60 shipping so it is a Christmas Noah's Ark animated inflatable blow-up draft tiger monkey Decoration that is super cool. Never seen that one before The next item we have here is this vintage art deco or Nate brass peacock a fireplace Screen folding fan paid twenty five dollars for this at a thrift store and it looks like it sold for a hundred and ninety eight ninety five shipping was seventy two sixty four was probably pretty big and With sales tax everything all in two hundred and ninety dollars and sixty cents for that. That is super cool Bought this calculator at an estate sale for two dollars listed at the same day. I bought it sold almost immediately listed it for seven hundred and ninety nine dollars and Took a best offer of seven hundred and fifty that is almost unbelievable right there It is an exactra ex ac t r a. It's a vintage calculator Texas instruments t I or t1-20 Star Wars bubble works So yeah, that's definitely interesting The next one says paid fifteen and sold for two hundred and fifty it does not say where they got it, but they are these Boots the Duke ostrich roper boots and the brand looks like it is t e c o v a s I've never heard of that brand, but Definitely a big money Bolo there two hundred and fifty dollars. Wow local Goodwill yesterday started auction at ninety nine dollars and ninety nine cents had a message within minutes asking you to give me a message Since had a message within minutes asking to buy it for two hundred But I let the bidding begin and it's at as of now at one oh two fifty with many watchers and views Let's see I Have a screenshot. I'm gonna put it right here of what it actually sold for I want to say it was like three or four hundred I think it went for over three hundred dollars, but it'll be right here the actual screenshot of the sold so Pick this up in a state sale for two dollars sold for full asking price in less than a week on Mercari it is a willow tree and they are trees and they are retired and it says nativity white Christmas 1999 Whoa, whoa two hundred and thirty five dollars. Oh my goodness Wow that one I am floored by I have sold some of the willow tree nativity And they are definitely a Bolo, but I did not have the trees. I wish I did. Wow. That is crazy Got this for nine dollars and fifty cents sold in three hours They are goose bumps books and these goose bump books can definitely be a big money Bolo Some of them can go upwards hundred two hundred dollars depending on which books you have how many you have and a lot of times You can get these at thrift stores and garage sales really cheap. So definitely be on the lookout for goose bumps Paid a dollar ninety nine at Goodwill sold within a few days on eBay for full asking price It is this vintage Joseph originals Christmas angel holding basket with candy canes sold for seventy four ninety nine plus shipping Purchased for ten dollars at a charity shop sold for a hundred plus shipping. It's a pottery barn cozy teddy bow fur throw 60 by 80 in mushroom All right starbucks to go ceramic tumbler local collection limited edition new mexico artists designed I got it for a christmas gift never liked it undersold it because I didn't know what it was at the time and guessed at the price Since there was none listed for sale when I comped it only one sold new with the box for 120 Mine wasn't with a box But in new condition it sat in my drafts for a few days then I listed it During that time another was listed and sold for 130 not in it as good of condition as mine sold mine for 80 And seven days, but I'll take it it was free. So it's a starbucks mug and this is what it looks like Paid seven dollars at a goodwill bends sold in seven days for a hundred and seventy nine dollars plus Fourteen dollars shipping youth catchers gear set under armor ages 12 through 16 with the helmet Wow, I probably would have walked right past that A state sale 50 cents sold for full asking price. It is a Gillette sensor razor from 1993 These old stock razors that they don't make anymore that are retired people will pay up for this This one sold for 74 81 Got this at the bends for one dollar and it sold for full asking price of 81 dollars. It is a Baldwin denim in Denim in denim, Kansas city usa snapback hat That is pretty cool and it looks like it's wool Purchased in a Barbie bag of Barbies and clothes at a local thrift Usually I lot everything up, but decided to check individual items couldn't believe one little doll dress could sell for anything Definitely checking doll clothing out now. So this is a vintage Barbie superstar era red hearts loving new dress valentine's replacement this one sold for 18 dollars and 99 cents plus shipping Yes, some Barbie clothes can be even hundreds of dollars for one outfit if you can find the old Black label tags Some of them if you can identify the outfit and get the right keywords in your title big money Sony portable blu-ray player purchased saturday at a yard sale for two dollars listed and sold for asking price in 30 minutes You'll see higher comps, but this one was in poor condition So it looks like it sold for 180 dollars and it is a sony portable blu-ray dvd player with Case and remote and charger Purchased for 50 cents at a yard sale got full asking price on mercury It is a hc triangle amber safety valve glass canning jar with glass lid sold for 400 dollars. Oh my goodness Oh my goodness, it makes me wonder what it would have done on auction You know because ebay auctions sometimes these things go crazy if you just get a couple people bidding on them 400 on mercury wow But koshmark mercury and ebay are my main platforms And if you guys aren't selling on those and you're interested I do have links below that you can get a coupon and I get a coupon if you use that link to sign up And list perfectly again is what I used a cross post If you uh want to check out the demo video I show you how I start on ebay and cross post over and if you like that video and you're interested You can use coupon referral code bolobuddies all one word to get 30 off your first month So check out those other links down in the description Okay got this in an online goodwill auction jewelry lot probably paid a dollar for it sold for full asking price of 99 dollars. It is a harley davidson Skeleton key silver tone seazy necklace and earring set How awesome is that goodwill auction? That's awesome all right This one comes from And i'm drawing a blank. I always forget his channel name. I think it's like manny dx And a number i'll pop it up right here. He is a bolobuddies member So I am featuring his channel. All right purchased at a family thrift center for two dollars sold for 50 plus shipping Very unique item went back the next day and saw another one also purchased for two dollars It says states quarter program 1999 2008 box set all 50 states complete new and wrap. That's what it looks like This one also comes from bolobuddies member mindful recycle terry She got this woody at an estate sale about a year ago dropped the price a bit and it sold She paid ten dollars for it and it sold for two hundred and forty nine dollars buyer paid shipping So it is new old stock NOS is a great thing you can put in the title a lot of people search that but anytime you can find toys That are in the original box. Definitely a good pickup, especially at ten dollars. That is fantastic And terry has an amazing channel. Definitely check her out and sub her up Bought a set of ashtrays for two dollars at a yard sale the bigger sold instantly for 50 And there was a smaller one that I took an offer for 20 so vintage edith he ceramics ashtrays Who know that who knew about that? Can't talk. Sorry guys Ashtrays are above all I guess check them out Ladies doc martin's discontinued color paid two at a yard sale sold for 85 plus shipping on facebook marketplace To a very happy buyer So Yeah, nice color of red My favorite for the month paid 20 at an antique mall sold in two to three days for full asking Oh, I love this vintage grumbocker soft pastels Uh, yeah, look how cool. This is in the original case. I can't tell if they're used or not, but 289 dollars and 99 cents amazing Paid four dollars at the goodwill thought it looked cool ended up being a feminist artist No comps sat on ebay for a while and sold quick on mercari again another reason to cross post Some things I doubt this is but some things are flooded on ebay You put them on mercari and bam mercari has a thing where um an ebay does too, but I think it's easier on mercari to follow Certain things. So let's say I wanted to follow vintage Cross stitch kits I could put that in at any time vintage cross stitch kits come up for sale When I look at the app, there's a whole section I can go to and it's just going to show me new cross stitch kits That are vintage So somebody may have been Had kiki k i k i as a key word and this popped up and they bought it. So Um, I think mercari is great for that and it sold for 132 plus shipping Picked up this we work mugs at goodwill for 299 apiece took a chance that the popularity of the we crashed series would spark interest I was shocked at the few comps and grabbed them took about two weeks But sold at full asking price plus shipping So we work always do what you love set of two coffee mugs sold for 60 plus shipping Paid three dollars and 99 cents never heard of this brand, but they were my daughter's size and very cute and definitely well made I looked at comps and decided to sell sold for full asking price within two days Okay, I don't see where she got it but 399 and they are Salvatore Uh, I know this one Ferragamo, I think I said it right I think donna telebotelino selling these over on her youtube channel right now You guys if you're not following donna telebotelino, definitely go sub her up. She wholesales stuff out to resellers Um from her youtube channel These shoes sold for 190 And I can't tell if it i'm guessing the buyer paid shipping Orvis fishing reel paid 50 and sold it for 250 in less than 24 hours. Check that out That is awesome Just purchased this yesterday for a dollar at an estate yard sale. I accidentally stumbled upon it Paid a dollar each for two only listed one because I have to clean the other one of my quicker flips to date All right. What is this thing? Chrysler town and country chrome OEM center cap sold it for 55 dollars. Awesome This one comes from bolo buddies member mom Mom knows treasures. That is her ebay store. She does not have a youtube channel She purchased three pairs of true religion jeans and shorts from a tuesday night youtube auction keniko treasures and callie reseller lewis for 25 So had about eight dollars and 33 cents into these sold within a week on posh for best offer of 60 dollars And buyer paid shipping. She had them listed for 85 The next one comes from Ozark mountain reseller. I'm gonna put the whole channel name right here She has a youtube channel. She is a bolo buddies member. Definitely check her out It says I bought this at an auction for five dollars is sold in two weeks for 35 dollars It is a fan forced heater thermostat And it looks like it's new old stock and she sold it for 35 plus shipping She also found these silver jeans at a garage sale for three bucks and sold in two days for 25 dollars and 99 cents So silver is um from what I understand a pretty solid find if you can pick them up cheap They sell at a decent price I don't sell clothing much anymore, but um I have heard that from other channels This one comes from flipping it good who is also a bolo buddies member. This is his channel. He does a lot of retail arbitrage but he also um buys at thrift stores estate sales and Uh, what is the newest thing he's doing? Oh Lost cargo crazy, right? He's got some videos on that. I found this set at a yard sale It came in a box full of toys. I paid five for the whole box. I am less than a dollar in for these I took an offer of 40 plus shipping. They're disney picks our toy story green alien figures great as cake toppers So anytime you have little mini figures like this cake topper is a great thing to put in the title Because a lot of times parents are wanting to decorate their own cakes and they will look for mini figures on ebay, so Definitely consider putting that in your title Here's a nice bolo picked up for a dollar at a local church thrift on saturday listed on sunday sold on McCurry for full asking price of 139 plus shipping on wednesday My rule of thumb for board games is if the guys from big bang theory would play it pick it up All right conquest of the empire 1984 milton bradley roman caesar board game 100 complete sold for 139 dollars on mccurry All right These were purchased at a thrift store for eight dollars total both sold in less than a week to different buyers by sending offers to watchers this one comes from msg treasures And he is a bolo buddies member. This is his youtube channel.  Go check him out these are Machinist tools and you can see both of them right here one sold for 75 and the other sold for 109 99 This one also comes from um bolo buddies member. I already talked about his channel mani DX something this is what it looks like. I found this at a goodwill for two dollars sold in a week for 2399 Plus shipping macasa is a really good bolo brand only two sold, but I took these those odd And it sold took those Typo I think off maybe and it sold Open box. Uh, it's a wine bottle stopper female nude torso All right cheating a little as this sold in march Uh, let's see. This is a single earring It came came out of a craft jewelry lot that I won from donna telebotilino in a giveaway It would have gone in a silver scrap pile except I saw that someone else had recently sold two mismatched single earrings from this brand So I listed it at 1499 I took a best offer of 12 dollars and 49 cents plus shipping Which is a lot higher than melt value would have been for this tiny piece a small sale But maybe unexpected for someone whose instinct would have been to not look twice at a single earring So it's a little turtle. How cute is that? What a great idea So somebody's probably gonna craft with this and because it's sterling, you know, that makes it more desirable And she said this came out of a craft jewelry lot that she run from donna telebotilino And she does have an unboxing of this over on her channel It's a susie q's never-ending jewelry party. I think is what it's called. You can check her out here I won it for ten dollars on an online high bid auction in february I listed it for a hundred dollars the buyer and I went back and forth on offers And I finally accepted her 70 dollar offer on april 12th It took two months to sell and I only had it listed on poshmark So, uh, Sharif sh-h-a-r-i-f I may be saying that wrong designer european leather textured croc snake skin Patchwork cross body sold it for 70 dollars. Check that out Got this for a dollar last summer at a yard sale didn't think much of it and almost put it in a reseller a lot But decided to check it out a bit more glad I did Mr. Christmas animated musical pocket watch clock musical horse sleigh and music box Yes, mr. Christmas always look up. Mr. Christmas a lot of the items are bolos and um Noelle farm girl scavenger has a video where she parted out a mr. Christmas item So definitely go over and check that out as well. Thank you guys so much for being here Thank you for watching. Let me know in the comments. What was your favorite? Bolo be sure to go over and join my facebook group here and under the announcement slash featured section you will see a um post that will say share your bolo It'll kind of be a screenshot like the one this month and um, I don't know Share a bolo you will not be mentioned in the video unless you're a member So it's completely anonymous just your bolo shown unless you um sign up for memberships. All right, you guys Thanks again for being here. There's gonna be some videos popping up down here subscribe if you're new here check out another video Thank you so much. Um, my channel is mainly about bolo items So if you want to learn about things you should be selling on ebay and other platforms This is the channel for you and check out the comments for um other things that I use to help me with my business All right, you guys thanks for watching Be sure to check out the description of the video like comment share and subscribe. Thanks for watching


In this lecture we are going to discuss about certain curves of discontinuity associated to second order quasi linear partial differential equations. So we start with a brief review of the lecture 3.1 and then we move on to discuss curves of discontinuity. So as you know the second order quasi linear equations we are denoting by 2ql and it stands for AUXX plus 2BUXY plus CUYY plus D equal to 0 where A, B, C, D are functions of this X, Y, U, UX and UY. So they are defined on some subset of R5 which is called omega 5 and a special case would be a linear equation second order linear equation it has the general linear equation looks like this. So let us start with the review of the previous lecture. We have considered the following Cauchy problem in the lecture 3.1. What is that? Find a solution to the second order quasi linear equation satisfying U of FSGS equal to HS and the normal derivative of U at point FSGS is chi S. What is FSGS? It is a curve parametrically given in a plane gamma 2 and the curve is a regular curve that means F dash and G dash do not vanish simultaneously. So along this curve we are specifying the value of U as H and the normal derivative of U as chi. So these functions H chi are given. So this is often called Cauchy data. Cauchy data along gamma 2. So we observed that the first order derivatives of U at points of gamma 2 can be computed using the Cauchy data. For that what all was needed is that the curve gamma 2 is a regular curve that was good enough. Then we also try to compute second order partial derivatives of U again along the curve gamma 2. It can be computed using Cauchy data and now we have to involve the partial differential equation as well. So the second order quasi linear equation using these two we can solve but one more condition was to be met. So that was delta of S is not equal to 0. What is delta of S? It is this expression.  These are the functions which describe the curve gamma 2 parametrically. Then what is zeta S? It is a 5 to pull which is F, S, G, S, H, S, P, S, Q, S. We have already solved for P, S and Q, S using chi and H. Therefore this makes sense and we can ask this condition. If this is non-zero delta S not 0 then we can compute second order derivatives and we have also shown that higher order derivatives can also be computed. No further extra conditions are needed. Now we would like to understand this condition in more detail. What is this curve? What is this? Where delta S is identically equal to 0, how that curve looks like? So let us assume to start with that the gamma 2 that we considered is not parametrically defined but let us say it is a graph of a function of the type x equal to phi y. It is a graph of a function of the variable y, x equal to phi y. Then what happens to gamma 2? x equal to F, S that will be phi S, y equal to G, S which is S. Y we parameterize as S, then x becomes phi S. So this is a parametric representation and S belongs to that set where y belongs to wherever this function phi is given the domain S belongs to the same domain. We are not writing that right now. Now what will happen to this equation? Now we need to substitute what is H S, P S and Q S. H S is still general. P S and Q S are to be determined from H S and chi S. So these are still unknown but what is known is F dash. F dash square is phi dash square, G dash is 1. So this equation becomes this equation. Of course if you want to know what function satisfy this condition we need to still know this H, P and Q. That is the problem with this equation because the equation is quasi-linear equation. So for a quasi-linear equation if you are interested in this question then you must be given a solution of the equation. Then you can ask what is that curve which will have this property. That can be now determined because solution is given therefore you know what is P and Q. So it makes sense. On the other hand if the equation is actually linear the A, B, C are not functions of zeta S at all. Zeta S is a phi tuple. They are simply functions of the first two variables F S and G S. And what is F S and G S? That is phi S and S. So therefore you know explicitly C, B and A only in terms of phi. So it will be a differential equation for phi. So it further reduces in the case of a second order linear equation to a simpler equation. For a quasi-linear equation however we need to be given a particular solution for which we can ask what are the curves x equal to phi y along which there is a problem in finding higher order derivatives. Problem in the sense we are unable to our scheme of things fails. Our scheme to compute the second order derivatives onwards fails because delta S is 0 there. So as we saw these are special to the PDE because the definition of course involves the equation. So for the linear equation this gets simplified to this x equal to phi y. So this is a differential equation nonlinear first order degree 2 nonlinear and coefficients will involve only two variables now because we have linear equation. So one can hope to solve this for phi. Then we would have got the curve x equal to phi y where phi is a solution of this ODE is a curve along which delta S is identically equal to 0 or there are troubles in solving for higher order derivatives. In other words along these curves there is some problem to determine higher order derivatives of the solution or of a possible solution. So even if you know solution there is a problem to determine that because of delta S being 0. Now the curves comma 2 for which delta S identically equal to 0 holds are special to the PDE as PDE also plays a role in their definition apart from gamma to itself. The same curves appear in a different context also. So for piecewise smooth solutions of the second order quasi-linear equations the curves of discontinuity okay curves of discontinuity also satisfy delta S identically equal to 0. So let us we are going to state a result in the form of a result it will be easier to remember. So hypothesis and notations suppose you have an open and connected set in R2 and take a curve in R2 gamma that divides omega into two parts. So that means that we have this let us say this is omega and we have a curve gamma which cuts this into two pieces. One is omega 1 other one is omega 2. So what is omega now? Omega consists of omega 1 omega 2 and this curve gamma the part of the curve gamma. We are going to assume that the curve gamma is given by x equal to phi y. We have already seen its interpretation in lecture 3.1 why do we consider x equal to phi y? Once again we will give at the end of this result. So given V1 in C of omega 1 bar which means that you are given a function V1 here which is continuous on omega 1 of course omega 1 open set but it should be continuous up to the boundary of omega 1. In other words what actually we want is its meaning on this curve. So therefore V1 on the curve gamma makes sense. Similarly V2 is in C of omega 2 bar means that the values of V2 on the curve gamma makes sense. It will guarantee that apart from of course on this boundary also they make sense because it is continuous up to the closure of the domains in this case omega 1 in this case omega 2. If such functions are given we can look at the value of V2 on gamma and V1 on gamma it makes sense meaningful therefore we can look at the difference. Let us see. Let us define a function V in omega 1 it is V1 in omega 2 it is V2. Let box of V denote the jump in the values of V across gamma. That means the definition is take a point x y take a point x y on gamma is omega 1 this is where V1 is defined this is where V2 is defined. We have seen V2 of x y makes sense when x y is in gamma let us call this part as the gamma may not be the outside part okay. V2 of x y makes sense V1 of x y makes sense because V1 is also continuous up to the boundary there in particulars values on gamma make sense and we can consider the difference. You could have even taken V1 minus V2 there is no problem and we are considering V2 minus V1. So this is called jump in the function V that means you have a function V defined on omega 1 here you have a function here you have a function which is continuous so that the values make sense along this curve gamma then you look at the jump in V as V2 minus V1 at points of gamma. Let U, Ux and Uy be continuous on omega and the restrictions of U to omega i they are C2 functions because we want them to be solutions to the PDE so that is why the C2ness and we want omega i bar because we are going to consider the jumps in second order derivatives. First of all derivative should be meaningful on the curve gamma okay and this curve gamma. So if I assume U is C2 of omega 1 bar we may put 1 on the head U1 is C2 of omega 1 bar it means that second order derivatives of U has are defined on gamma because they are continuous in omega 1 bar that is the reason why we have this condition. So let gamma be given by x equal to phi y where phi is a C1 function. Now the jumps in Uxx, Uxy and Uyy are not independent of one another okay it means they are interrelated to start with it looks like yes Uxx is jump in second order Uxx derivative this is jump in xy derivative this is jump in yy derivative why should they be connected. So let us denote lambda y as a jump in Uxx at a point and gamma a point and gamma looks like phi y, y so then this is the result jump in Uxy is in terms of lambda y and phi dash and jump in Uyy is lambda into phi dash square we are going to prove this so they are related observe that if lambda y is 0 what will happen lambda y is 0 means the right hands are 0 here which means jump in Uxy and Uyy are 0s that means if jump in Uxx is 0 then jump in Uxy as well as Uyy are 0 okay let us prove the conclusion 1 the restrictions of a function defined an omega to the regions omega 1, omega 2 are denoted using superscripts that is we had this as the omega and we had a curve which is making it into 2 parts omega 1 and omega 2 and suppose we have a function U defined on omega or any function U, Uxy we denote the restriction of U to omega 1 by U1 and here by U2 so Ui is U restricted to omega i. Since U, Uxy are assumed to be continuous on omega these functions are continuous across gamma also in other words there are no jumps across gamma so jump in U is U2 minus U1 phi y, is a point on the gamma similarly the jump in Ux defined by Ux2 minus Ux1 that is also 0 jump in Uy is also 0 so on differentiating the equations 2b and 2c the last 2 equations differentiate them because differentiating the first equation will not give you anything because if you differentiate this with respect to y what will you get nothing useful because we want to now consider jumps in second order derivatives that is the reason so we differentiate the last 2 equations on the previous slide we get this by differentiating the first equation and this by differentiating the second equation. Now in terms of the jumps this equation is nothing but jump in Uxx into phi dash plus jump in Uxy equal to 0 that is the first equation and the second equation is jump in Uxy which is this into phi dash and jump in Uyy equal to 0. So conclusion 1 of the theorem follows from the last 2 equations because we called Uxx jump as lambda then jump in Uxy is minus lambda phi dash therefore jump in Uxy is minus lambda phi dash that will give you jump in Uyy is minus lambda phi dash into phi dash that is the conclusion 1. Let us look at the conclusion 2 of the theorem for that we need to assume the hypothesis are U1 and U2 solve the quasi-linear equations in the regions omega 1 and omega 2 respectively. Let y be such that lambda y is not equal to 0 recall lambda is the jump in Uxx at the point phi y comma y conclusion denoting by zeta y equal to this quantity phi y comma y U at the point phi y comma y Ux at the point phi y comma y Uy at the point phi y comma y recall the point phi y comma y means x equal to phi y this is how a point on gamma looks like. So the following equation holds we are going to show this equation holds whenever lambda y is not equal to 0 at that point this equation holds. So if you assume lambda y is not equal to 0 at all the points then the equation holds for all y then this equation is same as delta s identically equal to 0. Proof is very simple we are going to assume that U1 and U2 are solutions therefore we can write down these equations in omega 1 and omega 2 with appropriate superscripts. So we have this now we have two equations we have to subtract one from the other and we have assumed that there are no jumps in Ux and Uy therefore the coefficients a, b, c, d they all are like this they are functions of x, y, u, u, x, y there is no jump in them so this a will come out to be a. So only you pick up the jump in Uxx so 2b will remain as it is because it is a continuous function and it is the same in both therefore along gamma what I mean by same in both is this. You have an expression for let us say here a is x, y, u1 of course of x, y, ux1, x, y, ux, uy1, x, y we have this and here what we have is exactly same but with 2. Now on this curve if you x, y is here then both are same because there is no jump Ux2 is same as Ux1 when x, y is on this curve gamma that is why when you subtract they come out as it as they are and the d term gets cancelled because the same in both of them when you are looking at points of gamma. So you pick up only the jumps jumps in Uxx jump in Uxy jump in Uyy they come here. So we have this. So using the conclusion one of theorem in the last equation we get 0 equal to a of zeta y lambda y minus 2b of zeta y lambda y phi dash plus c of zeta y lambda y phi dash y square. So if you take lambda y common what you get is this a minus 2b phi dash plus c phi dash square assuming that lambda y is not equal to 0 along gamma we get this the one in the brackets must be 0. If lambda y is not equal to 0 for all y then this the one in the parenthesis must be 0. So we get this different equation and this equation is the same as delta s equal to 0 for s in i same equation when x equal to phi y. So we have assumed that the curve is of the form x equal to phi y. The conclusion three of the theorem is as follows hypothesis assume U1 and U2 solve the linear equation in the regions omega 1 and omega 2 respectively the linear equation and U possesses third order partial derivatives that is required for stating this conclusion and have jump discontinuities across gamma. Let y be such that lambda y is not equal to 0 then lambda satisfies the following ODE 0 equal to 2 into b minus c phi dash into lambda dash plus this quantity into lambda. So this is a linear ODE with variable coefficients because they depend on y this depends on y. So it is a linear ODE with variable coefficients of course if b minus c phi dash equal to 0 then this will be a singular ODE otherwise it is a linear ODE. Now observe that if b minus c phi dash is not equal to 0 and abc phi are smooth functions then lambda y equal to 0 at isolated points implies that lambda y is identically equal to 0. Let us understand this carefully if lambda y is equal to 0 at some point this ODE may not hold but we are here the hypothesis lambda y equal to 0 at isolated points. That means the points where lambda y equal to 0 can be reached by the points where lambda y is not equal to 0 at which the ODE holds this ODE makes sense because whenever lambda is not 0 at some point the ODE happens the lambda satisfies this ODE. And you see this is equality as people say equality is a closed condition therefore it follows that even if lambda y equal to 0 at isolated points this ODE continues to hold and if you are assuming all these functions are smooth and this is non-zero then it turns out that the quantity in these brackets and the quantity in these brackets are smooth functions and they are locally lipsious functions then we can apply uniqueness theorems for the initial value problems and conclude that lambda y is identically equal to 0. So lambda y by definition is jump in u x x which is this differentiate both sides of this equation you get lambda dash with respect to y therefore you differentiate this with respect to x you get u triple x but phi is there therefore phi dash and from here you get u triple x into phi dash now differentiate u x x with respect to y variable you get this similarly this you get this. Therefore, we can express d lambda by dy as jump in u triple x into phi dash plus jump in u x x y now similarly we can also get derivative of u x y you write the equation for u x y jump differentiate with respect to y you will end up with this relation. Now we know that u x y jump is minus lambda times phi dash that is a conclusion 1 therefore this equation I can write it as this. Now we are going to use u i solve the linear equation in the domain omega i so we have this 2 equations 1 in omega 1 1 in omega 2 along gamma we will consider because we are going to take jumps. So first is to differentiate this with respect to x because we are interested in third order derivatives differentiate with respect to x then subtract one from another we get this expression. Now once again use the conclusion 1 of the theorem which expressed basically the relations of jump in u x x u x y and u y y in terms of lambda which is actually jump in u x x so we get this relation. So we have 3 equations this this and the one we just obtained this. Now eliminating the jumps in the third order derivatives of u across gamma and using this relation that a minus 2 b phi dash plus c phi dash square is 0 that is the equation phi has to satisfy right even for quasi linear equation therefore for linear equation also. So this equation is satisfied so how do you eliminate that is what you have to look at. So we want to remove these conditions we have 3 relations in them may be solve for them that is what it is and substitute and we get the ODE in conclusion 3 so this is left as exercise to you this is a simple algebraic exercise. Now we may interpret this lambda as the intensity of the jump in u x x intensity of the jump in u x x across gamma this interpretation is taken from the book of Fridgen on PDEs. So if lambda y not is 0 for some y not that is lambda 0 at some point and if the initial value problem that we had for the ODE has a unique solution what is the ODE that we were considering it is a linear equation for lambda which we saw 2 into b minus c phi dash into lambda dash plus a huge expression into lambda. If that has a unique solution of course it is a homogeneous linear equation 0 is always a solution and if it has uniqueness also then it must be that lambda is identically equal to 0 we already did this conclusion. So if u x x is continuous at some point this is the interpretation in terms of u x x what is lambda after all it is a jump in u x x if jump is 0 means what u x is continuous at that point then it is continuous at all points of gamma and therefore once you have u x is jump is 0 jump in u x y and u y y is also 0 from conclusion 1. So location and speed of jumps if the variable y is given the interpretation of time the equation x equal to phi y gives the location of the jump in u x s for various time instances at different instances of time the speed of propagation of discontinuities is given by dx by dy which is equal to phi dash of y dx by dy is phi dash of y and satisfies the differential equation a of zeta y minus 2 b zeta y phi dash plus c of zeta y phi dash square where zeta y is given by this phi tuple. So let us summarize this equation which is the ODE which is there on this slide it appeared in two different contexts in lecture 3.1 how it appeared if the Cauchy data is prescribed along the curve gamma 2 x equal to phi y where phi does not satisfy the above ODE derivatives of all orders for a solution to 2ql can be determined at all points of gamma 2. In this lecture if gamma given by x equal to phi y is a curve of discontinuity for second order partial derivatives for a piecewise smooth solution of 2ql as in the theorem that we have stated today in this lecture then phi solves the above ODE. Important question is for a second order quasi linear equation how useful is this equation since to write down this equation zeta of y it requires the knowledge of a solution to the 2ql that needs to be given right. So how is it helpful in identifying these curves x equal to phi y where phi solves this equation. Once the function is known can we find cause of discontinuity directly do we still need to solve this ODE answers if a solution is given then in principle possible curves gamma across which second order derivatives may have jump are already known. However the ODE gives an analytic characterization of such curves and thus may still be useful. Of course for semi linear equations the ODE is useful in both the contexts determine curves along which a Taylor series for a solution may be obtained or identifying curves across which piecewise smooth solutions will have discontinuities in the second order derivatives. So in forthcoming lectures the ODE will play an important role in reducing a linear second order PDE to a simpler form. In the simpler form the coefficients of second order derivatives will be constants to start with in a second order linear equation coefficients are functions of x and y. But this ODE will help us in obtaining a simpler form of these equations in which the coefficients of the second order derivatives are constants. The simpler form would be obtained using change of coordinates. The ODE plays an important role in determining the change of coordinates. Thank you.


So if you really want to improve the quality of your life, I highly, highly recommend start working with your dreams. Dreams are a wealth of knowledge and personally a huge factor in my own personal growth. So I know it will be for you as well. Dreams are a direct line to your subconscious mind, which is where we operate out of the majority of our life.


You know, our goals are the same as they've always been really, you know, we want to win the Mac. You know, the historically strong conference, something that we've been building towards for the last, you know, six or seven years. So for us, it's really, really important to remain focused on winning the league first and taking care of the little things. You know, week to week, you know, you can't look past anybody in this conference and it's a, you know, every game is important, and really trying to be focused on being one and oh every week as opposed to really looking at that big picture for us. You know, early on in the program's history, you know, it was more big picture stuff. It was, you know, getting guys, you know, lined up, right, constantly worrying about those things. But now that we have an experienced group, you know, those real finite details of the game, you know, have become very, very important. You know, in the two games that we didn't win last year, you know, it really came down to a handful of plays and a lack of attention to detail in those plays or what cost us those football games. So, you know, our focus in camp has been really taking care of the little things.  You know, we've got to be able to control and win the line of scrimmage consistently every Saturday. And it's something that we talk quite a bit about. You know, having Corey Patrick back on defense is obviously huge and returning three starters out of the secondary again big. You know, anybody time that you could get guys with multiple years of experience returning, certainly is very, very exciting as a coach. But again, it allows you the luxury of really focusing on the finite details when you're working with an experienced group of guys. You know, we're excited. It's been a fun group to coach so far. We've really, really worked on that finite focus, you know, one game at a time. You know, it's easy to, you know, to look at all the preseason stuff and kind of start taking stock of where you are. But the preseason stuff doesn't matter. You know, what's important to us is what happens in November. So, you know, to get to that point to play meaningful games in November, we've got to take care of the details and really that one week at a time mentality is going to be key for us.


drwy y ddwyloedd yng Ngysliw Llywodraeth. Eiceil. Yes, I'm happy to provide that confirmation. Thank you, that ends the ministerial statement. We now move on to the next item of business, which is a statement by Elin McLeod on the Scottish Greenhouse gas emissions annual target report 2013, reporting progress towards meeting the interim target. The minister will take questions at the end of his statement and there need to therefore be no interventions or interruptions. Can I just point out to members? In the previous statement I unfortunately had to drop three members who wished to ask a question because we'd run out of time. Can you bear that in mind when you're asking your questions? I now call Ailey McLeod. Minister. Thank you, Presiding Officer. In 2009 this Parliament acted unanimously to enshrine world-leading climate change targets in legislation. We were supported by huge numbers of people across Scotland in business, public sector, academia, in NGOs, in schools, in trade unions, in communities and in homes. Through its collective high ambition we were able to establish world-leading targets of a 42 per cent cut in emissions by 2020 and 80 per cent by 2050. Scotland was also the first national government in the world to establish a climate justice fund. I am proud of those actions, Presiding Officer, and of Scotland's ambition. Continued ambition and action are required from all of us if we are to tackle the environmental harm and social injustices caused by climate change. Through the recent Scottish Leaders climate change pledge, we have again, as political parties, shown our collective commitment to tackle this challenge. Across Scotland many people are doing the same, taking action as individuals, as families, as communities and as organisations. The Scottish Government is also committed and is leading by example. Our cabinet sub-committee on climate change demonstrates our commitment to tackling this issue at the highest level within government. We have pledged around £1 billion of funding over two years, 2014-15 and 2015-16 for climate change action. We have in place a comprehensive package of measures to meet our climate change targets out to 2027. Taking action, Presiding Officer, in climate change, we are investing in our people, our environment and our economy, creating a fairer and more prosperous Scotland. We are reducing the amount of energy that people use. We are already below the consumption level that is required to meet our 2020 12 per cent target seven years ahead of schedule. We are reducing levels of fuel poverty and since 2009 we have allocated over half a billion pounds on a range of fuel poverty and energy efficiency programmes with a budget of £119 million for the current financial year. In June, I announced that this would be a national infrastructure priority for government. We are reducing our dependence on fossil fuels by scaling up renewable energy and Scotland now generates almost half of its electricity demand from renewables. In 2014, the amount of heat generated by renewables in Scotland grew by 36 per cent. We are focused on community and locally owned energy. Last month reaching our 2020 target of 500 megawatts of community renewables five years early. Across Scotland, nearly 45,000 people are employed in the low-carbon economy and its supply chain. Taking action to reduce emissions from transport compared to 2013-14, we have increased investment in active travel by over 80 per cent. We are committed to rail electrification. We are working with partners to deliver our electric vehicle roadmap with more electric vehicles being sold in Scotland than ever before. We are encouraging waste reduction, extending recycling and reducing the waste to landfill. In 2014, 42.8 per cent of Scotland's household waste was composted, recycled or reused. For the first time, landfilling of household waste fell below 50 per cent. Scotland is taking action locally and being recognised globally. Christiana Fuguerys, who is the head of the United Nations climate body, has cited Scotland's ambition on renewables and low-carbon as a shining example to other countries. We have set the bar high with our world-leading targets and Scottish ministers have sought to push up global ambition since 2010. For example, while in Lima last year, in my first days as a minister, I signed the compact of states and regions, an international reporting platform for sub-national governments, representing 12.5 per cent of the world's GDP and over 325 million people. This year, when attending the World Summit climate and territories in Leong, I signed the under 2 MOU, another initiative between sub-national governments aimed at promoting high ambition ahead of Paris. In this milestone year, the international community will have to match Scotland's commitment if the Paris summit is to produce a truly effective global response on climate change. We hope that the Paris summit will be a big step forward. It is crucial that we push further to limit global warming to two degrees Celsius or less if we are to avoid the worst impacts of climate change falling on the world's poorest and most vulnerable people. Although Scotland's targets are challenging with much still to do, I want to emphasise today that we are making good progress. This morning, I laid before Parliament Scotland's report on progress towards meeting its interim target. The report shows that, in each of the years, from 2010 to 2013, the percentage reductions that we have achieved have exceeded those set out along the trajectory to meet the 42 per cent reduction in 2020. In fact, Scotland's emissions have fallen by 38.4 per cent from the 1990 baseline, leaving just a further 6 per cent reduction to meet the 2020 target over the next seven years. Scotland is clearly on track to meet its interim 2020 target. I believe that that is a message that we should focus on. It is a fantastic achievement. Of course, we know that the act requires even greater reductions to meet the 2050 target. There is no room for complacency, nor will we fail to recognise the challenges in meeting Scotland's annual targets. I recognise that the other report that I laid today shows that Scotland's 2013 annual target has been narrowly missed by 1.7 megatons. That is because of revisions to the baseline since the time when the fixed targets were set. I highlighted that in my statement to Parliament on the publication of the 2013 Scottish greenhouse gas statistics in June this year. In June, I also explained that changes to the methodology for calculating emissions have added 10.6 megatons to the 1990 baseline, making it harder to meet the annual target. Despite that, Scotland's emissions have fallen by 38.4 per cent from the baseline, which is far greater than the 31.7 per cent reduction envisaged when the target for 2013 was set. Had it not been for successive increases to the baseline, Scotland would have met and exceeded our target for 2013 and the three previous years. Against the 2020 and 2050 targets, Scotland is making significant progress, but we must continue to lift the pace of our actions against our fixed annual targets. That is why, in June, I announced further measures on energy efficiency, environment and transport aimed at reducing Scotland's emissions. As I also indicated in June, we will be ensuring that climate change is a top priority through a Cabinet agreement to embed climate change in the autumn budget process. I remain determined, Presiding Officer, that we make up for the cumulative shortfall that has resulted from Scotland's missed annual targets. We will do that by ensuring that our RPP3 addresses that, as well as setting out measures required to reduce emissions out to 2032, fulfilling our statutory requirements under sections 35 and 36 of the act. However, it is not just about government. It will take continued commitment and action by all of us if Scotland is to achieve the emission reductions required. That is why the production of RPP3 will be a wide participative process, building collective ownership and responsibility. We will have a conversation with people across Scotland listening to their views on climate change and the actions that we must collectively take. We have started that conversation, Presiding Officer, with events planned with community groups in the new year. Given the impact of decisions that are made now on future generations, we must give a voice to the next generation of Scottish leaders by involving the 2050 climate group. Of course, engaging the Scottish Parliament will be a key element with opportunities being developed to get involved alongside regular parliamentary business. Those are just a few of the plans that we are being put in place to make sure that our RPP3 is a truly collective endeavour. I call on this Parliament to agree that commitment and action are required from all of us if Scotland is to continue to lead by example in tackling climate change. That is the message that I want us to take to Paris demonstrating Scottish leadership and encouraging others to step up and embrace the climate change challenge. The minister will now take questions on issues raised in her statement. I intend to allow no more than 20 minutes of questions after which we must move on. It would be helpful if members wished to ask a question or to press a request, but now I call Sarah Boyack. I thank the minister for advance notice of her statement. Minister, failure in the last four years means that 18 megatons of carbon is now in our atmosphere, which would not have been there had the targets been met. That is equivalent to the whole of the Scottish energy sector's output in one year. Progress on renewables is nowhere near enough to compensate for failure on farming, transport, housing, buildings and infrastructure. The minister mentions a billion pound spending in the budget. Is this new money and will she publish details of these projects now? Given the rise in public sector emissions and failure on housing, surely the national infrastructure project must be brought forward to start now? Will the Scottish Government sign up to the existing homes alliance asks? Section 36 of the act requires ministers to detail how they will make up for missed targets in the early years. Where is that report, minister? Today's report confirms that there has been no reduction in household emissions and the climate act enables householders to get discounts on their council tax for energy efficiency measures. Yet last year, two households in the whole of Scotland benefited. Only two. Is the minister proud of that? Her predecessor, sitting beside her, correctly stated that failure to sort out our leaky drafty homes was a regular vulnerability which needed efficiency and decarbonisation of electricity, heat and generation. However, we are not seeing that, and pride in renewable heat is a staggering lack of ambition given the low target set. I am glad that the minister is going to Paris, but without radical action, today's statement and our act is meaningless. This statement reeks of complacency. Minister. Thank you, Presiding Officer. To say to Mr Boyack, our achievements, we have a long list of achievements and they demonstrate the good progress that we are making. Our energy consumption, our target to reduce consumption by 12 per cent by 2020, is already at the required level in 2013, down by 13.3 per cent from the 2005-07 baseline. On heat, the amount of heat generated by renewable sources in Scotland grew by 36 per cent during 2014. On housing, we have allocated over half a billion pounds since 2009 on a raft of fuel poverty and energy efficiency programmes. We continue to focus on increasing the energy efficiency of homes in Scotland to tackle fuel poverty with a budget of £119 million for the current year 2015-16. On renewables, our provisional annual statistics for 2014 show that the equivalent of 49.6 per cent of Scotland's girls' electricity consumption came from renewables, and that is just short of our interim target of 50 per cent by 2015. On community and locally-owned energy, we announced on 17 September that we have reached our target of 500 megawatts of renewables capacity by 2020, five years early. On transport, compared to 2013-14, we have increased investment in active travel by over 80 per cent from £21.35 million in 2013-14 to £39.2 million in 2015-16. That is at a time when our overall capital budget has decreased by 26 per cent. On section 36, I said that Boyack will know that producing a credible package of proposals and policies to make up that shortfall that is totaling 17.5 million metric tonnes of CO2 equivalent from previous annual targets and to get back on track to meet future annual targets will take time. Therefore, it is our intention that RPP3, as I said out, will set out proposals and policies in detail to compensate in future years for the excess emissions from previous annual targets. It is planned to lay a draft of RPP3 for scrutiny by the Parliament towards the end of 2016. We are making significant progress. We have cut our emissions by 38.4 per cent. We are more than three quarters of the way towards meeting our 42 per cent emission reduction in 2020 ahead of schedule. Alex Ferguson. I apologise, Presiding Officer. I didn't hear you call my name. I also thank the minister for the advance copy of her statement, which, with the best will in the world, does seem to bear remarkable similarity to last year's statement. However, in amongst all the good stuff, and I do not deny that there is good stuff within that statement, it is deeply disappointing that the government has yet again missed its target the fourth year in a row. The government has never actually met its target, and that begins to get surely much more than just deeply disappointing, because every time a target is missed, the gap between where we began and where we want to get to increases. The minister blames baseline revision. She did so last year as well. Can I ask why allowances do not appear to be made for these baseline revisions that we all know are coming as the annual targets and basis of policy is considered? The minister says that she will fulfil section 36 of the Climate Change Act, but she seemed to indicate in answer to Sarah Boyack that she would do so through RPP3. Well, I do not believe RPP3 fulfills section 36 of the Climate Change Act. Sarah Boyack asked where is that section 36 report, and I would repeat that call. Finally, Presiding Officer, forestry planting is a major role to play in emissions reductions. Thousands of hectares have been felled to make way for wind farms over the last few years, and they are supposed to be replaced by compensatory planting. So, could the minister tell us how many hectares of compensatory planting have taken place over the last three years, and what percentage that makes up of the total area of timber felled for wind farm development? If she cannot tell me today, which I quite understand, would she undertake to write to me with those figures? I say to Alex Ferguson that the fixed annual targets were established on the basis of the 1990 to 2008 inventory in order to meet an emission reduction of 42 per cent by 2020, and since then that baseline has risen by 10.6 megatons. Now, given the effect of cumulative upwards revisions to the inventories since the targets were established, the percentage reductions required to achieve the fixed targets are now out of line with the 42 per cent reduction target. As I said before, if it hadn't been for successive increases to the baseline since the targets were established, Scotland would have met and exceeded its annual target for this year and the three previous years also. The reason why we have fixed annual emission targets is due to the changes in the way in which the data is calculated as a result of methodological improvements. The level of progress that Scotland can make in reducing emissions is also dependent on the policies and actions of others, especially the UK and the EU. The UK Government cuts to energy efficiency and renewable measures are creating a worrying climate of uncertainty for low-carbon policy in the UK. A Lord Daven, who is the chair of the Committee on Climate Change, in a letter to the Secretary of State for Energy and Climate Change at Amber Rudd on 22 September said, The uncertainty that is created by changes to existing policies and a lack of replacement policies up to and after 2020 could well lead to stop-start investment, higher costs and a risk that targets to reducing emissions will be missed. In terms of your specific point on the forestry, I am happy to answer the member in full. In terms of our target, RPP2 was clear that the target of 10,000 hectares per year was an average of the period to 2022. We are reversing the historic decline in woodland planting rates, protecting this important carbon sink. In 2013, forestry was the only sector in which there has been a net emissions sink. Planting rates have increased to an average of 8,000 hectares per year during the period 2011-2012 to 2014-15, which equates to around 16 million trees a year. With the launch of the new Scottish Rural Development programme, we aim to raise the planting rates from 2015. Rob Gibson, followed by Claudia Beamish. I am sure that the minister will join me in welcoming the third peatland forum in conference that starts in my constituency today. Methane levels have been increasingly marked up in the greenhouse gas inventory. In what ways have the measurement of methane emissions from deep peats such as the flow country in Caithness in Sutherland helped to meet our stretching Scottish climate change targets? The new international reporting requirements, which came into force for the 2013 inventory, have increased the potency of methane as a greenhouse gas and makes it harder to meet our fixed annual targets. The measurement of methane in deep peat is not currently required under the greenhouse gas inventory under international reporting requirements. However, work is under way to estimate emissions caused by the human influence from drainage and rewetting of peatland. It is intended that those emissions will be included in the greenhouse gas inventory once research has been completed. However, while the work continues, we have been supporting restoration through the Scottish Natural Heritage-led peatland action initiative and the new SRDP. Claudia Beamish has my sympathy, but it is more important that she has my permission to stay seated for her contributions. In the lead-up to Paris, climate justice will be at the heart of Scottish policies. What is the Scottish Government doing to ensure that a just transition strategy is in place supporting communities that are likely to be affected? How is the minister working with other ministers to ensure that transferable skills leading to new local jobs are going to benefit those in the fossil fuel industries who are losing their jobs now but also for the long-term future? As I said, we still recognise the poor and the vulnerable at home and abroad who are the first to be affected by climate change.  Justices and all that are very clear and that is why the Scottish Government is championing climate justice. We want to make sure that what we see is a just transition to a low-carbon economy with the burdens of climate change and the benefits of the low-carbon economy shared equitably. The Scottish National Action Plan on Human Rights commits Scotland to continue to champion climate justice and to make sure that we are developing a co-ordinated approach to climate justice at home and abroad in bedding climate justice in the national performance framework and aligning it with the UN's post-2015 Sustainable Development Goals. We also have our innovative £6 million climate justice fund, which is supporting 11 water adaptation projects in four sub-Saharan African countries, Malawi, Zambia, Rwanda and Tanzania. We have £3.8 million from our international development fund since 2012 for community energy projects in Malawi. In the international engagements that I have been undertaking, I have also been championing climate justice, which I did so at the World Climate Summit in Leong, where I had the opportunity to do so during a plenarisation. One of every four of Dundee City Council's cars and vans are now electric, and in conjunction with Transport Scotland, a further £1 million has been invested in Evian's infrastructure across the city, contributing to 115 of the taxes that have been electric in Dundee, boasting one of the largest and fastest-growing fleets of electric car club vehicles. Can I ask the minister whether that progress is being mirrored across the other 31 local authority areas, or do we need greater buy-in from our councils if we are to get transport emissions down to something resembling an acceptable level? Back by £2.5 million of funding from Transport Scotland's Switched On Fleets initiative, Scotland's local authorities are leading the way in the adoption of electric vehicles. In a 2014 survey of 433 councils in the UK regarding how many electric vehicles they had in their fleets for the top five were from Scotland, Dundee came to talk with South Lanarkshire, Glasgow City Council and Fife Council, placing second, third and fifth respectively. Dundee is the only Scottish local authority on the shortlist for the UK Government's electric taxi scheme and the go-altra low-city scheme. If successful, those bids are worth more than £20 million to Dundee and its partners. I am sure that we would all want to wish Dundee every success with their bids. We will obviously share learning from the Dundee work across the country to enable the city and ultimately Scotland to be globally recognised as a leader for innovative electric vehicle deployment. I thank the minister for an advanced copy of her statement. She told Parliament just now that the RPP will not be produced and not be laid before Parliament until the end of 2016. My reading of the Climate Change Act says that a section 36 report should be produced and it is in law as soon as is reasonably practicable. Is the end of 2016 as soon as is reasonably practicable? I would say to Tavish Scott that we also have to go through a very thorough and from consultation process as well and also in terms of our opportunity to be able to lay that report in time for Parliament to make sure that we give it the proper scrutiny that it deserves as well as across the scrutiny from the other parliamentary committees as well. Gil Paterson, followed by Patrick Harvie. It is clear that action on climate change requires action at every level and by all. What will the Government do to encourage individuals and organisations to play their part? There is already a wide range of action on climate change being taken by individuals, families, communities, businesses and other organisations right across Scotland but we need to continue to do more. Our national ambitions to tackle climate change will only be realised by people across Scotland taking action. The pace of the transition to a low-carbon society will be determined by how we as individuals, households and communities adapt and change our behaviours. That is why in the new year it is part of the development of further measures to tackle climate change between now and 2032. We will be asking people across Scotland for their views on climate change and what action we can collectively take because all of us including businesses, public sector, communities and individuals have a vital role to play. Patrick Harvie, followed by Mike McMahon. There has been much talk of baseline revisions but the Government has the power under the act to come back to Parliament and ask to revise the targets themselves. They have not done so, in my view quite rightly, but surely we must draw from that that these targets remain reachable and that the commitment is still there to reach these annual targets. Therefore, would not today have been a good day for the minister to come to Parliament and tell us how much money is attached to the national infrastructure priority on energy efficiency when that work will begin? Has the minister been told by the Cabinet Secretary for Finance how much money is available? In terms of Patrick Harvie's questions on the Committee on Climate Change, when it published its report, the Scotland Progress report, back in March, it said in its report that inventory changes have made our legislative targets much harder to reach. It has also said that it will work with the Scottish Government to address the issue whether inventory changes are pending. It has recommended that the Scottish Government should continue to investigate further abatement from measures that go beyond our current policies. We also propose to agree a process and timeline with the Scottish Government to advise on the implications for Scottish targets of significantly improved inventory data that is expected later in 2015 and again in 2017. We will continue to work with the Committee on Climate Change on that. In terms of the progress that we have been making for our improvement in the energy efficiency of Scotland's homes and non-domestic building stock, the detail of that programme is being developed, but it will be a truly national programme providing support for all buildings across Scotland. We will work closely with stakeholders to design and develop the new programme over the next two years. In terms of the spending route, I obviously cannot pre-empt any discussions around that, but the Cabinet and the sub-committee have agreed that we will be embedding climate change within the budget process. I thank the minister for her statement, but I note that the minister congratulated herself on reducing the levels of fuel poverty. Does she accept however that almost one-third of Scots remain in fuel poverty and that this is completely unacceptable? Does she recognise that only 30 per cent of privately owned or rented homes achieve an energy performance certificate of sea rating, with 65 per cent achieving D and E rates? Will she commit to giving the same emphasis and investment to the private housing sector that our Government directs towards the social housing sector? When we've already allocated over £500 billion since 2009 on a raft of fuel poverty and energy efficiency programmes, nearly one in three of our households over £700,000 have now received energy efficiency support. Tackling fuel poverty, Presiding Officer, remains a priority for this Government, and this year we are spending unprecedented amounts on fuel poverty and energy efficiency with a record budget of £119 million for 2015-16. I apologise to the four members that have been unable to call for this statement. We need to move on to next site of business, which is a debate on motion number 14297. In the name of Margaret Mitchell on the Apologies Scotland bill, members who wish to take part in the debate should press...