NUMERICAL ERROR Student Notes. ENGR 351 Numerical Methods for Engineers Southern Illinois University Carbondale College of Engineering Dr. L.R. Chevalier. Objectives. To understand error terms Become familiar with notation and techniques used in this course.
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Numerical Methods for Engineers
Southern Illinois University Carbondale
College of Engineering
Dr. L.R. Chevalier
Consider a series expansion to estimate trigonometric functions
Estimate sin(p/ 2) to three significant figures. Calculate et and ea.
Stop when ea ≤ es
To gain insight consider the mathematical
formulation that is used widely in numerical
methods - TAYLOR SERIES
Zero order approximation
This is good if the function is a constant.
First order approximation
slope multiplied by distance
Still a straight line but capable of predicting an increase or decrease - LINEAR
Second order approximation - captures some of the curvature
Use zero through fourth order Taylor series expansion to approximate f(1) given f(0) = 1.2 (i.e. h = 1). Calculate et after each step.
f(1) = 0.2