Engineering Mathematics I

DESCRIPTION: Polar coordinates, parametric curves, vectors, vector geometry, vector-valued functions, partial derivatives, gradient, optimization, multiple integration, vector fields, and operations on vector fields. Emphasis on methods and applications. Math 215 and Math 113 cannot both be taken for credit. Similarly Math 215 and Math 214 cannot both be taken for credit.
TAUGHT: Winter, Summer, Fall
CONTENT AND TOPICS: (Note: As many as possible of the following topics are accompanied by applications.) Calculus in the contexts of conic sections, polar coordinates and parametric curves. Vectors in R^2 and R^3. The dot and cross products. Distance, angles, lines and planes. Quadric surfaces. Cylindrical and spherical coordinates. Vector-valued functions, limits, continuity, derivatives and integrals of the same. Tangential and normal components of acceleration. Arc length as a parameter and curvature. Projectile motion. Functions of several variables, limits, continuity, and partial derivatives of the same. The total differential and error estimation. Tangents, planes, normal lines, the gradient and directional derivatives. Free optimization, absolute extrema and LaGrange multipliers. Multiple and iterated integration, including Fubini's Theorem. Applications of multiple integration such as volume, surface area, the average value of a function, centers of mass and moments of inertia. Parameterized surfaces and integration in cylindrical and spherical coordinates. Vector field, div, grad, curl and their interpretation. Equivalent conditions for conservative vector fields.
GOALS AND OBJECTIVES: 1. Convert between rectangular and polar coordinates and plot several polar curves on a grapher (parabola, circle, ellipse, hyperbola).
2. Calculate the results of vector addition, subtraction, scalar multiplication, dot product and cross product.
3. Perform calculations for geometry in space.
4. Convert between cylindrical, spherical, and rectangular coordinates.
5. Explain the application of differentiation of vector-valued functions to velocity and acceleration.
6. Find arc length and curvature of a given curve.
7. Evaluate partial derivatives and explain their meaning geometrically.
8. Use local linear approximation applications.
9. Produce a directional derivative for any given direction.
10. Locate and classify extrema for functions of two variables.
11. Apply 2- and 3- dimensional integration to geometric and physical problems.
REQUIREMENTS: All students must have their own text. If a graphing calculator is to be used, the student must obtain their own. Assignments and exams are required by all faculty. Some faculty may require attendance, participation, projects, working in groups, graphing calculators, computer lab assignments or other forms of assessment.
PREREQUISITES: Math 112 or the equivalent.
EFFECTIVE DATE: January 2003