Teaching Assistant

M427L Advanced Calculus for Applications II

Syllabus: Click Here.

Regular Class: MWF 10:00-11:00 am @ RLP 0.130
Discussion Session: TTh 5:00-6:00 pm @ RLP 0.130
Dr. Shen’s Office Hour: MW 11:00-12:00 am, T 10:30-11:30 am @ RLM 13.142
My Office Hour: W 12:00-2:00 pm @ RLM 11.130

Download handout 2018-10-23 here.

Syllabus

THE GEOMETRY OF EUCLIDEAN SPACE (6 days)
1. Vectors in two- and three-dimensional space
2. The inner product, length, and distance
3. Matrices, determinants, and the cross product
4. Cylindrical and spherical coordinates
5. n-dimensional Euclidean space
DIFFERENTIATION (5-6 days)
1. The geometry of real-valued functions
2. Limits and continuity
3. Differentiation
4. Introduction to paths
5. Properties of the derivative
6. Gradients and directional derivatives
HIGHER-ORDER DERIVATIVES (3 days)
1. Iterated partial derivatives
2. Taylor’s theorem
3. Extrema of real-valued functions
4. Constrained extrema and Lagrange multipliers
5. The implicit function theorem (if time permits)
VECTOR-VALUED FUNCTIONS (5 days)
1. Acceleration and Newton’s Second Law
2. Arc length
3. Vector fields
4. Divergence and curl
DOUBLE AND TRIPLE INTEGRALS (3 days)
1. Introduction
2. The double integral over a rectangle
3. The double integral over more general regions
4. Changing the order of integration
5. The triple integral
THE CHANGE OF VARIABLES FORMULA (3 days)
1. The geometry of maps (not crucial)
2. The change of variables theorem (lightly)
3. Applications of double, triple integrals (if time permits)
INTEGRALS OVER PATHS AND SURFACES (7 days)
1. The path integral
2. Line integrals
3. Parametrized surfaces
4. Area of a surface
5. Integrals of scalar functions over surfaces
6. Surface integrals of vector functions
THEOREMS OF VECTOR ANALYSIS (5-6 days)
1. Green’s theorem
2. Stokes’ theorem
3. Conservative fields
4. Gauss’ theorem