Calc III SU2024
This is the course page for Calc III in the Summer 2024 semester. This course runs from June 10 to August 1.
Monday, Tuesday, Wednesday, Thursday, 3:00 PM - 4:30 PM in Cupples II, Room 200
Office Hours: Cupples I (I, not II), Room 216, Monday and Wednesday, 2:00-2:50 PM
Lecture/Class Notes:
These notes are what I'm using to organize and prepare myself for class, and they will more or less follow the content of Lang; for the most part, they'll essentially be an abridged version of Lang. Your mileage with these notes may vary.
Homework:
Homework 1 (Due Monday, June 17)
Homework 2 (Due Thursday, June 20)
Homework 3 (Due Monday, June 24)
Homework 4 (Due Thursday, June 27)
Homework 5 (Due Monday, July 1)
Homework 6 (Due Wednesday, July 3)
Homework 7 (Due Thursday, July 11)
Homework 8 (Due Thursday, July 18)
Grading:
Homework will count for 75% of your overall grade. There will be one final exam on the last day of class that counts for 25% of your grade.
Text: Calculus of Several Variables by Serge Lang. The plan is to cover Chapters 1-5, 8, 9, 10, 11, 12, and 17.
Topics:
Vectors, vector-valued functions
Dot product and cross product
Parametric lines
Planes
Derivatives
Length of curves
Functions of several variables
Graphs and level curves
Partial derivatives
Chain rule
Tangent plane
Directional derivatives
Minima and maxima
Critical points
Lagrange multipliers
Path integrals
Evaluating path integrals
Potential functions and their relation to path integrals
Double integrals
Polar coordinates
Green's Theorem
Triple integrals and surface integrals
Cylindrical and spherical coordinates
Stokes' Theorem and Divergence Theorem
Surface parametrization
The change of variables formula