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. 

• Opening Remarks

• Functions and Sets

• Coordinates and Vectors

• Differentiation of Vector-Valued Functions

• Functions of Several Variables and their Derivatives

• The Chain Rule and Gradient

• Critical Points, Minima, Maxima

• Vector Fields, Potentials

• Curve Integrals

• Double Integrals

• Double Integrals II

• Green's Theorem

• Triple Integrals

• Surface Integrals

• Curl, Divergence, Stokes' Theorem

• Finite-Dimensional Vector Spaces

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)

• Homework 9 (Due Thursday, July 25)

• Final Exam (Due August 2, 11:59 PM)

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. We will also pull some material from Linear Algebra Done Right by Sheldon Axler and Interactive Linear Algebra by Dan Margalit, Joseph Rabinoff.

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