calculus iii: multivariable and vector calculus

week 01

Class 01 (January 3, 2022): Introductions and Logistics, Intro to Functions of Two Variables

Pre-class:

• Watch: Introduction to Winter 2022, COVID Musings
• Watch: Homework Logistics

In-class content

• Topics: Intro to Functions of Two Variables
• Video of Class
• Handout: [Functions of two variables] [A table of numbers]

Class 02 (January 5, 2022): Contour Lines, Slices

In-class content:

• Class: Video of class
• Handout: [Graphs and Slices]

Class 03 (January 6, 2022): Planes

In-class content

• Recording of Class
• Handout: [Planes]

Homework 01 (Due Friday, January 7, 2022)

• Homework 01, due Friday, January 7.

Week 02

Class 04 (January 10, 2022): Vectors and Dot Products

In-class content

• Recording of Class
• Handout: [Intro to Vectors] [Intro to Dot Products]

Class 05 (January 12, 2022): More with Dot Products

In-class content

• Recording of Class
• Handout: [More with Dot Products]

Class 06 (January 14, 2022): The Partial Derivative!

In-class content

• Recording of Class
• Handouts: [The Partial Derivative] [More with Partial Derivatives] [A table of numbers]

Homework 02 (Due Friday, January 14, 2022)

• Homework 02, due Friday, January 14.

Week 03

Class 07 (January 17, 2022): Evaluating Partial Derivatives, Tangent Planes

In-class content

• Recording of Class
• Handout: [Evaluating Partial Derivatives] [Tangent Lines and Planes]

Class 08 (January 19, 2022): The Differential, Introduction to the Gradient Vector

In-class content

• Recording of Class
• Handout: [Directional Derivatives and the Gradient Vector]

Class 09 (January 20, 2022): More Directional Derivatives

In-class content

• Recording of Class
• Handout: [More Directional Derivatives]

Homework 03 (Due Friday, January 21, 2022)

• Homework 03, due Friday, January 21.

Week 04

Class 10 (January 24, 2022): Gradients in Space, Chain Rule, Higher-Order Derivatives

In-class content

• Recording of Class
• Handout: [Gradient Vectors, Chain Rules, Second Derivatives]

Class 11 (January 26, 2022): Optimization

In-class content

• Recording of Class (a little bit about second-order partial derivatives)
• Recording of Class (2016 version)
• Handout: [Optimization]

Class 12 (January 27, 2022): Lagrange Multipliers

In-class content

• Recording of Class (2016 version)
• Handout: [Lagrange Multipliers]

Homework 04 (Due Friday, January 28, 2022)

• Homework 04, due Friday, January 28.

Week 05

Class 13 (January 31, 2022): Introduction to Integrals of Two Variables

In-class content

• Recording of Class
• Handout: [(Re)Introducing Integration in 1D and 2D] [1D Integration Practice]

Class 14 (February 2, 2022): Evaluating 1D and 2D Integrals

In-class content

• Recording of Class
• Handout: [Evaluating 1D and 2D Integrals]

Class 15 (February 3, 2022): Evaluating 2D and 3D Integrals

In-class content

• Recording of Class
• Handout: [Evaluating 2D and 3D Integrals]

Homework 05 (Due Friday, February 4, 2022)

• Homework 05, due Friday, Feb 4 (ish).

Week 06

Class 16 (February 7, 2022): Evaluating 3D Integrals and Introduction to Polar Coordinates

In-class content

• Recording of Class
• Handout: [3D Integrals and Intro to Polar Coordinates]

Class 17 (February 9, 2022): More Polar Coordinates, Introduction to Cylindrical Coordinates

In-class content

• Recording of Class
• Handout: [Polar and Cylindrical Coordinates]

Class 18 (February 10, 2022): Cylindrical and Spherical Coordinates

In-class content

• Recording of Class
• Handout: [Cylindrical, and Spherical Coordinates]
• Class was cut short due to smoke from the hotel fire across the street.

Homework 06 (Due Friday, February 11, 2022)

• Homework 06, due Friday, Feb 11.

Week 07

Class 19 (February 14, 2022): MT Check-in and Spherical Coordinates, Introduction to Parametric Curves

In-class content

• Recording of Class
• Handout: [Cylindrical, and Spherical Coordinates] [Parametric Curves]

Class 20 (February 16, 2022): Parametric Curves

In-class content

• Recording of Class
• Handout: [Parametric Curves] [Derivatives of Parametric Curves]

Class 21 (February 17, 2022): Vector Fields

In-class content

• Recording of Class
• Handout: [Vector Fields] [More Vector Fields]

Homework 07 (Due Friday, February 18, 2022)

• Homework 07, due Friday, Feb 18.

Week 08

Class 22 (February 21, 2022): Introduction to Line Integrals

In-class content

• Recording of Class
• Handout: [The Idea of a Line Integral] [Evaluating Line Integrals]

Class 23 (February 23, 2022): Evaluating Line Integrals, Gradient Fields, and Path Independence

In-class content

• Recording of Class
• Handout: [More Evaluating Line Integrals] [Fundamental Theorem for Gradients]

Class 24 (February 24, 2022): Gradient Fields, and Path Independence, Green's Theorem

In-class content

• Recording of Class
• Handout: [Fundamental Theorem for Gradients] [Green's Theorem]

Week 09

Class 25 (February 28, 2022): Green's Theorem, Introduction to Flux Integrals

In-class content

• Recording of Class
• Handout: [Green's Theorem] [Intro to Flux Integrals]

Class 26 (March 2, 2022): More Flux Integrals, Introduction to Divergence

In-class content

• Recording of Class coming soon.
• Handout: [Intro to Flux Integrals] [Green's Theorem]

Class 27 (March 2, 2022): More Divergence, the Divergence Theorem

In-class content

• Recording of Class coming soon.
• Handout: [Divergence and the Divergence Theorem]

Week 10

Class 28 (March 7, 2022): Cross Products, Introduction to Curl

In-class content

• Recording of Class
• Handout: [Intro to Flux Integrals] [Curl]

Class 29 (March 9, 2022): Stokes Theorem

In-class content

• Recording of Class
• Handout: [Stokes Theorem]

Class 30 (March 10, 2022): Conclusion

In-class content

• Recording of Class coming soon
• Handout: [Summary]

Homework 10 (Due Friday, March 11, 2022)

• Homework 10, due Friday, March 11.