Vector Calculus and Linear Algebra II (Math 22b)

Vector Calculus and Linear Algebra II (Math 22b)

Oliver Knill | Spring 2019 | Harvard University

A continuation of Mathematics 22a.

General

Syllabus (2022)

Week 1

Lecture 1: Pythagoras

Lecture 2: Gauss-Jordan Elimination

Lecture 3: Definitions, Theorems and Proofs

Week 2

Lecture 4: Cross Product

Lecture 5: Surfaces

Lecture 6: Visual Proofs

Week 3

Lecture 7: Curves

Lecture 8: Arc Length

Lecture 9: Intuition

Week 4

Lecture 10: Coordinates

Lecture 11: Parametrization

Lecture 12: Creativity

Week 5

Lecture 13: Partial Differential Equations

Lecture 14: Keywords for First Hourly

Lecture 15: Contradiction and Deformation

Week 6

Lecture 16: Chain Rule

Lecture 17: Taylor Approximation

Lecture 18: Number Magic

Week 7

Lecture 19: Extrema

Lecture 20: Constraints

Lecture 21: Island Mathematics

Week 8

Lecture 22: Double Integrals

Lecture 23: Substitution

Lecture 24: How to Solve - Literature Samples

Week 9

Lecture 25: Solids

Lecture 26: Surface Area

Lecture 27: A Visit by Archimedes

Week 10

Lecture 28: Keywords for Second Hourly

Lecture 29: Line Integrals

Lecture 30: Perpetual Motion Machines

Week 11

Lecture 31: Green’s Theorem

Lecture 32: Stokes Theorem

Lecture 33: Discrete Vector Calculus

Week 12

Lecture 34: Gauss Theorem

Lecture 35: General Stokes

Lecture 36: A Discrete World

Week 13

Lecture 37: Review - Geometries and Fields

Lecture 38: Review - Calculus in Hyperspace

Lecture 39: Keywords for the Final

Exams

First hourly

First Midterm - Hourly 1

Practice Exam A: Question

Practice Exam A: Solution

Practice Exam B: Question

Practice Exam B: Solution

Second hourly

Second Midterm - Hourly 2

Practice Exam A: Question

Practice Exam A: Solution

Practice Exam B: Question

Practice Exam B: Solution

The Final Exam

Review Sheet for the Final

The Final Exam - Questions

The Final Exam - Solutions

Practice Exam A: Questions

Practice Exam A: Solutions

Practice Exam B: Questions

Practice Exam B: Solutions