MATH 2010 - Multivariable Calculus and Matrix Algebra
Video Lectures Fall 2020 and Spring 2021
Instructors: Mark Holmes and Gregor Kovacic

The following are the video lectures, and accompying pdf, developed over the Fall 2020 and Spring 2021 semesters. Also included are the quizzes (with answers) given in the spring semester. What are not inlcuded are the weekly hourlong Instructor Session videos, which did cover some material not in the video lectures.

## Multivariable Calculus

Chapter 14: Differentiation in Several Variables

Sec 14.3 Partial Derivatives.
Video and pdf

Quiz 1 Covers sections 12.2, 12.5, 12.6

Sec 14.4 Tangent Planes and Linear Approximations.
Video part 1 and pdf part 1
Video part 2 and pdf part 2
Sec 14.5 Gradient and Directional Derivatives.
Video part 1 and pdf part 1
Video part 2 and pdf part 2

Quiz 2 Covers sections 14.4, 14.5.

Sec 14.6 Calculus Rules.
Video and pdf
Sec 14.7 Optimization.
Video part 1 and pdf part 1
Video part 2 and pdf part 2

Quiz 3 Covers sections 14.6, 14.7.

Sec 14.8 Lagrange Multipliers.
Video and pdf

Chapter 15: Multiple Integration

Sec 15.1 Integration in Two Dimensions.
Video and pdf

Quiz 4 Covers sections 14.8, 15.1.

Sec 15.2 Double Integrals.
Video part 1 and pdf part 1
Video part 2 and pdf part 2
Sec 15.3 Triple Integrals.
Video part 1 and pdf part 1
Video part 2 and pdf part 2
Sec 15.4 Polar, Cylindrical and Spherical Coordinates.
Video part 1 and pdf part 1
Video part 2 and pdf part 2

Quiz 5 Covers sections 15.3, 15.4.

Chapter 16: Line and Surface Integrals

Sec 16.1 Vector Fields.
Video and pdf
Sec 16.2 Line Integrals.
Video part 1 and pdf part 1
Video part 2 and pdf part 2

Quiz 6 Covers sections 16.1, 16.2.

Sec 16.3 Conservative Vector Fields.
Video and pdf

Chapter 17: Fundamental Theorems of Vector Analysis

Sec 17.1 Green's Theorem.
Video and pdf

Quiz 7 Covers sections 16.3, 17.1.

## Matrix Algebra

Chapter 1: Matrices and Systems of Linear Equations

Sec 1.2 Echelon Form and Gaussian Elimination.
Video and pdf
Sec 1.3 Consistent Systems.
Video and pdf

Quiz 8 Covers sections 1.1, 1.2, 1.3.

Sec 1.5 and 1.6 Matrix Operations.
Video part 1 and and pdf part 1
Video part 2 and and pdf part 2
Sec 1.7 Linear Independence.
Video and pdf
Sec 1.9 Matrix Inverse.
Video and pdf

Chapter 3: The Vector Space R^n

Sec 3.2 Vector Space Properties.
Video and pdf
Sec 3.3 Subspaces.
Video and pdf

Quiz 9 Covers sections 1.9, 3.2, 3.3.

Sec 3.4 Bases for Subspaces.
Video and pdf
Sec 3.5 Dimension.
Video and pdf
Sec 3.6 Ortogonal Bases.
Video and pdf

Quiz 10 Covers sections 3.4, 3.5, 3.6.

Chapter 4: The Eigenvalue Problem

Introduction and Sec 4.2.
Video and pdf
Sec 4.1 and 4.4 Eigenvalues and the Characteristic Polynomial.
Video and pdf
Sec 4.5 Eigenvectors and Eigenspaces.
Video and pdf

Quiz 11 Covers sections 4.1, 4.2, 4.4, 4.5.

Sec 4.6 Complex Eigenvalues and Eigenvectors.
Video and pdf
Sec 4.7 Similarity and Diagonalization.
Video part 1 and pdf part 1
Video part 2 and pdf part 2