Math 375

Math 375 - 12/13


Notes on Math 375: Topics in Multi-Variable Calculus and Linear Algebra

Your comments and criticism are greatly welcomed.

Course Website

Syllabus

Lecture and Homework Schedule

Textbook

Calculus, Volume II, 2nd Edition, by Tom M. Apostol

Calendar

September

Mon (Dis) Tue (Lec) Wed (Dis) Thu (Lec) HW
- -  - 9/7 HW1
9/11 9/12 9/13 9/14 HW2
9/18 9/19 9/20 9/21 HW3
9/25 9/26 9/27 9/28 HW4

All notes from September in PDF format

October

Mon (Dis) Tue (Lec) Wed (Dis) Thu (Lec) HW
10/2 Exam 1 10/4 10/5 HW5
10/9 10/10 10/11 10/12 HW6
10/16 10/17 10/18 10/19 HW7
10/23 10/24 10/25 10/26 -
10/30 10/31  11/1  11/2 HW8

Midterm 1 Practice

All notes from October in PDF format

November

Mon (Dis) Tue (Lec) Wed (Dis) Thu (Lec) HW
 10/30 10/31 11/1 11/2 HW8
11/6 11/7 11/8 11/9 HW9
11/13 11/14 11/15 Exam 2 HW10
11/20 11/21 11/22 Holiday  -
11/27 11/28 11/29 11/30 HW11

Midterm 2 Practice 1

Midterm 2 Practice 2

All notes from November in PDF format

December

Mon (Dis) Tue (Lec) Wed (Dis) Thu (Lec) HW
12/4  12/5 12/6 12/7 HW12
12/11 12/12  12/13

Matrix Algebra Review

Lecture Outlines

Chapter 1: Linear Spaces

Week 01 - 9/7: Vector Space

Week 02 - 9/12: Proof Writing

Week 02 - 9/14: Subspace, Span of Vector Spaces, Linear Independence

Week 03 - 9/19: Linear Independence, Basis, Coordinates

Week 03 - 9/21: Theorems about Linear Dependence

Week 04 - 9/26: Inner Product, Length, Angle

Week 04 - 9/28: Distance, Triangle Inequality, Orthogonal, Gramm-Schmidt Process

Week 05 - 10/3: Midterm 1

Week 05 - 10/5: Best Approximation, Fourier Series

Chapter 2: Linear Transformations and Matrices

Week 06 - 10/10: Linear Transformations, Solving Systems of Equations

Week 06 - 10/12: Injective, Null Space, Range, Rank-Nullity Theorem

Week 07 - 10/17: Algebraic Operations on Linear Transformations, Injective, Inverse

Week 07 - 10/19: Matrix Representation of Linear Transformations, Matrix Multiplication

Week 08 - 10/24: Isomorphism Between Linear Transformations and Matrices, Solving Linear Equations using Matrix

Week 08 - 10/26: Solving Linear Equations

Chapter 3: Determinants

Week 09 - 10/31: Determinants

Week 09 - 11/2: Uniqueness Theorem, Properties of Determinants

Week 10 - 11/7: Determinant and Area, Inverse of Matrix, Minors and Cofactors

Week 10 - 11/9: Cofactor Expansion, Cramer's Rule, Linear Independence and Determinant

Chapter 4: Eigenvalues and Eigenvectors

Week 11 - 11/14: Eigenvalues, Eigenvectors

Week 11 - 11/16: Midterm 2

Week 12 - 11/21: Characteristic Polynomial, Trace, Diagonalization

Week 12 - 11/23: Thanksgiving Break

Chapter 8: Differential Calculus of Scalar and Vector Fields

Week 13 - 11/28: Open Balls, Limits, Continuity, Directional Derivative

Week 13 - 11/30: Partial Derivative, Total Derivative, Linear Approximation Formula

Week 14 - 12/5: Differentiable, Total Derivative, Continuity, Multivariable Chain Rule

Week 14 - 12/7: Differentiable, Chain Rule, Gradient, Level Sets

Week 15 - 12/12: Multivariable Chain Rule, Jacobian Matrix

Math 375 - 12/13

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