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