Math 375 – Multivariable & Linear Algebra
Notes on Math 375: Topics in Multi-Variable Calculus and Linear Algebra Your comments and criticism are greatly welcomed.
Course Website
Textbook
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 |
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 |
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 |
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