Welcome to APMA 0260 – Linear Algebra and Multivariable Calculus for Applied Mathematicians! This is the course to give you a head-start to the Applied Mathematics concentration. On this website, you can find the syllabus, lecture notes, homework assignments, and study materials.
Syllabus
APMA 0260 – Syllabus (Spring 2025)
Homework Extension Request Form
Lecture Notes
Note: The lecture notes will be frequently updated. Please refresh your webpage so that you have the most up-to-date version of the notes
| YouTube Videos | |||
|---|---|---|---|
| 1 | Jan 22 | Systems of Equations | Inconsistent Systems |
| 2 | Jan 24 | Row-reduction | Row-reduction |
| Infinitely Many Solutions | |||
| Solving ax + by | |||
| 3 | Jan 27 | Vectors | |
| 4 | Jan 29 | Span | Span |
| Row Theorem | |||
| Particular Solution | |||
| 5 | Jan 31 | Linear Independence | Linear Independence |
| 6 | Feb 3 | Linear Transformations (I) | Linear Transformations |
| 7 | Feb 5 | Linear Transformations (II) | Rotation Matrix |
| One-to-one and onto | |||
| 8 | Feb 7 | Matrix Algebra | Matrix Multiplication |
| AB vs BA | |||
| Magic Matrix (optional) | |||
| 9 | Feb 10 | The Inverse of a Matrix | |
| 10 | Feb 12 | Subspaces | |
| 11 | Feb 14 | Nul(A) and Col(A) | |
| 12 | Feb 19 | Dimension and Rank | |
| 13 | Feb 21 | Determinants | |
| 14 | Feb 24 | Applications of Determinants | |
| 15 | Feb 26 | Eigenvalues and Eigenvectors | |
| 16 | Feb 28 | Diagonalization | |
| 17 | Mar 3 | Midterm 1 – Review | |
| Mar 5 | Midterm 1 | ||
| 18 | Mar 7 | Applications of Diagonalization | |
| 19 | Mar 10 | Dot Products and Lengths | |
| 20 | Mar 12 | Orthogonality Awesomeness | |
| 21 | Mar 14 | Orthogonal Projections | |
| 22 | Mar 17 | Functions of Several Variables | |
| 23 | Mar 19 | Partial Derivatives | |
| 24 | Mar 21 | Tangent Planes | |
| 25 | Mar 31 | The Chain Rule | |
| 26 | Apr 2 | Gradients and Applications | |
| 27 | Apr 4 | Max and Min Values | |
| 28 | Apr 7 | Lagrange Multipliers | |
| 29 | Apr 9 | Double Integrals (I) | |
| 30 | Apr 11 | Double Integrals (II) | |
| 31 | Apr 14 | Midterm 2 – Review | |
| Apr 16 | Midterm 2 | ||
| 32 | Apr 18 | Triple Integrals | |
| 33 | Apr 21 | Change of Variables (I) | |
| 34 | Apr 23 | Change of Variables (II) | |
| 35 | Apr 25 | Final Exam – Review | |
| May 14 | Final Exam |
Homework Assignments
| Homework 1 | Jan 31 | Solutions |
| Homework 2 | Feb 7 | |
| Homework 3 | Feb 14 | |
| Homework 4 | Feb 21 | |
| Homework 5 | Feb 28 | |
| Homework 6 | Mar 14 | |
| Homework 7 | Mar 21 | |
| Homework 8 | Apr 4 | |
| Homework 9 | Apr 11 | |
| Homework 10 | Apr 25 | |
| Homework 11 | May 2 | Optional |
| Mini Project | May 2 |
Worksheets
| Worksheet 1 | Jan 30 | Solutions |
| Worksheet 2 | Feb 6 | |
| Worksheet 3 | Feb 13 | |
| Worksheet 4 | Feb 20 | |
| Worksheet 5 | Feb 27 | |
| Worksheet 6 | Mar 13 | |
| Worksheet 7 | Mar 20 | |
| Worksheet 8 | Apr 3 | |
| Worksheet 9 | Apr 10 | |
| Worksheet 10 | Apr 24 |
Quizzes
| Quiz 1 | Jan 30 | Solutions |
| Quiz 2 | Feb 6 | |
| Quiz 3 | Feb 13 | |
| Quiz 4 | Feb 20 | |
| Quiz 5 | Feb 27 | |
| Quiz 6 | Mar 13 | |
| Quiz 7 | Mar 20 | |
| Quiz 8 | Apr 3 | |
| Quiz 9 | Apr 10 | |
| Quiz 10 | Apr 24 |
Exams
Midterm 1: Wednesday, March 5, 2-2:50 pm covers Lec 1-14
Midterm 2: Wednesday, April 16, 2-2:50 pm, covers Lec 15-27
Final Exam: Wednesday, May 14, 2-5 pm, covers the entire course
Calendar