DIFFERENTIAL EQUATIONS WITH LINEAR ALGEBRA (M 427J)
Instructor: Paul Beckman (paul dot beckman at
austin dot utexas dot edu)
Office hours: Mon 10:00-11:00 AM, POB 3.408
Teaching assistant: William Pan (whpan at utexas dot edu)
Office hours: ---
Lectures: Mon/Wed/Fri 2:00-3:00 PM, ETC 2.108
Discussion sections: Tue/Thu 4:00-5:00 PM, RLP 0.126
COURSE DESCRIPTION
This course provides a rigorous introduction to the study of ordinary differential equations, linear algebra, and a brief introduction into partial differential equations. Students will learn the basic techniques for understanding and solving differential equations that arise in applications.
MATERIALS
Textbook: Martin Braun, Differential Equations and Their Applications, 4th. Ed
The full syllabus, announcements, etc. are available on the course Canvas page.
SCHEDULE
Numbers below indicate section numbers from the textbook covered in lecture.
| Mon | Wed | Fri | |
|---|---|---|---|
| Aug 24-28 | 1.1 Introduction | 1.2 First-order linear DEs | 1.4 Separable DEs |
| Aug 31-Sep 4 | 1.9 Exact equations | 1.13 Euler’s method | 2.1 Algebraic properties of solutions Quiz 1 |
| Sep 7-11 | Labor Day (no class) | 2.2 Constant-coefficient linear equations | 2.2.1 Complex roots Quiz 2 |
| Sep 14-18 | 2.2.2 Equal roots | 2.3 Nonhomogeneous equations | 2.5 Method of judicious guessing Quiz 3 |
| Sep 21-25 | 3.1 Linear systems | 3.2 Vector spaces | 3.3 Dimension of a vector space Quiz 4 |
| Sep 28-Oct 2 | 3.4 Linear algebra for DEs | Review | Midterm 1 |
| Oct 5-9 | 3.5 Determinants | 3.6 Solving linear systems | 3.7 Linear transformations Quiz 5 |
| Oct 12-16 | 3.8 Eigenvalues and eigenvectors | 3.8 (continued) | 3.9 Complex roots Quiz 6 |
| Oct 19-23 | 3.10 Equal roots | 3.11 Fundamental matrix solutions | 4.1 Equilibrium points Quiz 7 |
| Oct 26-30 | 4.1 Equilibrium points | 4.2 Stability of linear systems | 4.4 Phase space Quiz 8 |
| Nov 2-6 | 4.7 Phase portraits | Review | Midterm 2 |
| Nov 9-13 | 5.1 Two point BVPs | 5.1 (continued) | 5.2 Intro to PDEs Quiz 9 |
| Nov 16-20 | 5.3 Separation of variables | 5.3 (continued) | 5.4 Fourier series Quiz 10 |
| Nov 23-27 | Fall break (no class) | ||
| Nov 30-Dec 4 | 5.4 (continued) | 5.5 Even and odd functions | Bonus: The fast Fourier transform Quiz 11 |
| Dec 7-11 | Review | Study day (no class) | Final |