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 in POB 3.408, Fri 3:00-4:00 PM in POB 3.342
Teaching assistant: William Pan (whpan at utexas dot edu)
Office hours: Wed 4:30-5:30 PM in EER 0th Floor Atrium, Thu 1:00-2:00 PM in PMA 12.120
Lectures: Mon/Wed/Fri 2:00-3:00 PM, ETC 2.108
Discussion sections: Tue/Thu 5:00-6:00 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
Martin Braun, Differential Equations and Their
Applications, 4th Ed
Gilbert Strang, Linear Algebra and Its Applications, 4th Ed
The full syllabus, notes, announcements, etc. are available on the course Canvas page.
SCHEDULE
Numbers below indicate section numbers from Braun covered in lecture unless otherwise noted.
| Mon | Wed | Thu | Fri | |
|---|---|---|---|---|
| Aug 24-28 | 1.1 Introduction | 1.2 First-order linear DEs | 1.4 Separable DEs | |
| Aug 31-Sep 4 | 1.5 Population models 1.9 Exact equations |
1.9 (continued) 1.10 Existence-uniqueness theorem |
Quiz 1 | 2.1 Algebraic properties |
| Sep 7-11 | Labor Day (no class) | 2.2 Constant-coefficient linear equations | Quiz 2 | 2.2.1 Complex roots |
| Sep 14-18 | 2.2.2 Equal roots (On Zoom) | 2.3 Nonhomogeneous equations 2.4 Variation of parameters (On Zoom) |
Quiz 3 | 2.5 Method of judicious guessing |
| Sep 21-25 | 2.6 Mechanical vibrations 3.1 Linear systems |
3.2 Vector spaces | Quiz 4 | 3.3 Dimension of a vector space |
| Sep 28-Oct 2 | 3.4 Linear algebra for DEs [Strang] 1.1-1.5 Gaussian elimination |
Review | Midterm 1 | |
| Oct 5-9 | 3.5 Determinants | [Strang] 4.1-4.3 Determinants | Quiz 5 | [Strang] 1.6 Matrix inverse |
| Oct 12-16 | 3.8 Eigenvalues and eigenvectors | Predator-prey systems (see notes) | Quiz 6 | 3.9 Complex roots |
| Oct 19-23 | Equal roots (see notes) | The matrix exponential (see notes) | Quiz 7 | 4.1 Equilibrium points |
| Oct 26-30 | 4.1 Equilibrium points | 4.2 Stability of linear systems | Quiz 8 | 4.4 Phase space |
| Nov 2-6 | 4.7 Phase portraits | Review | Midterm 2 | |
| Nov 9-13 | 5.1 Two point BVPs | 5.1 (continued) | Quiz 9 | 5.2 Intro to PDEs |
| Nov 16-20 | 5.3 Separation of variables (On Zoom) | 5.3 (continued) (On Zoom) | Quiz 10 | 5.4 Fourier series |
| Nov 23-27 | Fall break (no class) | |||
| Nov 30-Dec 4 | 5.4 (continued) | 5.5 Even and odd functions | Quiz 11 | Bonus: The fast Fourier transform |
| Dec 7-11 | Review | Study day (no class) | Final | |