Lecture slides
The pdf files in the "Long" column are as they appeared in class (sometimes with a bit of editing based on discovered errors or feedback from students). The files under the "Short" column are a shorter versions in which every stage of a single slide is collapsed into a single page of the pdf. For staged slides in which things disappear and others appear in their place (only happens occasionally), the resulting "Short" version can be a bit of a mess. I suggest looking back at the "Long" slides in those instances.
Students that like to see the slides before and during class can look at last year's slides. The slides will be slightly different this year and might appear a bit earlier or later depending on how well I replicate last year's timing.
| Lecture | Long | Short | Description |
|---|---|---|---|
| Lecture 1 - Jan 3 | Intro to course, DEs as models, classifying DEs, DE definitions. Method of integrating factors. | ||
| Lecture 2 - Jan 5 | Integrating factors. ICs and IVPs. Structure of solutions. Separating variables. Qualitative behaviour of solutions - e.g. limits at infinity. | ||
| Lecture 3 - Jan 10 | A,B,C | Separable equations. Modeling tanks with inflow and outflow. | |
| Lecture 4 - Jan 12 | Saltwater inflow example. Independence of solutions and the Wronskian. Homogeneous second order linear ODE with constant coefficients - distinct roots to characteristic equation. | ||
| Lecture 5 - Jan 17 | A, B | Complex number review. Complex roots to characteristics equation. Repeated roots. Reduction of order. | |
| Lecture 6 - Jan 19 | Homogeneous and non-homogeneous equations (matrix and differential). Method of undetermined coefficients. | ||
| Lecture 7 - Jan 24 | Wrap up Method of Undetermined Coefficients, intro to mass-spring systems. | ||
| Lecture 8 - Jan 26 | Mass-spring systems, natural frequency, forced mass-spring systems, resonance. | ||
| Midterm 1 - Jan 31 | |||
| Lecture 9 - Feb 2 | Wrap up resonance (damped case), Intro to Systems of DEs, eigenvalue/eigenvector review, solutions to 2x2 systems with distinct eigenvalues. | ||
| Lecture 10 - Feb 7 | Shapes of solutions in the phase plane - distinct eigenvalue case. | ||
| Lecture 11 - Feb 9 | General solutions and their shapes in the phase plane - complex eigenvalue case. (new version with typo fixed) | ||
| Lecture 12 - Feb 14 | Repeated eigenvalue case and overall summary of 2x2 systems of linear equations. | ||
| Lecture 13 - Feb 23 | Summary of 2x2 systems. Non-homogeneous equations (constant vector). Tank applications. | ||
| Lecture 14 - Feb 28 | A, B | Laplace transforms for solving ODEs. | |
| Lecture 15 - Mar 2 | Solving ODEs using Laplace transforms, including those with step functions involved. | ||
| Lecture 16 - Mar 7 | Laplace transforms and step, ramp, and delta functions. | ||
| Lecture 17 - Mar 9 | Solving ODEs involving delta functions. Review questions are posted on the Handouts and solutions page. | ||
| Midterm 2 - Mar 14 | |||
| Lecture 18 - Mar 16 | Transfer functions. Method of undetermined coefficients for any periodic function. Fourier Series. | ||
| Lecture 19 - Mar 21 | Fourier series | ||
| Lectures 20 -23: Mar 23 - Apr 4 | pdf,pdf | pdf, pdf, FS formula | Diffusion equation and Fourier series |
