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 to very different this year but I usually don't have time to post them in advance so last year's slides is the best option.
| Lecture | Long | Short | Description |
|---|---|---|---|
| Lecture 1 - Jan 3 | Introduction to the course, classifying DEs, defining "solution", Integrating Factors. | ||
| Lecture 2 - Jan 5 | Integrating factors and separable equations. | ||
| Lecture 3 - Jan 10 | Separating variables (cont), modeling salt water in tanks, existence/uniqueness of solutions | ||
| Lecture 4 - Jan 12 | Linear independence, Wronskian, Second order linear homogeneous constant coefficient ODE with real distinct roots, complex number review. | ||
| Lecture 5 - Jan 17 | Second order linear nonhomogeneous constant coefficient equations, complex roots, repeated root, reduction of order. | ||
| Lecture 6 - Jan 19 | Connections between linear ODEs and matrix algebra, solving nonhomogeneous second order linear ODEs using method of undetermined coefficients. | ||
| Lecture 7 - Jan 24 | Method of undetermined coefficients, mass-spring equations, over-, critical- and underdamped mass spring systems. | ||
| Lecture 8 - Jan 26 | Force vibrations and resonance | ||
| Lecture 9 - Jan 31 | Systems of equations, direction fields, eigenvalues and eigenvectors, general solutions to systems. | ||
| Lecture 10 - Feb 2 | Shapes of solutions in the $x_1$-$x_2$ plane (distinct eigenvalue case). | ||
| Lecture 11 - Feb 9 | Systems of equations with complex eigenvalues. | ||
| Lecture 12 - Feb 21 | Complex eigenvalue example. Systems with repeated eigenvalue. Summary of 2x2 systems. | ||
| Lecture 13 - Feb 23 | Summary of 2x2 systems. Non-homogeneous two-tank example. Introduction to Laplace Transforms. | ||
| Lecture 14 - Feb 28 | Introduction to Laplace transforms, solving ODEs using Laplace transforms. | ||
| Lecture 15 - Mar 2 | Solving ODEs using Laplace transforms, the Heaviside function and associated step and ramp functions. | ||
| Lecture 16 - Mar 7 | Step and ramp functions (continued), the Dirac delta function and its applications. | ||
| Lecture 17 - Mar 9 | Modeling using the delta function, convolution, transfer functions. | ||
| Lecture 18 - Mar 14 | Fourier series - method of undetermined coefficients, orthogonality, formulae. | ||
| Lecture 19 - Mar 16 | Fourier series for functions extended periodically, and extended periodically as even/odd functions. | ||
| Lecture 20 - Mar 23 | Fourier series (even, odd functions), using Fourier series to solve the Diffusion Equation | ||
| Lecture 21 - Mar 28 | This lecture was all on the document camera so no slides to post. I posted a set of jpgs on the course Facebook page instead. | ||
| Lecture 22 - Mar 30 | Solving the diffusion equation with homogeneous and non-homogeneous boundary conditions using Fourier series. | ||
| Lecture 23 - Apr 4 | Diffusion equation examples and summary |
