Lecture slides/2015W2
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 MATH 256 and differential equations. Classifying DEs, basic DE terminology. Method of integrating factors. | ||
| Lecture 2 - Jan 5 | Integrating factors. The general structure of solutions to linear equations (homogeneous + particular) | ||
| Lecture 3 - Jan 10 | Structure of solutions, separable equations, modelling tanks with inflow/outflow. | ||
| Lecture 4 - Jan 12 | General solution, independence and the Wronskian. Homogenous second order linear DEs with constant coefficients. Complex number review. | ||
| Lecture 5 | Cancelled due to illness. | ||
| Lecture 6 - Jan 19 | A,B | A,B | First half (A):Euler's formula, complex roots to the characteristic equation., second half (B): Repeated roots. Nonhomogeneous equations. Analogy between the structure of matrix equations and linear ODEs. |
| Lecture 7 - Jan 24 | Method of Undetermined Coefficients. | ||
| Lecture 8 - Jan 26 | Mass-spring systems, natural frequency, forced mass-spring systems, resonance. | ||
| Midterm 1 - Jan 31 | |||
| Lecture 9 - Feb 2 | A,B,C | (A):Intro to systems of equations, vector/direction field in the phase plane., (B): Eigenvalues and eigenvector calculations, (C): Using eigenvalues and eigenvectors to solve systems of ODEs. | |
| Lecture 10 - Feb 7 | The shape of solutions in the phase plane. | ||
| Lecture 11 - Feb 9 | System of equations with complex eigenvalues. | ||
| Lecture 12 - Feb 21 | Systems of ODEs (2x2) - complex eigenvalues (how to determine direction of rotation), repeated eigenvalues, summary. | ||
| Lecture 13 - Feb 23 | Nonhomogeneous systems of ODEs. Introduction to Laplace transforms. | ||
| Lecture 14 - Feb 28 | Introduction to Laplace transforms. Solving second order linear constant coefficient ODEs - complex case (completing the square). | ||
| Lecture 15 - Mar 2 | Solving ODEs using Laplace transforms. Heaviside and other step functions. | ||
| Lecture 16 - Mar 7 | Piecewise linear forcing functions. | ||
| Lecture 17 - Mar 9 | Introduction to the Dirac delta function. Modelling with the delta function. | ||
| Midterm 2 - Mar 14 | |||
| Lecture 18 - Mar 16 | Convolution, transfer function, impulse response. Method of Undetermined Coefficients for periodic forcing (Fourier Series intro). | ||
| Lecture 19 - Mar 21 | Introduction to Fourier series ideas (dot product for functions, setup for method of undetermined coefficients, heat/diffusion equation). | ||
| Lecture 20 - Mar 23 | pdf, FS formula | Fourier series. Derivation of the Diffusion equation. Solving the Diffusion equation using Fourier series. | |
| Lecture 21 - Mar 28 | Using Fourier series to solve the Diffusion equation. | ||
| Lecture 22 - Mar 30 | Using Fourier series to solve the Diffusion equation (nonhomogeneous BCs). | ||
| Lecture 23 - Apr 4 | DIffusion equation, non-homogeneous BCs - examples and summary. |
