Difference between revisions of "Pre-lecture resources"
From UBCMATH WIKI
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| − | |Finding the inverse transform of | + | |[https://www.youtube.com/watch?v=M0JzOd-r3V4 Finding the inverse transform of 2/(s-3)]. |
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| + | |[ Inverting the result of a partial fraction decomposition]. | ||
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|[https://www.youtube.com/watch?v=HZTv4zCgEnA Partial fraction decomposition] by PatrickJMT | |[https://www.youtube.com/watch?v=HZTv4zCgEnA Partial fraction decomposition] by PatrickJMT | ||
Revision as of 17:21, 18 February 2016
These resources are pulled together from various online sources. I've tried to be as specific as possible to the problems in the pre-lecture assignments. However, many related videos can be found by the same authors as those posted below. If you find other videos (or other resources) that you found particularly useful, let me know.
Please send me requests for more suitable supplements when these do not prove sufficient.
| Pre-lecture assignment | link | |
|---|---|---|
| Week 1 - Thurs | Plugging in to check a solution | |
| Tuesday's lecture slides | ||
| Integrating factors by commutant (both the linked video and it's follow-up are useful) | ||
| Separating variables by commutant | ||
| Week 2 - Tues | Second order linear homogenous equation with constant coefficients by Kahn Academy. | |
| Salt water flowing in and out of a tank by commutant | ||
| Week 2 - Thurs | Section 2.3.1 of Notes on Diffy Qs | |
| Wronskian and linear independence | ||
| A review of complex numbers | ||
| Week 3 - Tues | Complex roots of the characteristic equations by PatrickJMT. | |
| Repeated Roots by Chris Tisdell or this one by SolveandGo on the same topic. | ||
| Week 3 - Thurs | Method of undetermined coefficients by Houston Math Prep. First 4 minutes (general idea) and examples at 12:15 and 23:00. | |
| Method of undetermined coefficients by Chris Tisdell. Start watching at 15:05 for help with Problem 1 part c. | ||
| Week 4 - Tues | Linear Combination of Sine and Cosine functions by SLCC Math Department. This video shows you how to convert from a sum of trig functions to a single cosine function. In the pre-lecture problems, you're asked to convert to a single sine function so you'll have to figure out how to modify the approach in the video appropriately - you just have to use a different trig identity but the rest is similar. | |
| Introduction to Vibrating Systems by Chris Tisdell. 1:07-4:45 for basic model. Forced vibrations starts at 15:50. | ||
| Week 4 - Thurs | Writing an equation from a sin/cos graph | |
| Damped oscillations | ||
| Week 5 - Tues | Converting a 2nd order ODE into a system of 1st order ODEs | |
| Calculating the determinant | ||
| From system of eqs to matrix | ||
| Week 5 - Thurs | Eigenvalues and eigenvectors by PatrickJMT. The example starts at 1:20. | |
| Week 6 - Tues | Refer to linear algebra resources (MATH 152 text or similar) | |
| Week 6 - Thurs | No pre-lecture assignment. | |
| Week 7 - Tues | System of ODEs with a repeated eigenvalue by Eric Cytrynbaum | |
| Week 7 - Thurs | No video. Note that a steady state solution must have zero derivative. | |
| Week 8 - Tues | Laplace transform playlist (including: Intro to Laplace transform, Transform of a sum of functions (linearity), and Transform of cos(2t)) | |
| Finding the inverse transform of 2/(s-3). | ||
| [ Inverting the result of a partial fraction decomposition]. | ||
| Partial fraction decomposition by PatrickJMT | ||
| Week 8 - Thurs | Short version of PJMT below skipping details of things covered previously. | |
| Laplace transform of the Heaviside function by Eric C | ||
| Writing a piecewise function in terms of Heavisides. | ||
| Solving non-homogeneous equations using Laplace transforms by PatrickJMT | ||
| A table of transforms by Paul Dawkins | ||
| Week 9 - Tues | Intro to delta functions by Kahn. This video is long but the first few minutes should serve as a good intro. | |
| Integrals with delta functions by MathPhysicsQuestions | ||
| Convolutions | ||
| Week 9 - Thurs | REPLACE: Fourier series made easy by Randell Heyman. - make one specific to ww question. | |
| Square wave example | ||
| Fourier series introduction by commutant. |
