gibson:teaching:fall-2015:math527:finalexamnotes
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gibson:teaching:fall-2015:math527:finalexamnotes [2015/12/10 12:25] gibson |
gibson:teaching:fall-2015:math527:finalexamnotes [2015/12/11 03:39] (current) gibson |
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| * exact | * exact | ||
| * 1st order linear | * 1st order linear | ||
| + | * substitutions: Bernoulli, homogeneous*, and $Ax + By + C$ | ||
| + | |||
| * 2nd and higher-order equations | * 2nd and higher-order equations | ||
| + | * reduction of order | ||
| * homogeneous constant coefficient ($y=e^{\lambda t}$ is your friend) | * homogeneous constant coefficient ($y=e^{\lambda t}$ is your friend) | ||
| * judicious guessing | * judicious guessing | ||
| * variation of parameters | * variation of parameters | ||
| + | |||
| * Laplace transforms | * Laplace transforms | ||
| * definitions, properties, and transforms & inverses of simple functions | * definitions, properties, and transforms & inverses of simple functions | ||
| * s-translation, t-translation | * s-translation, t-translation | ||
| * Heaviside and Dirac delta functions | * Heaviside and Dirac delta functions | ||
| - | * Systems of equations | + | |
| + | * Systems of linear equations | ||
| * matrices, vectors, $Ax=b$ problems, and determinants | * matrices, vectors, $Ax=b$ problems, and determinants | ||
| - | * the eigenvalue problem, how it arises from the ODE $x' = Ax$ | + | * the eigenvalue problem, how it arises from the ODE $x' = Ax$ and ansatz $x(t) = v e^{\lambda t}$ |
| * how to solve systems of ODEs with | * how to solve systems of ODEs with | ||
| * real eigenvalues, distinct | * real eigenvalues, distinct | ||
| Line 30: | Line 35: | ||
| * phase portraits | * phase portraits | ||
| + | Several of the teaching assistants have final exams for their graduate course Wednesday afternoon and Thursday. We do not expect to start grading the final exam until Friday morning. | ||
gibson/teaching/fall-2015/math527/finalexamnotes.1449779127.txt.gz · Last modified: 2015/12/10 12:25 by gibson
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