gibson:teaching:fall-2015:math527:finalexamnotes
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gibson:teaching:fall-2015:math527:finalexamnotes [2015/12/10 12:21] gibson created |
gibson:teaching:fall-2015:math527:finalexamnotes [2015/12/11 03:39] (current) gibson |
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| The final exam takes place Wed 12/16 8:00am-10:0am in Horton 4. You must take the final exam at the scheduled time. No early exams or make-up exams will be offered. | The final exam takes place Wed 12/16 8:00am-10:0am in Horton 4. You must take the final exam at the scheduled time. No early exams or make-up exams will be offered. | ||
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| + | The final exam is cumulative, including all topics covered in the course **except power series**. Think of the final exam as 2/3 (exam1 + exam2 + exam3 + systems of ODEs). There will be eight or so problems on the exam. You will have to decide which method to use for which problem. | ||
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| + | You are allowed a cheat sheet of one 8 1/2 x 11 inch paper, both sides. You can put anything you want on the cheat sheet. You do not have to turn the cheat sheet in. | ||
| The outline of topics is as follows | The outline of topics is as follows | ||
| Line 9: | Line 13: | ||
| * 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 26: | 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.1449778892.txt.gz · Last modified: 2015/12/10 12:21 by gibson
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