gibson:teaching:fall-2011:math527
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gibson:teaching:fall-2011:math527 [2011/12/10 09:17] gibson [Exams] |
gibson:teaching:fall-2011:math527 [2011/12/13 17:03] (current) ewg5 [Exams] |
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| * K-Z: DeMeritt 112 | * K-Z: DeMeritt 112 | ||
| - | Here is a {{:gibson:teaching:fall-2011:math527:exams:practicefinal.pdf|Practice Final Exam}}. | + | You will be allowed a cheat sheet of any material you want, in your own handwriting, on one side of an 8.5 x 11 inch sheet of paper. I advise you to use the cheat sheet for Laplace transforms and general prescriptions about the classification and methods of solution of ODEs, rather than copying worked-out examples. |
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| + | The approximate format of the exam will be | ||
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| + | * one 1st order problem (linear, separable, exact) | ||
| + | * one or two 2nd order linear const coeff problems (homogeneous, judicious guessing, variation of parameters, reduction of order) (maybe two of these) | ||
| + | * one 2nd order linear const coeff problem (Laplace transforms) | ||
| + | * one series solution problem | ||
| + | * one linear system problem (matrix ODE) | ||
| + | * one conceptual problem | ||
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| + | Here is a {{:gibson:teaching:fall-2011:math527:exams:practicefinal.pdf|Practice Final Exam}}. And here are some brief solutions {{:gibson:teaching:fall-2011:math527:homework:math527-practicefinal-solns.pdf|Practice Final Exam Solutions}}. | ||
| + | Good luck! | ||
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| * [[http://en.wikipedia.org/wiki/Partial_derivative| Partial derivatives]]. A pretty good explanation by wikipedia. The important parts are the [[http://en.wikipedia.org/wiki/Partial_derivative#Introduction|Introduction]], the first third of the [[http://en.wikipedia.org/wiki/Partial_derivative#Basic_definition|Basic Definition]], and the [[http://en.wikipedia.org/wiki/Partial_derivative#Antiderivative_analogue|Antiderivative Analog]] | * [[http://en.wikipedia.org/wiki/Partial_derivative| Partial derivatives]]. A pretty good explanation by wikipedia. The important parts are the [[http://en.wikipedia.org/wiki/Partial_derivative#Introduction|Introduction]], the first third of the [[http://en.wikipedia.org/wiki/Partial_derivative#Basic_definition|Basic Definition]], and the [[http://en.wikipedia.org/wiki/Partial_derivative#Antiderivative_analogue|Antiderivative Analog]] | ||
| * [[http://www.wolframalpha.com|Wolfram Alpha]] and [[http://mathworld.wolfram.com | Wolfram Mathworld]]. Check your homework, deepen your knowledge. | * [[http://www.wolframalpha.com|Wolfram Alpha]] and [[http://mathworld.wolfram.com | Wolfram Mathworld]]. Check your homework, deepen your knowledge. | ||
| + | * The Tacoma Narrows Bridge collapse: [[http://www.youtube.com/watch?v=j-zczJXSxnw | video]] and [[http://www.ketchum.org/billah/Billah-Scanlan.pdf | explanation]]. Note that the explanation I gave in class yesterday was wrong, according to this paper! | ||
| + | * [[http://www.youtube.com/watch?v=ICMIDHdq6g4 | The eigenvectors of a compound pendulum.]] This movie shows a 3-part pendulum with initial conditions set to match three linearly independent eigenvectors of the linearized dynamics. Once the pendulum bobs are released, you can see that the motion of the system in comprised of a fixed shape (the displacement of the three bobs corresponding to the three components of an eigenvector) multiplied by an oscillation in time (the complex part of the eigenvalue) and a slow decay of the magnitude of oscillation (the real part of the eigenvalue). | ||
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gibson/teaching/fall-2011/math527.1323537436.txt.gz · Last modified: 2011/12/10 09:17 by gibson
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