Midterm I Review
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(New page: == Mid Term I Review == To prepare for this midterm I can only remind you of the topics that we have covered and suggest ways in which you should prepare. Methods: #Make sure you know ho...) |
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− | #You should totally grok the calculus review part of the course. While there will not be a question specifically asking about this part, you can bet that many problems will have this material as required skill. | + | #You should totally grok the calculus review part of the course. While there will not be a question specifically asking about this part, you can bet that many problems will have this material as required skill. Example problem: |
+ | <math>\sum_{i=1}^\N \frac1i</math> can be bounded using an an appropriate integral of a smooth function. Draw the relevant picture and find the bounds (plural because I want 2 bounds, one from above and one from below). | ||
+ | Another example: | ||
+ | Explain a derivation of the sum <math> \sum_{i=0}^N \lambda^i</math>. | ||
#Taylor Series, with/without remainder term, go over all our derivations of error for various expressions. Example for question: Calculate the error in the approximation <math> f'(x) \approx \frac{f(x+h)-f(x-h)}{2h} + a h^p </math>. | #Taylor Series, with/without remainder term, go over all our derivations of error for various expressions. Example for question: Calculate the error in the approximation <math> f'(x) \approx \frac{f(x+h)-f(x-h)}{2h} + a h^p </math>. | ||
+ | #Fixed point methods. You should understand the conditions for convergence and the methods of proof. You should remember the definition of order of convergence. |
Revision as of 22:01, 4 March 2009
Mid Term I Review
To prepare for this midterm I can only remind you of the topics that we have covered and suggest ways in which you should prepare.
Methods:
- Make sure you know how to do all the homework problems given to date.
- Make sure you know the solution to the quiz.
- Read the relevant chapters in the reader.
- Discuss the material with your peers. I highly recommend this as a method of studying.
Material:
- You should totally grok the calculus review part of the course. While there will not be a question specifically asking about this part, you can bet that many problems will have this material as required skill. Example problem:
can be bounded using an an appropriate integral of a smooth function. Draw the relevant picture and find the bounds (plural because I want 2 bounds, one from above and one from below).
Another example:
Explain a derivation of the sum .
- Taylor Series, with/without remainder term, go over all our derivations of error for various expressions. Example for question: Calculate the error in the approximation .
- Fixed point methods. You should understand the conditions for convergence and the methods of proof. You should remember the definition of order of convergence.