Midterm I Review
From Yossi Farjoun's Homepage
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.