Preparation for the Final
The test will be available at 8:30 a.m. from my office on Wednesday morning.
It will be about two hours long.
I will be in my office from 8:30 a.m. to 9:30 a.m., and from 10:45 a.m. to noon,
in case you have questions before you start the test, or during the test.
Calculators will be allowed, and mathematica for checking your answers, but as usual you should show all of your work for full credit. You may take the test on the second floor of the library, or in a classroom in Palmer Hall.
Calculus Part:
| Logarithm Function | Solve a decay or growth problem, chap 25, 26 |
| Volumes | Set up integrals for volumes of solids of revolution or otherwise |
| Integration | Substitution, Integration by parts, Trig Substitution. On the exam question will have to decide for yourself which method to use. |
| Improper Integrals | Comparison Test |
| Differential Equations | Solve by separating the variables, or estimate the solution using direction fields. Be able to calculate the equilibrium solutions for a predator prey system. |
| Series | All the tests on the handout, except for the limit
comparison test. On the exam question will have to decide for
yourself which method to use. Also, calculate Taylor series terms |
| Parametric Curves | Find areas, arclengths, and derivatives using parametric curves |
| Newton's Method | Be able to calculate the sequence of iterates, and determine which is the appropriate basin of attraction |
Chaos Part
| From Chapter Three: | Be able to compute the fractal dimension of fractals. Understand the method by which natural fractal dimension is calculated Know some of the application of natural fractal dimension |
| From Chapter Seven: | Understand what the Mandelbrot set is, and be able to define it. Understand what a Julia set is, and be able to define one. Understand the connections with the logistic map and the bifurcation diagram. Be able to do complex arithmetic |
| From Chapter Eight: | Understand Newton's method. Be able to determine basins of attraction. |
| Studying infinity: | Understand the idea of countable and uncountable infinities. |