FINAL EXAM:

Monday, May 11, 9:45-11:45

(last updated Monday, May 04, 2009)

    1. As usual, only provided calculator allowed.
    2. As usual, you may bring in one page of notes (both sides OK this time)
    3. There might be a page of MULTIPLE CHOICE problems
    4. Food and Drink is OK if it is stable (don't spill a 40oz coffee) and quiet (no loud cellophane wrappers)
    5. I will give you a copy of the table of integrals you've seen before

FINAL EXAM DETAILS:

Chapter 8 (Integrals)

You should absolutely expect a problem of each of the following types:

  1. Integration by parts
  2. Products or powers of trig functions
  3. Trig substitutions
  4. An improper integral
  5. Something involving partial fractions

For the last, I won't give you a very difficult partial fractions problem, but I will either give you a complete integral on which you need to do a fairly simple partial fractions decomposition, or I will give you a rational function and ask you to do the partial fractions decomposition

Chapter 10 (Series)

You should expect problems of each of the following types:

  1. At least 2 problems where you test a positive series for convergence
  2. A test for absolute/conditional convergence
  3. A radius/interval of convergence problem
  4. A remainder estimate for an alternating series
  5. Computing the actual sum of a series (either because it is geometric, telescoping, or the Taylor series at a known value)
  6. A Taylor polynomial `from scratch' (ie, you'll need to take the derivative a few times and correctly use the formula). A small part ofthe prioblem might include estimating the error.
  7. Problems of the 10.7 type (termwise derivatives/integrals of series, using series for limits, etc)

Some of these problems might be combined; for example, to approximate 5^0.2 to 3 decimal places, you might first get a series for (1+x)^0.2 (Binomial series), realize that it alternates when you plug in x=4, and so use an alternating series remainder estimate to decide how many digits to take.

Chapter 9,15 (ODEs)

There will be problems from among the following:

  1. 1st order ODE solvable by separation of variables
  2. 1st order nonhomogeneous ODE
  3. 2nd order homogeneous ODE with constant coefficients (possibly extra credit for a nonhomogeneous problem)
  4. A series solution for an ODE

These might be combined. You will also be expected to be identify the degree of an ODE, whether it is "homogeneous", etc.