The Final Exam will be in the usual classroom on Friday, December 16, 2011, starting at 8:00 a. m. You may work until 10:15, if you wish. The current draft has 75 points.

As usual, there will be a mix of problems, some basic or straightforward, others intended to be more difficult. Grades in the 90% range are certainly not required to be doing A work. The emphasis will be on material since Exam III, and some other topics including those listed below.

Calculators are not needed, although you may, if you really want to, use a non-graphics simple arithmetic calculator without even trig functions, but no mechanical or electronic device more sophisticated that this (including iPods, earpieces, etc.). I will provide blank paper on which you can write your answers. Please put your name on your exam paper itself and all pages of your solutions, and hand them all in together, although without any pages of scratch work that is not to be graded.

Definitions of important concepts and statements of major theorems are (of course) perfectly reasonable questions, and although you do not need to know them word-for-word, you should be able to write down a coherent and accurate definition of any major concept or term, and a reasonably accurate statement of any of the major theorems.

The following topics are very likely to appear, although the exam is not limited to them:

1. The Fundamental Theorem of Calculus (it is, after all, fundamental), the Mean Value Theorem. Statements and applications.
2. Our definition of the rate of change f '(a) using the error of linear approximation.
3. Riemann sums and the definition of the integral.
4. Techniques of integration, including integration by parts, partial fractions, integrals involving trig functions, inverse trig substitutions.
5. l'Hôpital's rule.
6. Improper integrals.
7. Simpson's Rule.
8. Length of curves, the length element ds, surface area.

The exam will give you any unusual trig identities needed for calculations, or you can ask me during the exam. You are expected to be able to compute ds, however, and know and understand the formula in Simpson's Rule (but not the error formula). The following do not appear on this exam: inverse hyperbolic trig functions, derivation of the areas under the parabolic segments in Simpson's Rule, error estimate for Simpson's Rule, detailed material from earlier in the course such as inductive verification of summation formulas, direct calculation of integrals using the definition, calculations of volume.

Previous exams I have written for regular and honors calculus classes are available at their course pages on my website. Links to those pages are listed at course pages page).