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Mathematics 2433-001H - Honors Calculus III - Fall 2007

Information about Final Exam

The Final Exam will be in the usual classroom on Tuesday, December 11 at 1:30 p. m. You may work until 3:45 p. m if you need the extra time.

Grades will be posted on our website as soon as they are ready, but since I will be traveling it will probably not be until some time the following Monday or Tuesday. You may pick up your final exam any time during the next year; after one year they will be discarded.

The Final Exam will be worth 80 points, plus a 6-point bonus problem. Here is an approximate breakdown of the sections of the book that will be directly covered:

11.3 5
12.2 5
12.4 14
12.6 2
12.8 13
12.10 6
13.3 4
13.4 6
13.5 5
13.7 3
14.1 2
14.2 6
14.3 5
14.4 4
Total 80


The following topics will definitely be covered, although the exam in not limited to these topics:
  1. Graphing polar curves of the form r = f (\theta)
  2. Series and convergence, conditional convergence, examples.
  3. The Comparison Test and the Limit Comparison Test.
  4. Power series: center, radius of convergence, analyzing the convergence behavior of a power series, examples.
  5. Taylor series: the general form of a Taylor series.
  6. Dot and cross product of vectors.
  7. Curves as vector-valued functions: velocity, acceleration, unit tangent and normals, curvature.

You will need to know the general form of the Taylor series, but not the formulas for analyzing the error of approximation by Taylor polynomials. You will need to know how to compute dot and cross products. You should be able to compute the unit tangent vector T(t) and the unit normal vector N(t) to a curve, and should know the definition of curvature, but you do not need to memorize the formulas for curvature or the tangential and normal components of the acceleration.

The following topics will not appear, at least, not explicitly: finding parameterizations of curves defined by geometric constructions, calculus of polar curves, areas and lengths in polar coordinates, the epsilon-delta definition of convergence of a sequence, Newton's method, remainder estimate for the integral test, alternating series estimation theorem, multiplication and division of power series, error of approximation by Taylor polynomials, binomial series, Law of Cosines, intersecting versus skew lines, quadric surfaces, cylindrical coordinates, rotation of coordinates and dimension of the space of rotations, Frenet formulas.

Final exams that I wrote for this course in previous semesters can be found on their course pages (links are on the course pages page).