CARNEGIE MELLON UNIVERSITY
DEPARTMENT OF MATHEMATICAL SCIENCES
21-256 Review Exam 4 (Final Exam), Spring 2004

Your final exam will consist of 4 parts, clearly identified on your exam. Each part will consist of 5 questions. The exam will be on Monday, May 3rd, 5:30-8:30 P.M., room DH2210. Please see course web site for conflict policy and procedure. We will review on Wed. April 28th for part 4, and Friday April 30th for all parts.

1. Part 1. This will consist of material from exam 1.
   1. Expect 1 question on sequences,
   2. 3 questions on testing series,
   3. and 1 question on Power Seies (Interval of Convergence, Radius of Convergence, Representation of Functions by Power Series) and Taylor Series.
   Please examine the review sheet for exam 1 for a complete description of these topics.

2. Part 2. This will consist of material from exam 2.
   1. Expect 1 question on linear independence, or span
   2. expect 1 question on determinants
   3. expect 1 question on solving a system of linear equations
   4. and 2 questions on basic geometry: lines, planes, dot product, and cross product.
   Please examine the review sheet for exam 2 for a complete description of these topics.

3. Part 3. This will consist of material from exam 3.
   1. Expect 1 question on determining limits of functions of 2 variables,
   2. expect 1 question on partial derivatives, and verifying a PDE
   3. expect 1 question on determining a tangent plane, and computing or using a linear approximation,
   4. expect 1 question on the chain rule,
   5. and expect 1 question on directional derivatives and the gradient vector.
   Please examine the review sheet for exam 3 for a complete description of these topics.

4. Part 4. This will consist of material covered since exam 3. Specifically, sections 14.7 and 14.8 of Stewart, and sections 5.5 and 5.6 of Walker.
   1. Expect 1 question on unconstrained optimization, function of 2 variables, as in section 14.7,
   2. expect 1 question on unconstrained optimization, function of more than 2 variables, as in section 5.6
   3. expect 1 question on linear least squares approximation, as in section 5.5 linear approximation,
   4. expect 1 question on constrained optimization, function of 2 variables on a closed bounded domain, as in section 14.7 (27-34,37-41). Note that one may use Lagrange multipliers if appropriate on the boundary,
   5. and expect 1 question on constrained optimization, Lagrange multipliers, as in section 14.8.