Appendix IB. Course Syllabi

Math 265 Calculus III

1. Course Name: Math 265. Calculus III.

2. Catalog Description (1999 — 2001 Bulletin)
4 credits; Multiple integrals, vector fields and vector integrals, sequences and series.

3. Prerequisites:
Grade of C— or better in 166 or 166H.

4. Textbook / Materials:
Johnston and Mathews. Calculus for Engineering and the Sciences. (custom edition).

5. Course Learning Objectives:

1. Develop problem solving ability and flexibility in using the tools of multivariable and vector calculus and series in problem solving. This includes appropriate use of technology and the ability to use graphical, numerical, and symbolic techniques in investigating problems.
2. Know and be able to discuss the definition of differentiabiality for functions with domain and range in R,, R², R³. Be able to write the Jacobian matrix for such functions.
3. Understand the statement of the Chain rule for vector-valued functions of several variables and use the chain rule to calculate derivatives and Jacobian matrices for such functions.
4. Be able to model and solve optimization problems for functions of several variables. This includes optimization with constraints and the use of Lagrange multipliers.
5. Understand the definition of multiple integral for real-valued functions of two and three variables. Be able to set up an iterated integral for evaluation of a multiple integral and be able to evaluate iterated integrals.
6. Know the definition of linear function and be able to show that a function is linear (or that it is not.)
7. Be able to work with matrices, including representation of linear functions and applications involving determinants.
8. Understand and be able to work with lines and planes in three dimensions.
9. Be able to construct Taylor polynomials for simple elementary functions.
10. Understand the meaning and importance of error when dealing with approximations, and be able to work with and provide error estimates for approximation with Taylor polynomials.
11. Determine intervals for convergence for power series and construct power series representations for simple elementary functions.
12. Be able to use comparison, integral, ration, and / or alternating series test to analyze convergence / divergence of series of constants.

6. Topics Covered:
Functions of several variables, gradients, multiple integrals, line and surface integrals, infinite series and sequences.

7. Class / Laboratory Schedule: 4 hrs lecture per week

8. Contribution of Course to Meeting the Professional Component:

9. Relationship of Course to Program Learning Outcomes and Program Educational Objectives:

10. Person Preparing Document:
Ann Dieterich — College of Engineering Assessment Resource Coordinator 5/1/ 00
Mathematics Contact — Jim Peake