Course Abstract Details

MATH-205, Multivariable Calculus

Credits: 4

Course Description

MATH-205, Multivariable Calculus, continues MATH-136 with vectors and analytic geometry in three dimensions, partial derivatives, multiple integrals, line and surface integrals, and vector field theory. Students will be required to use a graphing calculator and significant mathematical software such as Mathematica, Maple, or MATLAB throughout the course. See Mathematics Department web site for details. Prerequisite: MATH-136 with a "C" grade or better. Five hours lecture each week. Four credits. Four billable hours. Offered every Fall Term. GENERAL EDUCATION

Course Objectives and Grading Information

MAJOR COURSE OBJECTIVES: Upon completing this course the student should be able to:

1. Perform vector operations with dot and cross products. (GE3, PG1, PG4)

2. Graph lines and surfaces in 3-dimensional space. (GE3, PG1, PG4)

3. Compute derivatives and integrals for vector functions. (GE3, PG1, PG4)

4. Analyze torsion and curvature. (GE2, GE3, PG1, PG3, PG4)

5. Compute partial derivatives for multi-variable functions. (GE3, PG1, PG4)

6. Compute directional derivatives and gradients. (GE3, PG1, PG4)

7. Apply maximization techniques to multi-variable functions. (GE2, GE3, PG1, PG3, PG4)

8. Compute multiple integrals. (GE3, PG1, PG4)

9. Apply multiple integration to physical problems. (GE2, GE3, PG1, PG3, PG4)

10. Derive and apply Green's and Stoke's Theorems. (GE2, GE3, PG1, PG3, PG4)

11. Apply vector analysis to potential and conservation of energy problems. (GE2, GE3, PG1, PG3, PG4)

12. Set-up and solve application problems using technology, such as graphing calculators and mathematical software. (GE1, GE2, GE3, PG1, PG2, PG3, PG4)

Larson, R. and Farber, B. Calculus, 9th edition. Brooks/Cole, Cengage Learning, 2010. [ISBN-13: 978-0-547-16702-2]

Learning Goals

The abbreviations in parentheses represent Learning Goals which have been identified for this course and program of study:

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