# MATH242 Calculus III

## Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH242 Calculus III
II. Number of Credits
4 credits
III. Number of Instructional Minutes
3000
IV. Prerequisites
MATH141 (C or better)
Corequisites
None
V. Other Pertinent Information
At least 4 hours of testing are given.
VI. Catalog Course Description
This course is a continuation of Math 141. Topics for this course include: vectors and solid analytic geometry, surfaces, partial and directional derivatives, Lagrange multipliers, multiple integrals, cylindrical and spherical coordinates, line and surface integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
VII. Required Course Content and Direction
1. ### Course Learning Goals

Students will:

1. use vector-valued functions to parameterize curves and describe motion in space, find unit tangent and normal vectors, find tangential and normal components of acceleration, and find arc length and curvature;
2. find partial derivatives of functions of several variables, find directional derivatives and gradients, find tangent planes, and use Lagrange multipliers to find extrema;
3. evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates, and use multiple integrals to find areas, volumes, centers of mass, and surface areas; and
4. evaluate line and surface integrals, find work done in a vector field, use Green's Theorem, Stokes' Theorem, and the Divergence Theorem to evaluate integrals.
2. ### Planned Sequence of Topics and/or Learning Activities

1. Vectors in the Plane
2. Vectors in three Dimensions
3. The Dot Product
4. The Cross Product
5. Lines and Planes in Space
6. Surfaces
7. Vector Valued Functions and Limits
8. Derivatives and Integrals of Vector-Valued Functions
9. Velocity and Acceleration
10. Tangent Vectors and Normal Vectors
11. Arc Length and Curvature
12. Functions of Several Variables
13. Limits and Continuity
14. Partial Derivatives
15. Chain Rules
17. Differentials
18. Tangent Planes
19. Extrema of Functions of Several Variables
20. Applications of Extrema of Functions of Two Variables
21. Lagrange Multipliers
22. Iterated Integrals and Area
23. Double Integrals and Volume
24. Double Integrals in Polar Coordinates
25. Surface Area
26. Triple Integrals and Volume
27. Triple Integrals in Cylindrical and Spherical Coordinates
28. Center of Mass
29. Vector Fields
30. Line Integrals
31. Conservative Vector Fields
32. Green’s Theorem
33. Divergence and Curl
34. Surface Integrals
35. Stokes’ Theorem
36. Divergence Theorem
3. ### Assessment Methods for Course Learning Goals

The student applies mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment consists of open-ended questions reflecting theoretical and applied situations.
4. ### Reference, Resource, or Learning Materials to be used by Student:

Departmentally-selected textbook. Details provided by the instructor of each course section. See course syllabus.

Review/Approval Date - 1/99; Revised 4/06; Revised 09/2013; New Core 8/2015