Course Description
This course is an introduction to vector calculus as well as application of differentiation and integration to functions of several variables. Topics include partial derivatives, directional derivatives, motion in space, line integrals, and multiple integration. IAI: MTH 903 Mathematics. IAI: M1 900-3.
Prerequisite(s)
MATH 2524 with a grade of C or better - Must be completed prior to taking this course.
At the end of this course, students will be able to:
- Use the mathematics of vectors to find directed derivatives, arc length, and curvature, and apply them to applications in physics.
- Solve problems involving partial derivatives using, but not limited to, chain rules and differentials
- Evaluate multiple integrals in rectangular, polar, and spherical coordinates
- Use line integrals in applications in areas of vector fields.
Topical Outline
1. Parametric Equations
2. Polar Coordinate System
3. Calculus of Polar Functions
4. Conic Sections
2. Polar Coordinate System
3. Calculus of Polar Functions
4. Conic Sections
5. Lines and Curves in Space
6. Calculus of Vector-Valued Functions
7. Motion in Space
8. Lengths of Curves
9. Curvature and Normal Vectors
10. Planes and Surfaces
11. Graphs and Level Curves
12. Limits and Continuity
13. Partial Derivatives
14. The Chain Rule
15. Directional Derivatives and the Gradient
16. Maximum/Minimum Problems
17. Lagrange Multipliers
18. Double Integrals over Rectangular Regions
19. Double Integrals over General Regions
20. Double Integrals in Polar Coordinates
21. Triple Integrals
22. Triple Integrals in Cylindrical and Spherical Coordinates
23. Integrals in Mass Calculations
24. Vector Fields
25. Line Integrals
26. Conservative Vector Fields
27. Green's Theorem
28. Divergence and Curl
29. Surface Integrals
30. Stokes' Theorem
31. Divergence Theorem