MATH 2534: Calculus and Analytic Geometry III

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Subject:
Mathematics
Credit hours: 4 Lecture hours: 4 Lab hours: 0
PCS code (Local ID):
Baccalaureate/Transfer
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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.

Prerequisite(s)

MATH 2524 with a grade of C or better

IAI Number
M1 900-3
MTH 903
IAI Title
Calculus III
Calculus III
Topical Outline
  1. Parametric Equations
  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

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.