Multivariable Calculus

Calculus in 3-Space, Partial Differentiation, Multiple Integration, and Vector Calculus

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Description

This is a complete course in Multivariable calculus. Multivariable calculus is an extension of single variable calculus to calculus with functions of two or more variables. It is expected that anyone taking this course has already knows the basics from single variable calculus: limits and continuity, differentiation and integration.

In this course you will learn how to perform calculus on functions of two or more variables, as well as vector-valued functions. In particular, the topics covered include the basics of three dimensional space and vectors,  vector-valued functions including the calculus of vector-valued functions (limits, differentiation, and integration), differentiation of functions of two or more variables, integration of functions of two or more variables, and vector calculus.


Single variable Calculus is a prerequisite for this course.


Here is a complete list of the topics that will be covered:

    Three-dimensional Space and Vectors

  1. Rectangular Coordinates in 3-space

  2. Vectors

  3. Dot Product

  4. Cross Product

  5. Equations of Lines

  6. Equations of Planes

  7. Quadric Surfaces

  8. Vector-valued Functions

  9. Arc Length and the TNB-Frame

  10. Curvature


    Functions of Multiple Variables and Partial Differentiation

  11. Functions of Two or More Variables

  12. Limits and Continuity

  13. Partial Derivatives

  14. Differentiability

  15. Chain Rule

  16. Directional Derivatives

  17. Maxima and Minima of Functions of Two Variables


    Multiple Integrals

  18. Double Integrals

  19. Double Integrals over Nonrectangular Regions

  20. Double Integrals over Polar Regions

  21. Triple Integrals

  22. Cylindrical and Spherical Coordinates

  23. Triple Integrals in Cylindrical and Spherical Coordinates


    Vector Calculus

  24. Vector Fields

  25. Line Integrals

  26. Independence of Path

  27. Green’s Theorem

  28. Parametric Surfaces

  29. Surface Integrals

  30. Orientable Surfaces and Flux

  31. Stoke’s Theorem

  32. Divergence Theorem

What You Will Learn!

  • Calculus in 3-space
  • Partial Differentiation
  • Multiple Integration
  • Vector Calculus

Who Should Attend!

  • Students that want to learn Multivariable Calculus and Vector Analysis