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