List of Topics


The following is a list of topics that will be covered in this course along with the chapter and section numbers. The chapter and section numbers are taken from the textbook "Vector Calculus" (5th Edition), by J. Marsden and A. Tromba. There will also be several concepts presented that are not in the book.

CHAPTER 4. VECTOR-VALUED FUNCTIONS

4.1 Acceleration and Newton's second Law
4.2 Arc Length
4.3 Vector fields
4.4 Divergence and curl

CHAPTER 5. DOUBLE AND TRIPLE INTEGRALS

5.2 The double integral over a rectangle
5.3 The double integral over more general regions
5.4 Changing the order of integration
5.6 The triple integral

CHAPTER 6. THE CHANGE OF VARIABLES FORUMLA AND APPLICATIONS OF INTEGRATION

6.1 The geometry of maps from R2 to R2
6.2 The change of variables theorem
6.3 Applications of double and triple integrals

CHAPTER 7. INTEGRALS OVER PATHS AND SURFACES

7.1 The path integral
7.2 Line integral
7.3 Parametrized surfaces
7.4 Area of surface
7.5 Integrals of scalar functions over surface
7.6 Surface integrals of vector functions

CHAPTER 8. THE INTEGRAL THEOREMS OF VECTOR ANALYSIS

8.1 Green's theorem
8.2 Stoke's theorem
8.3 Conservative fields
8.4 Gauss's theorem
8.5 Applications to physics, engineering, and differential equations

ADDITIONAL TOPICS

1. Fourier series
2. Laplace transforms