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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 1. THE GEOMETRY OF EUCLIDEAN SPACE

1.1 Vectors in two and three dimensional space

Section 1.1 Slides

1.2 The inner product, length, and distance

Section 1.2 Slides

1.3 Matrices, determinants, and cross product

Section 1.3 Slides

1.4 Cylindrical and spherical coordinates

Section 1.4 Slides

1.5 n-dimensional Euclidean space

Section 1.5 Slides

Section 1.1 Slides

1.2 The inner product, length, and distance

Section 1.2 Slides

1.3 Matrices, determinants, and cross product

Section 1.3 Slides

1.4 Cylindrical and spherical coordinates

Section 1.4 Slides

1.5 n-dimensional Euclidean space

Section 1.5 Slides

CHAPTER 2. DIFFERENTIATION

2.1 The geometry of real-valued functions

Section 2.1 Slides

2.2 Limits and continuity

Section 2.2 Slides

2.3 Differentiation

Section 2.3 Slides

2.4 Introduction to paths

Section 2.4 Slides

2.5 Properties of the derivative

Section 2.5 Slides

2.6 Gradients and directional derivatives

Section 2.6 Slides

Section 2.1 Slides

2.2 Limits and continuity

Section 2.2 Slides

2.3 Differentiation

Section 2.3 Slides

2.4 Introduction to paths

Section 2.4 Slides

2.5 Properties of the derivative

Section 2.5 Slides

2.6 Gradients and directional derivatives

Section 2.6 Slides

CHAPTER 3. HIGHER-ORDER DERIVATIVES; MAXIMA AND MINIMA

3.1 Iterated partial derivatives

Section 3.1 Slides

3.2 Taylor's theorem

Section 3.2 Slides

3.3 Extrema of real-valued functions

Section 3.3 Slides

3.4 Constrained extrema and Lagrange multipliers

Section 3.4 Slides

Section 3.1 Slides

3.2 Taylor's theorem

Section 3.2 Slides

3.3 Extrema of real-valued functions

Section 3.3 Slides

3.4 Constrained extrema and Lagrange multipliers

Section 3.4 Slides

CHAPTER 4. VECTOR-VALUED FUNCTIONS

4.1 Acceleration and Newton's second Law

Section 4.1 Slides

C. Cube paper

4.2 Arc Length

Section 4.2 Slides

4.3 Vector fields

Section 4.3 Slides

4.4 Divergence and curl

Section 4.4 Slides

Section 4.1 Slides

C. Cube paper

4.2 Arc Length

Section 4.2 Slides

4.3 Vector fields

Section 4.3 Slides

4.4 Divergence and curl

Section 4.4 Slides

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

5.3 The double integral over more general regions

5.4 Changing the order of integration

5.6 The triple integral

Exam I

100 pts Friday Oct. 10

Exam II

100 pts Friday Nov. 21

Final Exam

200 pts Friday Dec. 12

8:00 am - 11:00 am

Homework 100 pts

Project 100 pts

Total Points 600 pts

A..100%-90%

B..89%-80%

C..79%-70%

D..69%-60%

F..59%-0%

+/- Grades may be given for borderline percentages.

To compute your grade, (your total points)/600 * 100.