Math 20C Lecture Examples

Text: Calculus, Early Transcendentals by Rogawski

(There are no lecture examples for Sections 13.4, 13.5, or 13.6.)

CHAPTER 12. VECTOR GEOMETRY
Section 12.1. Vectors in the plane
Section 12.2. Vectors in three dimensions
Section 12.3. The dot product
Section 12.4. The cross product
Section 12.5. Planes in three space

CHAPTER 13. CALCULUS OF VECTOR-VALUED FUNCTIONS
Sections 13.1 and 11.1. Vector-valued functions
Sections 13.2, 13.3, and 11.2. Calculus of vector-valued functions

CHAPTER 14. DIFFERENTIATION IN SEVERAL VARIABLES
Section 14.1, Part 1. Functions of two variables
Section 14.1, Part 2. Functions of three or more variables
Sections 14.2 and 14.3. Limits and partial derivatives
Section 14.4. Linear approximation and tangent planes
Section 14.5. The gradient and directional derivatives
Section 14.6. The Chain Rule
Section 14.7, Part 1. The First-Derivative Test
Section 14.7, Part 2. The Second-Derivative Test
Section 14.8. Lagrange multipliers

CHAPTER 15. MULTIPLE INTEGRATION
Sections 15.1 and 15.2. Double integrals
Section 15.3. Triple integrals
Section 15.4. Integrals in polar and cylindrical coordinates