Math 20B Lecture Examples

Text: Calculus, Early Transcendentals by Rogawski

(There are no lecture examples for Sections 6.4, 6.5, 7.4, or 7.5.)

CHAPTER 5. THE INTEGRAL
Sections 5.1 through 5.5. Review of the definition of the integral and the Fundamental Theorem
Section 5.6. Subnstitution Method
Section 5.7. Further transcendental functions

CHAPTER 6. APPLICATIONS OF THE INTEGRAL
Section 6.1. Area between two curves
Section 6.2. Volume, density, and average values
Section 6.3. Volumes of revolution

CHAPTER 7. TECHNIQUES OF INTEGRATION
Section 7.1. Numerical integration
Section 7.2. Integration by parts
Section 7.3. Trigonometric integrals
Section 7.6. The method of partial fractions
Section 7.7. Improper integrals

CHAPTER 9. INTRODUCTION TO DIFFERENTIAL EQUATIONS
Sections 9.1 and 9.2, Part 1. Solving differential equations
Sections 9.1 and 9.2, Part 2. Solving differential equations

CHAPTER 10. INFINITE SERIES
Section 10.1. Sequences
Section 10.2. Summing an infinite series
Section 10.3. Convergence of series with positive terms
Section 10.4. Absolute and conditional convergence
Section 10.5. The Ratio Test
Sections 10.6 and 10.7. Power and Taylor series

CHAPTER 11. POLAR COORDINATES
Section 11.3. Polar coordinates
Section 11.4. Area and arc length in polar coordinates