The text for Math 19AB, *Calculus for Science. Mathematics, and Engineering*, is** Calculus, Early Transcendentals**, second edition, by Jon Rogawski.

Chapters 2–4, on limits and differentiation are covered in Math 19A; chapters 5–10, on integration and infinite series, are covered in Math 19B.

#### Chapter 2: Limits

2.1 Limits, Rates of Change, and Tangent Lines

2.2 Limits: A Numerical and Graphical Approach

2.3 Basic Limit Laws

2.4 Limits and Continuity

2.5 Evaluating Limits Algebraically

2.6 Trigonometric Limits

2.7 Limits at Infinity

2.8 Intermediate Value Theorem

#### Chapter 3: Differentiation

3.1 Definition of the Derivative

3.2 The Derivative as a Function

3.3 Product and Quotient Rules

3.4 Rates of Change

3.5 Higher Derivatives

3.6 Trigonometric Functions

3.7 The Chain Rule

3.8 Derivatives of Inverse Functions

3.9 Derivatives of General Exponential and Logarithmic Functions

3.10 Implicit Differentiation

3.11 Related Rates

#### Chapter 4: Applications of the Derivative

4.1 Linear Approximation and Applications

4.2 Extreme Values

4.3 The Mean Value Theorem and Monotonicity

4.4 The Shape of a Graph

4.5 L’Hopital’s Rule

4.6 Graph Sketching and Asymptotes

4.7 Applied Optimization

4.8 Newton’s Method

#### Chapter 5: The Integral

5.1 Approximating and Computing Area

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus, Part I

5.4 The Fundamental Theorem of Calculus, Part II

5.5 Net Change as the Integral of a Rate

5.6 Substitution Method

5.7 Further Transcendental Functions

5.8 Exponential Growth and Decay

#### Chapter 6: Applications of the Integral

6.1 Area Between Two Curves

6.2 Setting Up Integrals: Volume, Density, Average Value

6.3 Volumes of Revolution

6.4 The Method of Cylindrical Shells

6.5 Work and Energy

#### Chapter 7: Techniques of Integration

7.1 Integration by Parts

7.2 Trigonometric Integral

7.3 Trigonometric Substitution

7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

7.5 The Method of Partial Fractions

7.6 Improper Integrals

7.7 Probability and Integration

7.8 Numerical Integration

#### Chapter 8: Further Applications of the Integral and Taylor Polynomials

8.1 Arc Length and Surface Area

8.2 Fluid Pressure and Force

8.3 Center of Mass

8.4 Taylor Polynomials

#### Chapter 10: Infinite Series

10.1 Sequences

10.2 Summing an Infinite Series

10.3 Convergence of Series with Positive Terms

10.4 Absolute and Conditional Convergence

10.5 The Ratio and Root Tests

10.6 Power Series

10.7 Taylor Series