# Calculus I with Integrated Precalculus

## First EditionLaura Taalman

©2014
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*Calculus I with Integrated Precalculus* weaves together calculus with precalculus and algebra in a manner suitable for math and science majors. You don't have to retake a precalculus course.

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Learn More## Table of Contents

**I Differential Calculus**

**0 Functions and Precalculus**

0.1 Numbers and Sets

0.2 Equations

0.3 Inequalities

0.4 Functions and Graphs

0.5 A Basic Library of Functions

0.6 Operations, Transformations, and Inverses

0.7 Logic and Mathematical Thinking**Chapter Review, Self-Test, and Capstones*

**1 Limits**

1.1 An Intuitive Introduction to Limits

1.2 Formal Definition of a Limit

1.3 Delta-Epsilon Proofs*

1.4 Continuity and Its Consequences

1.5 Limit Rules and Calculating Basic Limits

1.6 Infinite Limits and Indeterminate Forms*Chapter Review, Self-Test, and Capstones*

**2 Derivatives**

2.1 An Intuitive Introduction to Derivatives

2.2 Formal Definition of the Derivative

2.3 Rules for Calculating Basic Derivatives

2.4 The Chain Rule and Implicit Differentiation*Chapter Review, Self-Test, and Capstones*

**3 Applications of the Derivative**

3.1 The Mean Value Theorem

3.2 The First Derivative and Curve Sketching

3.3 The Second Derivative and Curve Sketching

3.4 Optimization

3.5 Related Rates*Chapter Review, Self-Test, and Capstones*

**II Exploring Functions with Calculus**

**4 Calculus with Power, Polynomial, and Rational Functions**4.1 Advanced Algebraic Techniques

4.2 Power Functions

4.3 Polynomial Functions

4.4 Rational Functions

*Chapter Review, Self-Test, and Capstones*

**5 Calculus with Exponential and Logarithmic Functions**

5.1 Defining Exponential and Logarithmic Functions

5.2 Limits of Exponential and Logarithmic Functions

5.3 Derivatives of Exponential and Logarithmic Functions

5.4 Applications of Exponential Functions

5.5 L’Hopital’s Rule*Chapter Review, Self-Test, and Capstones*

**6 Calculus with Trignometric and Inverse Trigonometric Functions**

6.1 Defining the Trigonometric Functions

6.2 Trigonometric Identities

6.3 Limits and Derivatives of Trigonometric Functions

6.4 Inverse Trigonometric Functions*Chapter Review, Self-Test, and Capstones*

**III Integral Calculus**

**7 Definite Integrals**

7.1 Addition and Accumulation

7.2 Riemann Sums

7.3 Definite Integrals

7.4 Indefinite Integrals

7.5 The Fundamental Theorem of Calculus

7.6 Areas and Average Values

7.7 Functions Defined by Integrals*Chapter Review, Self-Test, and Capstones*

**8 Techniques of Integration**

8.1 Integration by Substitution

8.2 Integration by Parts

8.3 Partial Fractions and Other Algebraic Techniques

8.4 Trigonometric Integrals

8.5 Trigonometric Substitution

8.6 Improper Integrals

8.7 Numerical Integration**Chapter Review, Self-Test, and Capstones*

**9 Applications of Integration**

9.1 Volumes by Slicing

9.2 Volumes by Shells

9.3 Arc Length and Surface Area

9.4 Real-World Applications of Integration

9.5 Differential Equations**Chapter Review, Self-Test, and Capstones*

Answers to Odd Problems

Index