1

PRELIMINARIES

1.1

Real Numbers, Estimation, and Logic

1.2

Inequalities and Absolute Values

1.3

The Rectangular Coordinate System

1.4

Graphs of Equations

1.5

Functions and Their Graphs

1.6

Operations on Functions

1.7

Exponential and Logarithmic Functions

1.8

The Trigonometric Functions

1.9

The Inverse Trigonometric Functions

1.10

Chapter Review

2

LIMITS

2.1

Introduction to Limits

2.2

Rigorous Study of Limits

2.3

Limit Theorems

2.4

Limits at Infinity; Infinite Limits

2.5

Limits Involving Trigonometric Functions

2.6

Natural Exponential, Natural Log, and Hyperbolic Functions

2.7

Continuity of Functions

2.8

Chapter Review

3

THE DERIVATIVE

3.1

Two Problems with One Theme

3.2

The Derivative

3.3

Rules for Finding Derivatives

3.4

Derivatives of Trigonometric Functions

3.5

The Chain Rule

3.6

Higher-Order Derivatives

3.7

Implicit Differentiation

3.8

Related Rates

3.9

Derivatives of Exponential and Logarithmic Functions

3.10

Derivatives of Hyperbolic and Inverse Trigonometric Functions

3.11

Differentials and Approximations

3.12

Chapter Review

4

APPLICATIONS OF THE DERIVATIVE

4.1

Maxima and Minima

4.2

Monotonicity and Concavity

4.3

Local Extrema and Extrema on Open Intervals

4.4

Practical Problems

4.5

Graphing Functions Using Calculus

4.6

The Mean Value Theorem for Derivatives

4.7

Solving Equations Numerically

4.8

Antiderivatives

4.9

Introduction to Differential Equations

4.10

Exponential Growth and Decay

4.11

Chapter Review

5

THE DEFINITE INTEGRAL

5.1

Introduction to Area

5.2

The Definite Integral

5.3

The 1st Fundamental Theorem of Calculus

5.4

The 2nd Fundamental Theorem of Calculus

and the Method of Substitution

5.5

The Mean Value Theorem for Integrals & the Use of Symmetry

5.6

Numerical Integration

5.7

Chapter Review

6

APPLICATIONS OF THE INTEGRAL

6.1

The Area of a Plane Region

6.2

Volumes of Solids: Slabs, Disks, Washers

6.3

Volumes of Solids of Revolution: Shells

6.4

Length of a Plane Curve

6.5

Work and Fluid Pressure

6.6

Moments and Center of Mass

6.8

Probability and Random Variables

6.8

Chapter Review

7

TECHNIQUES OF INTEGRATION &

DIFFERENTIAL EQUATIONS

7.1

Basic Integration Rules

7.2

Integration by Parts

7.3

Some Trigonometr