Essential Calculus with Applications, 3rd Edition

0.1 Real Numbers and Number Lines

0.2 Integer Exponents

0.3 Fractional Exponents and Radicals

0.4 Polynomials and Factoring

0.5 Lines and Their Graphs

0.6 Linear Equations in One Variable

0.7 Quadratic Equations in One Variable

0.8 Rational and Radical Equations

1.1 Introduction to Functions

1.2 Operations with Functions

1.3 Functions and Models

1.4 Functions and Their Graphs: A Calculator Section

2.1 One-Sided Limits

2.2 Limits

2.3 More about Limits

2.4 Continuity

2.5 Average Rate of Change

2.6 Instantaneous Rate of Change

2.7 Definition of the Derivative and the Power Rule

2.8 Techniques for Finding Derivatives

2.9 Applications: Marginal Analysis

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

3.4 Increasing and Decreasing Intervals

3.5 Critical Values and the First Derivative Test

3.6 Absolute Maximum and Minimum

4.1 Concavity and Points of Inflection

4.2 The Second Derivative Test

4.3 Curve Sketching: Polynomial Functions

4.4 Curve Sketching: Rational Functions

4.5 Business Applications

4.6 Other Applications: Optimization, Distance, and Velocity

4.7 Differentials

5.1 Exponential Functions

5.2 The Natural Logarithm

5.3 Derivatives of Logarithmic Functions

5.4 Derivatives of Exponential Functions

5.5 Growth and Decay

5.6 Elasticity of Demand

6.1 The Indefinite Integral

6.2 Integration by Substitution

6.3 Area and Riemann Sums

6.4 The Definite Integral and the Fundamental Theorem of Calculus

6.5 Area under a Curve (with Applications)

6.6 Area between Two Curves (with Applications)

6.7 Differential Equations

7.1 Integration by Parts

7.2 Annuities and Income Streams

7.3 Tables of Integrals

7.4 Improper Integrals

7.5 Probability

7.6 Volume

8.1 Functions of Several Variables

8.2 Partial Derivatives

8.3 Local Extrema for Functions of Two Variables

8.4 Lagrange Multipliers

8.5 The Method of Least Squares

8.6 Double Integrals

9.1 Trigonometric Functions

9.2 Derivatives of Trigonometric Functions

9.3 Integration of Trigonometric Functions

9.4 Inverse Trigonometric Functions

10.1 Sequences and Series

10.2 Taylor Polynomials

10.3 Taylor Series, Power Series, and Their Applications