Calculus with Applications: Pearson New International Edition

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals



1. Linear Functions

1.1 Slopes and Equations of Lines

1.2 Linear Functions and Applications

1.3 The Least Squares Line

Chapter 1 Review

Extended Application: Using Extrapolation to Predict Life Expectancy



2. Nonlinear Functions

2.1 Properties of Functions

2.2 Quadratic Functions; Translation and Reflection

2.3 Polynomial and Rational Functions

2.4 Exponential Functions

2.5 Logarithmic Functions

2.6 Applications: Growth and Decay; Mathematics of Finance

Chapter 2 Review

Extended Application: Characteristics of the Monkeyface Prickleback



3. The Derivative

3.1 Limits

3.2 Continuity

3.3 Rates of Change

3.4 Definition of the Derivative

3.5 Graphical Differentiation

Chapter 3 Review

Extended Application: A Model for Drugs Administered Intravenously



4. Calculating the Derivative

4.1 Techniques for Finding Derivatives

4.2 Derivatives of Products and Quotients

4.3 The Chain Rule

4.4 Derivatives of Exponential Functions

4.5 Derivatives of Logarithmic Functions

Chapter 4 Review

Extended Application: Electrical Potential and Electric Field



5. Graphs and the Derivative

5.1 Increasing and Decreasing Functions

5.2 Relative Extrema

5.3 Higher Derivatives, Concavity, and the Second Derivative Test

5.4 Curve Sketching

Chapter 5 Review

Extended Application: A Drug Concentration Model for Orally Administered Medications



6. Applications of the Derivative

6.1 Absolute Extrema

6.2 Applications of Extrema

6.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand

6.4 Implicit Differentiation

6.5 Related Rates

6.6 Differentials: Linear Approximation

Chapter 6 Review

Extended Application: A Total Cost Model for a Training Program



7. Integration

7.1 Antiderivatives

7.2 Substitution

7.3 Area and the Definite Integral

7.4 The Fundamental Theorem of Calculus

7.5 The Area Between Two Curves

7.6 Numerical Integration

Chapter 7 Review

Extended Application: Estimating Depletion Dates for Minerals



8. Further Techniques and Applications of Integration

8.1 Integration by Parts

8.2 Volume and Average Value

8.3 Continuous Money Flow

8.4 Improper Integrals

Chapter 8 Review

Extended Application: Estimating Learning Curves in Manufacturing with Integrals



9. Multivariable Calculus

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Maxima and Minima

9.4 Lagrange Multipliers

9.5 Total Differentials and Approximations

9.6 Double Integrals

Chapter 9 Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design



10. Differential Equations

10.1 Solutions of Elementary and Separable Differential Equations

10.2 Linear First-Order Differential Equations

10.3 Euler's Method

10.4 Applications of Differential Equations

Chapter 10 Review

Extended Application: Pollution of the Great Lakes



11. Probability and Calculus

11.1 Continuous Probability Models

11.2 Expected Value and Variance of Continuous Random Variables

11.3 Special Probability Density Functions

Chapter 11 Review

Extended Application: Exponential Waiting Times



12. Sequences and Series

12.1 Geometric Sequences

12.2 Annuities: An Application of Sequences

12.3 Taylor Polynomials at 0

12.4 Infinite Series

12.5 Taylor Series

12.6 Newton's Method

12.7 L'Hopital's Rule

Chapter 12 Review

Extended Application: Living Assistance and Subsidized Housing