Calculus & Its Applications 15th Edition Larry J. Goldstein

Prerequisite Experience Diagnostic Test

Introduction

0. Functions
   • 0.1 Functions and Their Graphs
   • 0.2 Some Important Functions
   • 0.3 The Algebra of Functions
   • 0.4 Zeros of Functions – The Quadratic Method and Factoring
   • 0.5 Exponents and Power Functions
   • 0.6 Functions and Graphs in Applications
   • Chapter Summary and Chapter Review Exercises
1. The Derivative
   • 1.1 The Slope of a Straight Line
   • 1.2 The Slope of a Curve at a Point
   • 1.3 The Derivative and Limits
   • *1.4 Limits and the Derivative
   • *1.5 Differentiability and Continuity
   • 1.6 Some Rules for Differentiation
   • 1.7 More About Derivatives
   • 1.8 The Derivative as a Rate of Change
   • Chapter Summary and Chapter Review Exercises
2. Applications of the Derivative
   • 2.1 Describing Graphs of Functions
   • 2.2 The First- and Second-Derivative Tests
   • 2.3 The First- and Second-Derivative Tests and Curve Sketching
   • 2.4 Curve Sketching (Conclusion)
   • 2.5 Optimization Problems
   • *2.6 Additional Optimization Problems
   • *2.7 Applications of Derivatives to Business and Economics
   • Chapter Summary and Chapter Review Exercises
3. Techniques of Differentiation
   • 3.1 The Product and Quotient Rules
   • 3.2 The Chain Rule
   • *3.3 Implicit Differentiation and Related Rates
   • Chapter Summary and Chapter Review Exercises
4. The Exponential and Natural Logarithm Functions
   • 4.1 Exponential Functions
   • 4.2 The Exponential Function e^x
   • 4.3 Differentiation of Exponential Functions
   • 4.4 The Natural Logarithm Function
   • 4.5 The Derivative of ln x
   • 4.6 Properties of the Natural Logarithm Function
   • Chapter Summary and Chapter Review Exercises
5. Applications of the Exponential and Natural Logarithm Functions
   • 5.1 Exponential Growth and Decay
   • 5.2 Compound Interest
   • *5.3 Applications of the Natural Logarithm Function to Economics
   • *5.4 Additional Applications in Business and Economics
   • Chapter Summary and Chapter Review Exercises
6. The Definite Integral
   • 6.1 Antidifferentiation
   • 6.2 The Definite Integral and Net Change of a Function
   • 6.3 The Definite Integral and Area Under a Graph
   • 6.4 Areas in the xy-Plane
   • 6.5 Applications of the Definite Integral
   • Chapter Summary and Chapter Review Exercises
7. Functions of Multiple Variables
   • 7.1 Examples of Functions of Multiple Variables
   • 7.2 Partial Derivatives
   • 7.3 Maxima and Minima of Functions of Multiple Variables
   • 7.4 Lagrange Multipliers and Constrained Optimization
   • *7.5 The Method of Least Squares
   • *7.6 Double Integrals
   • Chapter Summary and Chapter Review Exercises
8. The Trigonometric Functions
   • 8.1 Radian Measure of Angles
   • 8.2 The Sine and the Cosine
   • 8.3 Differentiation and Integration of sin t and cos t
   • 8.4 The Tangent and Other Trigonometric Functions
   • Chapter Summary and Chapter Review Exercises
9. Techniques of Integration
   • 9.1 Integration by Substitution
   • 9.2 Integration by Parts
   • 9.3 Analysis of Definite Integrals
   • *9.4 Approximation of Definite Integrals
   • *9.5 Applications in Business and Economics
   • 9.6 Improper Integrals
   • Chapter Summary and Chapter Review Exercises
10. Differential Equations
    • 10.1 Solutions of Differential Equations
    • 10.2 Separation of Variables
    • *10.3 First-Order Linear Differential Equations
    • *10.4 Applications of First-Order Linear Differential Equations
    • 10.5 Graphing Solutions of Differential Equations
    • 10.6 Applications of Differential Equations
    • *10.7 Numerical Solution of Differential Equations
    • Chapter Summary and Chapter Review Exercises
11. Taylor Polynomials and Infinite Series
    • 11.1 Taylor Polynomials
    • *11.2 The Newton–Raphson Algorithm
    • 11.3 Infinite Series
    • 11.4 Series with Positive Terms
    • 11.5 Taylor Series
    • Chapter Summary and Chapter Review Exercises
12. Probability and Calculus
    • 12.1 Discrete Random Variables
    • 12.2 Continuous Random Variables
    • 12.3 Expected Value and Variance
    • 12.4 Exponential and Normal Random Variables
    • 12.5 Poisson and Geometric Random Variables
    • Chapter Summary and Chapter Review Exercises

*These sections are optional in the sense that they are not prerequisites for later material.

Appendix: Areas under the Normal Standard Curve

Learning Objectives

Resources

Selected Solutions

Index of Applications

Index