Calculus & Its Applications
by Larry J. Goldstein, David C. Lay, David I. Schneider
15th Edition
Publisher: Pearson
Book Details
| Print ISBN | 9780137590612 |
| eText ISBN | 9780137590896 |
| Publisher | Pearson |
| Publishing Year | 2023 |
| Edition | 15th Edition |
| Language | English |
Calculus & Its Applications, 15th Edition, is a textbook designed to make calculus accessible by developing conceptual intuition before presenting analytical material. It uses a distinctive topic arrangement and introduces applications early to make mathematical concepts more digestible.
The text covers foundational functions, single-variable differential and integral calculus, multivariable functions, and trigonometry. It also explores differential equations, Taylor polynomials, infinite series, and probability concepts.
Comprehensive exercise sets accommodate different types of courses. For the 2023 edition, co-author Edward Tavernetti joined the writing team to expand applied coverage, update data across examples and exercises, and introduce new material on modeling with differential equations.
Table of Contents
Chapter 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 Formula and Factoring
- • 0.5 Exponents and Power Functions
- • 0.6 Functions and Graphs in Applications
- • Chapter Summary and Chapter Review Exercises
Chapter 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
Chapter 2: Applications of the Derivative
- • 2.1 Describing Graphs of Functions
- • 2.2 The First- and Second-Derivative Rules
- • 2.3 The First- and Section-Derivative Tests and Curve Sketching
- • 2.4 Curve Sketching (Conclusion)
- • 2.5 Optimization Problems
- • *2.6 Further Optimization Problems
- • *2.7 Applications of Derivatives to Business and Economics
- • Chapter Summary and Chapter Review Exercises
Chapter 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
Chapter 4: The Exponential and Natural Logarithm Functions
- • 4.1 Exponential Functions
- • 4.2 The Exponential Function ex
- • 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
Chapter 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 Further Applications in Business and Economics
- • Chapter Summary and Chapter Review Exercises
Chapter 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
Chapter 7: Functions of Several Variables
- • 7.1 Examples of Functions of Several Variables
- • 7.2 Partial Derivatives
- • 7.3 Maxima and Minima of Functions of Several 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
Chapter 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
Chapter 9: Techniques of Integration
- • 9.1 Integration by Substitution
- • 9.2 Integration by Parts
- • 9.3 Evaluation 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
Chapter 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
Chapter 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
Chapter 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
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