Calculus & Its Applications, 15th edition
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Overview
Calculus & Its Applications builds intuition with key concepts before presenting analytical material, using a strategic and distinctive topic organization to make learning calculus more accessible. Significant applications introduced early on make the mathematics more digestible, and comprehensive exercise sets suit different types of courses. The 15th Edition introduces fresh insights from new coauthor Edward Tavernetti of University of California  Davis. It improves and expands applications, updates example and exercise data, and provides new material on modeling with differential equations.
Published by Pearson (January 22nd 2022)  Copyright © 2023
ISBN13: 9780137590728
Subject: Finite Math & Applied Calculus
Category: Applied Calculus
Table of contents
Prerequisite Skills Diagnostic Test
Introduction
 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
 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
 Applications of the Derivative
 2.1 Describing Graphs of Functions
 2.2 The First and SecondDerivative Rules
 2.3 The First and SectionDerivative 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
 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
 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
 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
 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 xyPlane
 6.5 Applications of the Definite Integral
 Chapter Summary and Chapter Review Exercises
 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
 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
 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
 Differential Equations
 10.1 Solutions of Differential Equations
 10.2 Separation of Variables
 *10.3 FirstOrder Linear Differential Equations
 *10.4 Applications of FirstOrder 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
 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
 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 Standard Normal Curve
Learning Objectives
Sources
Selected Answers
Index of Applications
Index
Your questions answered
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