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 co-author 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
ISBN-13: 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 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
- 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 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
- 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 xy-Plane
- 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 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
- 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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