Calculus with Applications, 12th edition

  • Margaret L. Lial, 
  • Raymond N. Greenwell, 
  • Nathan P. Ritchey

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Overview

Calculus with Applications make mathematics relevant and accessible through timely applications, real data, examples, exercise sets and supplementary resources. You'll have ample opportunity to relate what you're learning to realistic career situations, while preparing for success in your career.

Published by Pearson (July 8th 2021) - Copyright © 2022

ISBN-13: 9780137419340

Subject: Finite Math & Applied Calculus

Category: Applied Calculus

Table of contents

Preface 

Prerequisite Skills Diagnostic Test 


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: Predicting 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: Power Functions 


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: Electric 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 

6.4 Implicit Differentiation 

6.5 Related Rates 

6.6 Differentials: Linear Approximation 

Chapter 6 Review 

Extended Application: A Total 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 at 0 

12.6 Newton’s Method 

12.7 L’Hôpital’s Rule 

Chapter 12 Review 

Extended Application: Living Assistance and Subsidized Housing 


13. The Trigonometric Functions

13.1 Definitions of the Trigonometric Functions 

13.2 Derivatives of Trigonometric Functions 

13.3 Integrals of Trigonometric Functions 

Chapter 13 Review 

Extended Application: The Shortest Time and the Cheapest Path 
 

Appendix 

  1. Solutions to Prerequisite Skills Diagnostic Test 
  2. Tables 

Complete Instructor Answers

Credits

Index of Applications

Index 

Sources 

Your questions answered

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