Calculus with Applications, 12th edition
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Overview
Calculus with Applications, 13th Edition prepares you for career success with timely applications throughout. Known for using real data in their examples and exercises, the authors make mathematics meaningful and relevant in the narrative, examples, exercise sets and supplementary resources. You'll have ample opportunity to relate what you're learning to career situations through the Apply It question at the beginning of sections, the applied examples and exercises, and the Extended Application at the end of each chapter.
Published by Pearson (July 8th 2021) - Copyright © 2022
ISBN-13: 9780137419340
Subject: Finite Math & Applied Calculus
Category: Applied Calculus
Overview
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
- Solutions to Prerequisite Skills Diagnostic Test
- Tables
Complete Instructor Answers
Credits
Index of Applications
Index
Sources
Your questions answered
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