# Applied Calculus, 5ed

ISBN: 9788126574315

568 pages

Exclusively distributed by I.K. International

## Description

The 5^{th} Edition of Applied Calculus continues to exhibit the same strengths from earlier editions including a focus on creative conceptual and modeling problems and the "Rule of Four", an emphasis on concepts and modeling, exposition that teaches a flexible approach to technology.

1 Functions And Change

1.1 What Is A Function?

1.2 Linear Functions

1.3 Average Rate Of Change And Relative Change

1.4 Applications Of Functions To Economics

1.5 Exponential Functions

1.6 The Natural Logarithm

1.7 Exponential Growth And Decay

1.8 New Functions From Old

1.9 Proportionality And Power Functions

1.10 Periodic Functions

2 Rate Of Change: The Derivative

2.1 Instantaneous Rate Of Change

2.2 The Derivative Function

2.3 Interpretations Of The Derivative

2.4 The Second Derivative

2.5 Marginal Cost And Revenue

3 Shortcuts To Differentiation

3.1 Derivative Formulas For Powers And Polynomials

3.2 Exponential And Logarithmic Functions

3.3 The Chain Rule

3.4 The Product And Quotient Rules

3.5 Derivatives Of Periodic Functions

4 Using The Derivative

4.1 Local Maxima And Minima

4.2 Inflection Points

4.3 Global Maxima And Minima

4.4 Profit, Cost, And Revenue

4.5 Average Cost

4.6 Elasticity Of Demand

4.7 Logistic Growth

4.8 The Surge Function And Drug Concentration

5 Accumulated Change: The Definite Integral

5.1 Distance And Accumulated Change

5.2 The Definite Integral

5.3 The Definite Integral As Area

5.4 Interpretations Of The Definite Integral

5.5 Total Change And The Fundamental Theorem Of Calculus

5.6 Average Value

6 Antiderivatives And Applications

6.1 Analyzing Antiderivatives Graphically And Numerically

6.2 Antiderivatives And The Indefinite Integral

6.3 Using The Fundamental Theorem To Find Definite Integrals

6.4 Application: Consumer And Producer Surplus

6.5 Application: Present And Future Value

6.6 Integration By Substitution

6.7 Integration By Parts

7 Probability

7.1 Density Functions

7.2 Cumulative Distribution Functions And Probability

7.3 The Median And The Mean

8 Functions Of Several Variables

8.1 Understanding Functions Of Two Variables

8.2 Contour Diagrams

8.3 Partial Derivatives

8.4 Computing Partial Derivatives Algebraically

8.5 Critical Points And Optimization 381

8.6 Constrained Optimization 387

9 Mathematical Modeling Using Differential Equations

9.1 Mathematical Modeling: Setting Up A Differential Equation

9.2 Solutions Of Differential Equations

9.3 Slope Fields

9.4 Exponential Growth And Decay

9.5 Applications And Modeling

9.6 Modeling The Interaction Of Two Populations

9.7 Modeling The Spread Of A Disease

10 Geometric Series

10.1 Geometric Series

10.2 Applications To Business And Economics

10.3 Applications To The Natural Sciences

Review Problems

Strengthen Your Understanding

Projects: Do You Have Any Common Ancestors?, Harrod-Hicks Model Of An Expanding National Economy, Probability Ofwinning In Sports, Medical Case Study: Drug Desensitization Schedule

Appendix

A Fitting Formulas To Data

B Compound Interest And The Number E

C Spreadsheet Projects

1. Malthus: Population Outstrips Food Supply

2. Credit Card Debt

3. Choosing A Bank Loan

4. Comparing Home Mortgages

5. Present Value Of Lottery winnings

6. Comparing Investments

7. Investing For The Future: Tuition Payments

8. New Or Used?

9. Verhulst: The Logistic Model

10. The Spread Of Information: A Comparison Of Two Models

11. The Flu In World War I

Answers To Odd-Numbered Problems

Pretest

Index