Brief Calculus: An Applied Approach, 8th Edition

by Sullivan, Michael

• ISBN13: 9780471707615
• ISBN10: 0471707619
• Edition: 8th
• Format: Hardcover
• Copyright: 2012-02-20
• Publisher: Wiley

Summary

This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. Applications using real data enhances student motivation. Many of these applications include source lines, to show how mathematics is used in the real world. NEW! Conceptual problems ask students to put the concepts and results into their own words. These problems are marked with an icon to make them easier to assign. More opportunities for the use of graphing calculator, including screen shots and instructions, and the use of icons that clearly identify each opportunity for the use of spreadsheets or graphing calculator. Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned. Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items, Fill in the Blanks and Review Exercises. Includes Mathematical Questions from Professional Exams (CPA)

Author Biography

Michael Sullivan is Professor Emeritus in the Department of Mathematics and Computer Science at Chicago State University where he taught for 35 years before retiring a few years ago. Dr. Sullivan is a member of the American Mathematical Society, the Mathematical Association of America, and the American Mathematical Society, the Mathematical Association of America, and the American Mathematical Association of Two year Colleges. he is President of the Text and Academic Authors Association and Represents that organization on the Authors Coalition of America. Mike has been writing textbooks in mathematics for over 30 years. He currently has 13 books in print: 3 texts with John Wiley & Sons and 10 with Prentice-Hall. Six of these titles are co-authored with his son, Michael Sullivan III.

Mike has four children: Kathleen, who teaches college mathematics; Michael, who teaches college mathematics, Dan, who is a Prentice-Hall sales representative , and Colleen, who teaches middle-School mathematics. Nine grandchildren round out the family.

Table of Contents

CHAPTER 0 REVIEW	1	(96)
0.1 Real Numbers	2	(14)
0.2 Algebra Review	16	(13)
0.3 Polynomials and Rational Expressions	29	(11)
0.4 Solving Equations	40	(11)
0.5 Intervals; Solving Inequalities	51	(13)
0.6 nth Roots; Rational Exponents	64	(7)
0.7 Geometry Review	71	(5)
0.8 Rectangular Coordinates	76	(5)
0.9 Lines	81	(16)
CHAPTER 1 FUNCTIONS AND THEIR GRAPHS	97	(66)
1.1 Graphs of Equations	98	(11)
1.2 Functions	109	(11)
1.3 Graphs of Functions; Properties of Functions	120	(17)
1.4 Library of Functions; Piecewise-defined Functions	137	(11)
1.5 Graphing Techniques: Shifts and Reflections	148	(8)
Chapter Review	156	(6)
Chapter Project: Evaluating Car Rental Costs	162	(1)
CHAPTER 2 CLASSES OF FUNCTIONS	163	(73)
2.1 Quadratic Functions	164	(14)
2.2 Power Functions; Polynomial Functions; Rational Functions	178	(8)
2.3 Exponential Functions	186	(16)
2.4 Logarithmic Functions	202	(12)
2.5 Properties of Logarithms	214	(9)
2.6 Continuously Compounded Interest	223	(4)
Chapter Review	227	(7)
Chapter Project: Predicting Population Growth	234	(2)
CHAPTER 3 THE LIMIT OF A FUNCTION	236	(37)
3.1 Finding Limits using Tables and Graphs	237	(6)
3.2 Techniques for Finding Limits of Functions	243	(8)
3.3 One-sided Limits; Continuous Functions	251	(7)
3.4 Limits At Infinity; Infinite Limits; End-Behavior; Asymptotes	258	(9)
Chapter Review	267	(4)
Chapter Project: Tax Rates and Continuous Functions	271	(2)
CHAPTER 4 THE DERIVATIVE OF A FUNCTION	273	(74)
4.1 The Definition of a Derivative	274	(12)
4.2 The Derivative of a Power Function; Sum and Difference Formulas	286	(9)
4.3 Product and Quotient Formulas	295	(8)
4.4 The Power Rule	303	(5)
4.5 The Derivatives of the Exponential and Logarithmic Functions; the Chain Rule	308	(12)
4.6 Higher-Order Derivatives	320	(8)
4.7 Implicit Differentiation	328	(6)
4.8 The Derivative of f(x) = xp/q	334	(6)
Chapter Review	340	(4)
Chapter Project: Testing Blood Efficiently	344	(3)
CHAPTER 5 APPLICATIONS: GRAPHING FUNCTIONS; OPTIMIZATION	347	(73)
5.1 Horizontal and Vertical Tangent Lines; Continuity and Differentiability	348	(6)
5.2 Increasing and Decreasing Functions; the First Derivative Test	354	(11)
5.3 Concavity; the Second Derivative Test	365	(16)
5.4 Optimization	381	(12)
5.5 Elasticity of Demand	393	(5)
5.6 Related Rates	398	(7)
5.7 The Differential and Linear Approximations	405	(7)
Chapter Review	412	(5)
Chapter Project: Inventory Control	417	(3)
CHAPTER 6 THE INTEGRAL OF A FUNCTION AND APPLICATIONS	420	(65)
6.1 Antiderivatives; The Indefinite Integral; Marginal Analysis	421	(11)
6.2 Integration Using Substitution	432	(5)
6.3 Integration by Parts	437	(5)
6.4 The Definite Integral; Learning Curves; Sales over Time	442	(8)
6.5 Finding Areas; Consumer's Surplus, Producer's Surplus; Maximizing Profit over Time	450	(13)
6.6 Approximating Definite Integrals Using Rectangles	463	(7)
6.7 Differential Equations	470	(7)
Chapter Review	477	(5)
Chapter Project: Inequality of Income Distribution	482	(3)
CHAPTER 7 OTHER APPLICATIONS AND EXTENSIONS OF THE INTEGRAL	485	(26)
7.1 Improper Integrals	486	(4)
7.2 Average Value of a Function	490	(3)
7.3 Continuous Probability Functions	493	(12)
Chapter Review	505	(4)
Chapter Project: A Mathematical Model for Arrivals	509	(2)
CHAPTER 8 CALCULUS OF FUNCTIONS OF TWO OR MORE VARIABLES	511	(47)
8.1 Rectangular Coordinates in Space	512	(4)
8.2 Functions and Their Graphs	516	(6)
8.3 Partial Derivatives	522	(9)
8.4 Local Maxima and Local Minima	531	(7)
8.5 Lagrange Multipliers	538	(9)
8.6 The Double Integral	547	(5)
Chapter Review	552	(4)
Chapter Project: Move Inventory Control with Calculus	556	(2)
APPENDIX GRAPHING UTILITIES	558
A.1 The Viewing Rectangle	558	(2)
A.2 Using a Graphing Utility to Graph Equations	560	(4)
A.3 Square Screens	564	(1)
A.4 Using a Graphing Utility To Locate Intercepts and Check for Symmetry	565	(2)
A.5 Using a Graphing Utility to Solve Equations	567
Answers to Odd-Numbered Problems	AN-1
Photo Credits	PC-1
Index	I-1