Applied Calculus With Infotrac

by Waner, Stefan; Costenoble, Steven

• ISBN13: 9780534419585
• ISBN10: 0534419585
• Format: Hardcover
• Copyright: 2003-07-16
• Publisher: Brooks Cole

Summary

Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice.

Table of Contents

Chapter 1 FUNCTIONS AND LINEAR MODELS	2	(78)
1.1 Functions from the Numerical and Algebraic Viewpoints	3	(14)
1.2 Functions from the Graphical Viewpoint	17	(13)
1.3 Linear Functions	30	(11)
1.4 Linear Models	41	(18)
1.5 Linear Regression	59	(15)
Case Study: Modeling Spending on Internet Advertising	74	(6)
Optional Internet Topic:
New functions from Old: Scaled and Shifted Functions
Chapter 2 NONLINEAR MODELS	80	(58)
2.1 Quadratic Functions and Models	81	(13)
2.2 Exponential Functions and Models	94	(16)
2.3 Logarithmic Functions and Models	110	(11)
2.4 Logistic Functions and Models	121	(12)
Case Study: Checking Up on Malthus	133	(5)
Optional Internet Topics:
Inverse Functions
Linear and Exponential Regression
Using and Deriving Algebraic Properties of Logarithms
Chapter 3 INTRODUCTION TO THE DERIVATIVE	138	(102)
3.1 Average Rate of Change	139	(15)
3.2 The Derivative: Numerical and Graphical Viewpoints	154	(23)
3.3 The Derivative: Algebraic Viewpoint	177	(9)
3.4 Derivatives of Powers, Sums, and Constant Multiples	186	(12)
3.5 A First Application: Marginal Analysis	198	(11)
3.6 Limits: Numerical & Graphical Approaches (Optional)	209	(10)
3.7 Limits and Continuity (Optional)	219	(6)
3.8 Limits and Continuity: Algebraic Approach (Optional)	225	(10)
Case Study: Reducing Sulfur Emissions	235	(5)
Optional Internet Topics:
Proof of the Power Rule
Sketching the Graph of the Derivative Continuity and Differentiability
Chapter 4 TECHNIQUES OF DIFFERENTATION	240	(50)
4.1 The Product and Quotient Rules	241	(10)
4.2 The Chain Rule	251	(10)
4.3 Derivatives of Logarithmic and Exponential Functions	261	(12)
4.4 Implicit Differentiation	273	(7)
Case Study: Projecting Market Growth	280	(10)
Optional Internet Topic:
Linear Approximation and Error Estimation
Chapter 5 APPLICATIONS OF THE DERIVATIVE	290	(62)
5.1 Maxima and Minima	291	(13)
5.2 Applications of Maxima and Minima	304	(13)
5.3 The Second Derivative and Analyzing Graphs	317	(12)
5.4 Related Rates	329	(8)
5.5 Elasticity	337	(9)
Case Study: Production Lot-Size Management	346	(6)
Chapter 6 THE INTEGRAL	352	(56)
6.1 The Indefinite Integral	353	(11)
6.2 Substitution	364	(9)
6.3 The Definite Integral as a Sum: A Numerical Approach	373	(11)
6.4 The Definite Integral as Area: A Geometric Approach	384	(7)
6.5 The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus	391	(12)
Case Study: Wage Inflation	403	(5)
Optional Internet Topic:
Numerical Integration
Chapter 7 FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL	408	(58)
7.1 Integration by Parts	409	(7)
7.2 Area between Two Curves and Applications	416	(14)
7.3 Averages and Moving Averages	430	(8)
7.4 Continuous Income Streams	438	(4)
7.5 Improper Integrals and Applications	442	(8)
7.6 Differential Equations and Applications	450	(8)
Case Study: Estimating Tax Revenues	458	(8)
Chapter 8 FUNCTIONS OF SEVERAL VARIABLES	466	(72)
8.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints	467	(12)
8.2 Three-Dimensional Space and the Graph of a Function of Two Variables	479	(11)
8.3 Partial Derivatives	490	(8)
8.4 Maxima and Minima	498	(10)
8.5 Constrained Maxima and Minima and Applications	508	(10)
8.6 Double Integrals	518	(9)
Case Study: Modeling Household Income	527	(11)
Chapter 9 TRIGONOMETRIC MODELS	538
9.1 Trigonometric Functions, Models, and Regression	539	(16)
9.2 Derivatives of Trigonometric Functions and Applications	555	(8)
9.3 Integrals of Trigonometric Functions and Applications	563	(6)
Case Study: Predicting Cocoa inventories	569	(3080623)
Chapter S CALCULUS APPLIED TO PROBABILITY AND STATISTICS OPTIONAL INTERNET TOPIC
S.1 Continuous Random Variables and Histograms
S.2 Probability Density Functions: Uniform, Exponential, Normal, and Beta
S.3 Mean, Median, Variance and Standard Deviation
Case Study: Creating a Family Trust
Appendix A ALGEBRA REVIEW	A1
A.1 Real Numbers	A1
A.2 Exponents and Radicals	A6
A.3 Multiplying and Factoring Algebraic Equations	A16
A.4 Rational Expressions	A20
A.5 Solving Polynomial Equations	A22
A.6 Solving Miscellaneous Equations	A28
ANSWERS TO SELECTED EXERCISES	A33
INDEX	A65