Calculus and Its Applications

by Bittinger, Marvin L.

• ISBN13: 9780201338645
• ISBN10: 0201338645
• Edition: 7th
• Format: Hardcover
• Copyright: 1999-10-01
• Publisher: Pearson College Div

Summary

Calculus and Its Applications has, for years, been a best-selling text for one simple reason: it anticipates, then meets the needs of today's applied calculus student. Knowing that calculus is a course in which students typically struggle--both with algebra skills and visualizing new calculus concepts--Bittinger and Ellenbogen speak to students in a way they understand, taking great pains to provide clear and careful explanations.&Since most&students taking this course will go on to careers in the business world, &large quantities of real data, especially as they apply to&business, are included as well.

Table of Contents

Functions, Graphs, and Models	1	(94)
Graphs and Equations	2	(12)
Functions and Models	14	(15)
Finding Domain and Range	29	(11)
Slope and Linear Functions	40	(16)
Other Types of Functions	56	(18)
Mathematical Modeling and Curve Fitting	74	(21)
Summary and Review	86	(3)
Test	89	(2)
Extended Technology Application The Ecological Effect of Global Warming	91	(4)
Differentiation	95	(90)
Limits and Continuity: Numerically and Graphically	96	(13)
Limits: Algebraically	109	(5)
Average Rates of Change	114	(10)
Differentiation Using Limits of Difference Quotients	124	(14)
Differentiation Techniques: The Power and Sum--Difference Rules	138	(11)
Instantaneous Rates of Change; Business Applications	149	(9)
Differentiation Techniques: The Product and Quotient Rules	158	(8)
The Chain Rule	166	(8)
Higher-Order Derivatives	174	(11)
Summary and Review	178	(10)
Test	188
Extended Technology Application Path of a Baseball: The Tale of the Tape	181	(4)
Applications of Differentiation	185	(100)
Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs	186	(16)
Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs	202	(14)
Graph Sketching: Asymptotes and Rational Functions	216	(18)
Using Derivatives to Find Absolute Maximum and Minimum Values	234	(15)
Maximum--Minimum Problems: Business and Economics Applications	249	(17)
Differentials	266	(7)
Implicit Differentiation and Related Rates	273	(12)
Summary and Review	279	(2)
Test	281	(2)
Extended Technology Application Maximum Sustainable Harvest	283	(2)
Exponential and Logarithmic Functions	285	(78)
Exponential Functions	286	(14)
Logarithmic Functions	300	(17)
Applications: The Uninhibited Growth Model, dP/dt = kP	317	(15)
Applications: Decay	332	(13)
The Derivatives of ax and loga X	345	(5)
An Economics Application: Elasticity of Demand	350	(13)
Summary and Review	356	(2)
Test	358	(2)
Extended Technology Application The Business of Motion-Picture Box-Office Revenue	360	(3)
Integration	363	(70)
Integration	364	(9)
Area and Definite Integrals	373	(14)
Limits of Sums and Accumulations	387	(13)
Properties of Definite Integrals	400	(8)
Integration Techniques: Substitution	408	(6)
Integration Techniques: Integration by Parts	414	(8)
Integration Techniques: Tables	422	(11)
Summary and Review	428	(1)
Test	429	(2)
Extended Technology Application Total Sales of Sherwin-Williams, Intel, Sprint, and The Gap	431	(2)
Applications of Integration	433	(62)
An Economics Application: Consumer's Surplus and Producer's Surplus	434	(6)
Applications of the Models ∫ To Poekt dt and ∫ To Poe-kt dt	440	(8)
Improper Integrals	448	(6)
Probability	454	(11)
Probability: Expected Value; The Normal Distribution	465	(12)
Volume	477	(3)
Differential Equations	480	(15)
Summary and Review	489	(2)
Test	491	(2)
Extended Technology Application Curve Fitting and the Volume of a Bottle of Soda	493	(2)
Functions of Several Variables	495	(54)
Functions of Several Variables	496	(7)
Partial Derivatives	503	(6)
Higher-Order Partial Derivatives	509	(3)
Maximum--Minimum Problems	512	(11)
An Application: The Least-Squares Technique	523	(8)
Constrained Maximum and Minimum Values: Lagrange Multipliers	531	(8)
Multiple Integration	539	(10)
Summary and Review	543	(2)
Test	545	(1)
Extended Technology Application Minimizing Employees' Travel Time in a Building	546	(3)
Cumulative Review	549	(4)
Appendix: Review of Basic Algebra	553	(16)
Tables
Table 1 Integration Formulas	567	(2)
Table 2 Areas for a Standard Normal Distribution	569
Answers	A-1
Index	I-1