Mathematics with Applications

by Lial, Margaret L.; Hungerford, Thomas W.; Holcomb, John

• ISBN13: 9780201755299
• ISBN10: 0201755297
• Edition: 8th
• Format: Hardcover
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

Best known for realistic and varied applications, an abundance of helpful pedagogy, and solid algebra review, the new edition of this text offers updated and new applications, and increased optional graphing calculator technology.

Table of Contents

Preface	ix
To the Student	xv
Algebra and Equations	1	(65)
The Real Numbers	1	(10)
Polynomials	11	(6)
Factoring	17	(5)
Rational Expressions	22	(7)
Exponents and Radicals	29	(10)
First-Degree Equations	39	(11)
Quadratic Equations	50	(16)
Chapter 1 Summary	60	(1)
Chapter 1 Review Exercises	61	(3)
Case 1 Consumers Often Defy Common Sense	64	(2)
Graphs, Lines, and Inequalities	66	(54)
Graphs	66	(10)
Equations of Lines	76	(13)
Linear Models	89	(11)
Linear Inequalities	100	(8)
Polynomial and Rational Inequalities	108	(12)
Chapter 2 Summary	114	(1)
Chapter 2 Review Exercises	115	(3)
Case 2 Using Extrapolation to Predict Life Expectancy	118	(2)
Functions and Graphs	120	(72)
Functions	120	(8)
Graphs of Functions	128	(13)
Applications of Linear Functions	141	(11)
Quadratic Functions	152	(7)
Applications of Quadratic Functions	159	(9)
Polynomial Functions	168	(9)
Rational Functions	177	(15)
Chapter 3 Summary	187	(1)
Chapter 3 Review Exercises	188	(4)
Exponential and Logarithmic Functions	192	(39)
Exponential Functions	192	(7)
Applications of Exponential Functions	199	(8)
Logarithmic Functions	207	(8)
Logarithmic and Exponential Equations	215	(16)
Chapter 4 Summary	225	(1)
Chapter 4 Review Exercises	226	(3)
Case 3 Characteristics of the Monkeyface Prickleback	229	(2)
Mathematics of Finance	231	(44)
Simple Interest and Discount	231	(7)
Compound Interest	238	(11)
Future Value of an Annuity and Sinking Funds	249	(10)
Present Value of an Annuity and Amortization	259	(16)
Chapter 5 Summary	268	(1)
Chapter 5 Review Exercises	269	(4)
Case 4 Time, Money, and Polynomials	273	(2)
Systems of Linear Equations and Matrices	275	(68)
Systems of Linear Equations	275	(16)
The Gauss-Jordan Method	291	(11)
Basic Matrix Operations	302	(8)
Matrix Products and Inverses	310	(14)
Applications of Matrices	324	(19)
Chapter 6 Summary	336	(1)
Chapter 6 Review Exercises	337	(4)
Case 5 Matrix Operations and Airline Route Maps	341	(2)
Linear Programming	343	(72)
Graphing Linear Inequalities in Two Variables	343	(8)
Linear Programming: The Graphical Method	351	(7)
Applications of Linear Programming	358	(8)
The Simplex Method: Maximization	366	(14)
Maximization Applications	380	(7)
The Simplex Method: Duality and Minimization	387	(9)
The Simplex Method: Nonstandard Problems	396	(19)
Chapter 7 Summary	409	(1)
Chapter 7 Review Exercises	410	(3)
Case 6 Cooking with Linear Programming	413	(2)
Sets and Probability	415	(66)
Sets	415	(9)
Applications of Venn Diagrams	424	(9)
Introduction to Probability	433	(8)
Basic Concepts of Probability	441	(10)
Conditional Probability and Independent Events	451	(14)
Bayes' Formula	465	(16)
Chapter 8 Summary	472	(2)
Chapter 8 Review Exercises	474	(5)
Case 7 Medical Diagnosis	479	(2)
Counting, Probability Distributions, and Further Topics in Probability	481	(64)
Permutations and Combinations	481	(14)
Applications of Counting	495	(8)
Binomial Probability	503	(7)
Probability Distributions and Expected Value	510	(12)
Markov Chains	522	(12)
Decision Making	534	(11)
Chapter 9 Summary	538	(1)
Chapter 9 Review Exercises	539	(3)
Case 8 Optimal Inventory for a Service Truck	542	(3)
Introduction to Statistics	545	(52)
Frequency Distributions and Measures of Central Tendency	545	(15)
Measures of Variation	560	(10)
Normal Distributions	570	(13)
Normal Approximation to the Binomial Distribution	583	(14)
Chapter 10 Summary	590	(1)
Chapter 10 Review Exercises	591	(3)
Case 9 Statistics in the Law---The Castaneda Decision	594	(3)
Differential Calculus	597	(98)
Limits	597	(12)
Rates of Change	609	(12)
Tangent Lines and Derivatives	621	(16)
Techniques for Finding Derivatives	637	(13)
Derivatives of Products and Quotients	650	(8)
The Chain Rule	658	(12)
Derivatives of Exponential and Logarithmic Functions	670	(9)
Continuity and Differentiability	679	(16)
Chapter 11 Summary	687	(2)
Chapter 11 Review Exercises	689	(3)
Case 10 Price Elasticity of Demand	692	(3)
Applications of the Derivative	695	(56)
Derivatives and Graphs	695	(16)
The Second Derivative	711	(13)
Optimization Applications	724	(14)
Curve Sketching	738	(13)
Chapter 12 Summary	746	(1)
Chapter 12 Review Exercises	747	(2)
Case 11 A Total Cost Model for a Training Program	749	(2)
Integral Calculus	751	(70)
Antiderivatives	751	(10)
Integration by Substitution	761	(9)
Area and the Definite Integral	770	(12)
The Fundamental Theorem of Calculus	782	(11)
Applications of Integrals	793	(12)
Tables of Integrals (Optional)	805	(2)
Differential Equations	807	(14)
Chapter 13 Summary	815	(1)
Chapter 13 Review Exercises	816	(3)
Case 12 Bounded Population Growth	819	(2)
Multivariate Calculus	821	(34)
Functions of Several Variables	821	(12)
Partial Derivatives	833	(9)
Extrema of Functions of Several Variables	842	(13)
Chapter 14 Summary	851	(1)
Chapter 14 Review Exercises	852	(1)
Case 13 Global Warming and the Method of Least Squares	853	(2)
Appendix A Graphing Calculators	855	(2)
Appendix B Tables	857
Table 1: Formulas from Geometry	857	(1)
Table 2: Areas Under the Normal Curve	858	(2)
Table 3: Integrals	860
Answers to Selected Exercises	1	(1)
Index of Applications	1	(8)
Index	9