College Mathematics : Solving Problems in Finite Mathematics and Calculus

by Armstrong, Bill; Davis, Don

• ISBN13: 9780130891310
• ISBN10: 0130891312
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Pearson College Div

Summary

This book, modern in its writing style as well as in its applications, contains numerous exercises--both skill oriented and applications--, real data problems, and a problem solving method. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews. For anyone who wants to see and understand how mathematics are used in everyday life.

Table of Contents

Preface	xv
Linear Models and Systems of Linear Equations	1	(70)
Problem Solving: Linear Equations	2	(9)
Introduction to Linear Functions	11	(13)
Linear Models	24	(12)
Solving Systems of Linear Equations Graphically	36	(15)
Solving Systems of Linear Equations Algebraically	51	(20)
Chapter Review Exercises	65	(5)
Chapter 1 Project	70	(1)
Systems of Linear Equations and Matrices	71	(68)
Matrices and Gauss-Jordan	72	(13)
Matrices and Operations	85	(10)
Matrix Multiplication	95	(13)
Matrix Inverses and Solving Systems of Linear Equations	108	(15)
Leontief Input-Output Models	123	(16)
Chapter Review Exercises	131	(6)
Chapter 2 Project	137	(2)
Linear Programming: The Graphical Method	139	(52)
Problem Solving: Linear Inequalities	140	(11)
Graphing Systems of Linear Inequalities	151	(12)
Solving Linear Programming Problems Graphically	163	(10)
Applications of Linear Programming	173	(18)
Chapter Review Exercises	186	(4)
Chapter 3 Project	190	(1)
Linear Programming: The Simplex Method	191	(64)
Introduction to the Simplex Method	192	(13)
Simplex Method: Standard Maximum Form Problems	205	(15)
Simplex Method: Standard Minimum Form Problems and Duality	220	(14)
Simplex Method: Nonstandard Problems	234	(21)
Chapter Review Exercises	247	(6)
Chapter 4 Project	253	(2)
Mathematics of Finance	255	(52)
Simple Interest	256	(10)
Compound Interest	266	(14)
Future Value of an Annuity	280	(10)
Present Value of an Annuity	290	(17)
Chapter Review Exercises	302	(3)
Chapter 5 Project	305	(2)
Sets and the Fundamentals of Probability	307	(90)
Problem Solving: Probability and Statistics	308	(11)
Sets and Set Operations	319	(11)
Principles of Counting	330	(10)
Introduction to Probability	340	(13)
Computing Probabilities Using the Addition Rule	353	(12)
Computing Probabilities Using the Multiplication Rule	365	(11)
Bayes' Theorem and Its Applications	376	(21)
Chapter Review Exercises	389	(7)
Chapter 6 Project	396	(1)
Graphical Data Description	397	(64)
Graphing Qualitative Data	398	(14)
Graphing Quantitative Data	412	(16)
Measures of Centrality	428	(14)
Measures of Dispersion	442	(19)
Chapter Review Exercises	454	(5)
Chapter 7 Project	459	(2)
Probability Distributions	461	(64)
Discrete Random Variables	462	(13)
Expected Value and Standard Deviation of a Discrete Random Variable	475	(14)
The Binomial Distribution	489	(13)
The Normal Distribution	502	(23)
Chapter Review Exercises	519	(5)
Chapter 8 Project	524	(1)
Markov Chains	525	(42)
Introduction to Markov Chains	526	(12)
Regular Markov Chains	538	(11)
Absorbing Markov Chains	549	(18)
Chapter Review Exercises	562	(3)
Chapter 9 Project	565	(2)
Game Theory	567	(34)
Strictly Determined Games	568	(8)
Mixed Strategies	576	(10)
Game Theory and Linear Programming	586	(15)
Chapter Review Exercises	596	(4)
Chapter 10 Project	600	(1)
Functions, Models, and Average Rate of Change	601	(128)
The Coordinate System and Functions	602	(11)
Introduction to Problem Solving	613	(9)
Linear Functions and Average Rate of Change	622	(19)
Quadratic Functions and Average Rate of Change on an Interval	641	(11)
Operations on Functions	652	(18)
Rational, Radical, and Power Functions	670	(15)
Exponential Functions	685	(14)
Logarithmic Functions	699	(11)
Modeling Data with Functions (Optional Section---Requires Graphing Calculator)	710	(19)
Chapter Review Exercises	721	(7)
Chapter 11 Project	728	(1)
Limits, Instantaneous Rate of Change, and the Derivative	729	(96)
Limits	730	(13)
Limits and Asymptotes	743	(15)
Problem Solving: Rates of Change	758	(14)
The Derivative	772	(12)
Derivatives of Constants, Powers, and Sums	784	(13)
Derivatives of Products and Quotients	797	(11)
Continuity and Nondifferentiability	808	(17)
Chapter Review Exercises	818	(5)
Chapter 12 Project	823	(2)
Applications of the Derivative	825	(38)
The Differential and Linear Approximations	826	(9)
Marginal Analysis	835	(12)
Measuring Rates and Errors	847	(16)
Chapter Review Exercises	857	(4)
Chapter 13 Project	861	(2)
Additional Differentiation Techniques	863	(56)
The Chain Rule	864	(9)
Derivatives of Logarithmic Functions	873	(8)
Derivatives of Exponential Functions	881	(10)
Implicit Differentiation and Related Rates	891	(13)
Elasticity of Demand	904	(15)
Chapter Review Exercises	914	(3)
Chapter 14 Project	917	(2)
Further Applications of the Derivative	919	(80)
First Derivatives and Graphs	920	(17)
Second Derivatives and Graphs	937	(15)
Graphical Analysis and Curve Sketching	952	(13)
Optimizing Functions on a Closed Interval	965	(14)
The Second Derivative Test and Optimization	979	(20)
Chapter Review Exercises	992	(6)
Chapter 15 Project	998	(1)
Integral Calculus	999	(104)
The Indefinite Integral	1000	(13)
Area and the Definite Integral	1013	(12)
Fundamental Theorem of Calculus	1025	(8)
Problem Solving: Integral Calculus and Total Accumulation	1033	(13)
Integration by u-Substitution	1046	(11)
Integrals That Yield Logarithmic and Exponential Functions	1057	(13)
Differential Equations: Separation of Variables	1070	(10)
Differential Equations: Growth and Decay	1080	(23)
Chapter Review Exercises	1096	(5)
Chapter 16 Project	1101	(2)
Applications of Integral Calculus	1103	(92)
Average Value of a Function and the Definite Integral in Finance	1104	(14)
Area between Curves and Applications	1118	(14)
Economic Applications of Area between Two Curves	1132	(15)
Integration by Parts	1147	(13)
Numerical Integration	1160	(14)
Improper Integrals	1174	(21)
Chapter Review Exercises	1189	(5)
Chapter 17 Project	1194	(1)
Calculus of Several Variables	1195	(87)
Functions of Several Independent Variables	1196	(12)
Level Curves, Contour Maps, and Cross-sectional Analysis	1208	(14)
Partial Derivatives and Second-order Partial Derivatives	1222	(15)
Maxima and Minima	1237	(11)
Lagrange Multipliers	1248	(13)
Double Integrals	1261	(21)
Chapter Review Exercises	1275	(5)
Chapter 18 Project	1280	(2)
Appendix A Prerequisites	1282	(11)
A.1 Percents, Decimals, and Fractions	1282	(3)
A.2 Evaluating Expressions and Order of Operations	1285	(2)
A.3 Properties of Integer Exponents	1287	(4)
A.4 Rational Exponents and Radicals	1291	(2)
Appendix B Algebra Review	1293	(24)
B.1 Multiplying Polynomial Expressions	1293	(3)
B.2 Factoring Trinomials	1296	(5)
B.3 Solving Linear Equations	1301	(3)
B.4 Solving Quadratic Equations	1304	(5)
B.5 Properties of Logarithms	1309	(3)
B.6 Geometric Sequence and Series	1312	(5)
Appendix C Calculator Programs	1317	(9)
Appendix D Standard Normal Table	1326	(1)
Appendix E Selected Proofs	1327	(9)
Appendix F Photo and Illustration Credicts	1336
Answers to Odd-Numbered Exercises	1	(1)
Index	1

Excerpts

Audience In preparing to write the two components that comprise this text, we talked with many colleagues who teach finite mathematics and a brief or applied calculus course to find out if they experienced the same difficulties in teaching these subjects that we have encountered. What we learned is that while there is very little similarity in the topics covered or in how much time is spent on each area, there is remarkable uniformity in the needs of students who enroll in these diverse courses. Professors at Community Colleges, Universities, and Liberal Arts Colleges all told us that their students are generally unmotivated, unsure of their algebra skills, uncomfortable with translating English into mathematics, and unschooled in how to set up problems for solution. Armed with this knowledge, we preparedCollege Mathematics: Solving Problems in Finite Mathematics and Calculusto address these fundamental needs. As with other college mathematics textbooks, our text is designed for a two-term course for students majoring in economics, business, social or behavioral sciences. The book is organized into two parts. The first ten chapters cover the topics most frequently taught in a finite mathematics course. The second part of the book consists of eight chapters of applied calculus. We have organized the topics for maximum flexibility within each part so that the text may be adapted to any college or university's curriculum. However, that is where the similarity ends. We have crafted this book around six key principles designed to address student's needs: Present the mathematics in language that students can read and understand Teach good problem solving techniques and provide ample practice Use real data applications to keep it interesting Provide timely reinforcement of algebra and other essential skills Let Instructor's decide whether to incorporate technology Present Probability and Statistics with clarity and precision