Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences

by Haeussler, Ernest F.; Paul, Richard S.; Wood, Richard J.

• ISBN13: 9780131139480
• ISBN10: 0131139487
• Edition: 11th
• Format: Hardcover
• Copyright: 2008-01-01
• Publisher: Prentice Hall

Summary

This classic book continues to provide a foundation for mathematical literacy in business, economics, and the life and social sciences.& Covers concepts ranging from introductory equations and functions through curve sketching, integration, and multivariable calculus. Helps readers connect concepts with the world around them through genuine applications, covering such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology. Updates exercises, problems, and Mathematical Snapshots throughout. Improves writing style and mathematical derivations without sacrificing the book's signature flavor.& For anyone interested in learning more about introductory mathematical analysis.

Table of Contents

Preface	ix
CHAPTER 0 Algebra Refresher	1	(49)
0.1 Sets of Real Numbers	2	(1)
0.2 Some Properties of Real Numbers	3	(7)
0.3 Exponents and Radicals	10	(6)
0.4 Operations with Algebraic Expressions	16	(5)
0.5 Factoring	21	(3)
0.6 Fractions	24	(6)
0.7 Linear Equations	30	(11)
0.8 Quadratic Equations	41	(7)
Mathematical SNAPSHOT: Modeling Load Cell Behavior	48	(2)
CHAPTER 1 Applications of Equations and Inequalities	50	(26)
1.1 Applications of Equations	51	(8)
1.2 Linear Inequalities	59	(5)
1.3 Applications of Inequalities	64	(4)
1.4 Absolute Value	68	(4)
1.5 Review	72	(2)
Mathematical SNAPSHOT: Variable-Quality Recording	74	(2)
CHAPTER 2 Functions and Graphs	76	(46)
2.1 Functions	77	(8)
2.2 Special Functions	85	(4)
2.3 Combinations of Functions	89	(6)
2.4 Inverse Functions	95	(3)
2.5 Graphs in Rectangular Coordinates	98	(10)
2.6 Symmetry	108	(6)
2.7 Translations and Reflections	114	(3)
2.8 Review	117	(3)
Mathematical SNAPSHOT: A Taxing Experience!	120	(2)
CHAPTER 3 Lines, Parabolas and Systems	122	(54)
3.1 Lines	123	(9)
3.2 Applications and Linear Functions	132	(7)
3.3 Quadratic Functions	139	(8)
3.4 Systems of Linear Equations	147	(12)
3.5 Nonlinear Systems	159	(2)
3.6 Applications of Systems of Equations	161	(9)
3.7 Review	170	(4)
Mathematical SNAPSHOT: Wireless Phone Billing Plans	174	(2)
CHAPTER 4 Exponential and Logarithmic Fine	176	(40)
4.1 Exponential Functions	177	(13)
4.2 Logarithmic Functions	190	(7)
4.3 Properties of Logarithms	197	(7)
4.4 Logarithmic and Exponential Equations	204	(6)
4.5 Review	210	(4)
Mathematical SNAPSHOT: Drug Dosages	214	(2)
CHAPTER 5 Mathematics of Finance	216	(32)
5.1 Compound Interest	217	(5)
5.2 Present Value	222	(5)
5.3 Annuities	227	(11)
5.4 Amortization of Loans	238	(5)
5.5 Review	243	(3)
Mathematical SNAPSHOT: Treasury Securities	246	(2)
CHAPTER 6 Matrix Algebra	248	(62)
6.1 Matrices	249	(7)
6.2 Matrix Addition and Scalar Multiplication	256	(7)
6.3 Matrix Multiplication	263	(12)
6.4 Solving Systems by Reducing Matrices	275	(11)
6.5 Solving Systems by Reducing Matrices (continued)	286	(5)
6.6 Inverses	291	(10)
6.7 Leontief's Input-Output Analysis	301	(4)
6.8 Review	305	(3)
Mathematical SNAPSHOT: Insulin Requirements as a Linear Process	308	(2)
CHAPTER 7 Linear Programming	310	(72)
7.1 Linear Inequalities in Two Variables	311	(4)
7.2 Linear Programming	315	(12)
7.3 Multiple Optimum Solutions	327	(2)
7.4 The Simplex Method	329	(14)
7.5 Degeneracy, Unbounded Solutions, and Multiple Optimum Solutions	343	(6)
7.6 Artificial Variables	349	(11)
7.7 Minimization	360	(6)
7.8 The Dual	366	(10)
7.9 Review	376	(4)
Mathematical SNAPSHOT: Drug and Radiation Therapies	380	(2)
CHAPTER 8 Introduction to Probability and Statistics	382	(84)
8.1 Basic Counting Principle and Permutations	383	(7)
8.2 Combinations and Other Counting Principles	390	(12)
8.3 Sample Spaces and Events	402	(9)
8.4 Probability	411	(12)
8.5 Conditional Probability and Stochastic Processes	423	(14)
8.6 Independent Events	437	(11)
8.7 Bages's Formula	448	(10)
8.8 Review	458	(6)
Mathematical SNAPSHOT: Probability and Cellular Automata	464	(2)
CHAPTER 9 Additional Topics in Probability	466	(30)
9.1 Discrete Random Variables and Expected Value	467	(8)
9.2 The Binomial Distribution	475	(5)
9.3 Markov Chains	480	(11)
9.4 Review	491	(3)
Mathematical SNAPSHOT: Markov Chains in Game Theory	494	(2)
CHAPTER 10 Limits and Continuity	496	(40)
10.1 Limits	497	(10)
10.2 Limits (Continued)	507	(9)
10.3 Interest Compounded Continuously	516	(4)
10.4 Continuity	520	(7)
10.5 Continuity Applied to Inequalities	527	(4)
10.6 Review	531	(3)
Mathematical SNAPSHOT: National Debt	534	(2)
CHAPTER 11 Differentiation	536	(54)
11.1 The Derivative	537	(8)
11.2 Rules for Differentiation	545	(8)
11.3 The Derivative as a Rate of Change	553	(10)
11.4 Differentiability and Continuity	563	(2)
11.5 Product and Quotient Rules	565	(10)
11.6 The Chain Rule and the Power Rule	575	(9)
11.7 Review	584	(4)
Mathematical SNAPSHOT: Marginal Propensity to Consume	588	(2)
CHAPTER 12 Additional Differentiation Topics	590	(42)
12.1 Derivatives of Logarithmic Functions	591	(5)
12.2 Derivatives of Exponential Functions	596	(6)
12.3 Elasticity of Demand	602	(6)
12.4 Implicit Differentiation	608	(6)
12.5 Logarithmic Differentiation	614	(4)
12.6 Newton's Method	618	(5)
12.7 Higher-Order Derivatives	623	(4)
12.8 Review	627	(3)
Mathematical SNAPSHOT: Population Change over Time	630	(2)
CHAPTER 13 Curve Sketching	632	(54)
13.1 Relative Extrema	633	(11)
13.2 Absolute Extrema on a Closed interval	644	(3)
13.3 Concavity	647	(7)
13.4 The Second-Derivative Test	654	(2)
13.5 Asymptotes	656	(9)
13.6 Applied Maxima and Minima	665	(14)
13.7 Review	679	(5)
Mathematical SNAPSHOT: Sketching the Phillips Curve	684	(2)
CHAPTER 14 Integration	686	(80)
14.1 Differentials	687	(5)
14.2 The Indefinite Integral	692	(7)
14.3 Integration with Initial Conditions	699	(5)
14.4 More Integration Formulas	704	(8)
14.5 Techniques of Integration	712	(5)
14.6 Summation	717	(3)
14.7 The Definite Integral	720	(8)
14.8 The Fundamental Theorem of Integral Calculus	728	(10)
14.9 Approximate Integration	738	(6)
14.10 Area	744	(4)
14.11 Area between Curves	748	(8)
14.12 Consumers' and Producers' Surplus	756	(3)
14.13 Review	759	(5)
Mathematical SNAPSHOT: Delivered Price	764	(2)
CHAPTER 15 Methods and Applications of Integration	766	(46)
15.1 Integration by Parts	767	(4)
15.2 Integration by Partial Fractions	771	(7)
15.3 Integration by Tables	778	(7)
15.4 Average Value of a Function	785	(2)
15.5 Differential Equations	787	(8)
15.6 More Applications of Differential Equations	795	(7)
15.7 Improper Integrals	802	(4)
15.8 Review	806	(4)
Mathematical SNAPSHOT: Dieting	810	(2)
CHAPTER 16 Continuous Random Variables	812	(22)
16.1 Continuous Random Variables	813	(7)
16.2 The Normal Distribution	820	(6)
16.3 The Normal Approximation to the Binomial Distribution	826	(4)
16.4 Review	830	(2)
Mathematical SNAPSHOT: Cumulative Distribution from Data	832	(2)
CHAPTER 17 Multivariable Calculus	834	(67)
17.1 Functions of Several Variables	835	(6)
17.2 Partial Derivatives	841	(6)
17.3 Applications of Partial Derivatives	847	(7)
17.4 Implicit Partial Differentiation	854	(2)
17.5 Higher-Order Partial Derivatives	856	(3)
17.6 Chain Rule	859	(4)
17.7 Maxima and Minima for Functions of Two Variables	863	(10)
17.8 Lagrange Multipliers	873	(8)
17.9 Lines of Regression	881	(7)
17.10 A Comment on Homogeneous Functions	888	(2)
17.11 Multiple Integrals	890	(4)
17.12 Review	894	(4)
Mathematical SNAPSHOT: Data Analysis to Model Cooling	898	(3)
Appendix A Concepts for Calculus	901	(52)
A.1 Interpreting Graphs	902	(5)
A.2 Modeling	907	(6)
A.3 Average Rate of Change	913	(5)
A.4 Instantaneous Rate of Change: The Derivative	918	(6)
A.5 Area under A Curve	924	(4)
A.6 Sigma Notation	928	(5)
A.7 Areas and Integrals	933	(7)
A.8 Applications of Derivatives and Integrals	940	(9)
A.9 Review	949	(4)
Appendix B Compound Interest Tables	953	(16)
Appendix C Table of Selected Integrals	969	(4)
Appendix D Areas Under the Standard Normal Curve	973
Answers to Odd-Numbered Problems	AN1
Index	I-1
Photo Credits	P-1