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

by Haeussler, Ernest F.

• ISBN13: 9780130338556
• ISBN10: 0130338559
• Edition: 10th
• Format: Hardcover
• Copyright: 2001-07-01
• Publisher: PRENTICE HALL

Summary

An introductory textbook beginning with noncalculus topics such as equations, functions, matrix algebra, linear programming, mathematics of finance, and probability, then progressing through both single and multivariable calculus, including continuous random variables.

Table of Contents

Preface	ix
Algebra Refresher	1	(34)
Purpose	2	(1)
Sets and Real Numbers	2	(1)
Some Properties of Real Numbers	3	(4)
Operations with Real Numbers	7	(3)
Exponents and Radicals	10	(8)
Operations with Algebraic Expressions	18	(5)
Factoring	23	(3)
Fractions	26	(9)
Mathematical Snapshot: Modeling Load Cell Behavior	33	(2)
Equations	35	(26)
Linear Equations	36	(7)
Equations Leading to Linear Equations	43	(4)
Quadratic Equations	47	(8)
Supplement	55	(1)
Review	56	(5)
Mathematical Snapshot: Real Growth of an Investment	58	(3)
Applications of Equations and Inequalities	61	(26)
Applications of Equations	62	(8)
Linear Inequalities	70	(5)
Applications of Inequalities	75	(4)
Absolute Value	79	(4)
Review	83	(4)
Mathematical Snapshot: Variable-Quality Recording	85	(2)
Functions and Graphs	87	(40)
Functions	88	(7)
Special Functions	95	(4)
Combinations of Functions	99	(5)
Graphs in Rectangular Coordinates	104	(11)
Symmetry	115	(5)
Translations and Reflections	120	(2)
Review	122	(5)
Mathematical Snapshot: A Taxing Experience!	125	(2)
Lines, Parabolas, and Systems	127	(54)
Lines	128	(8)
Applications and Linear Functions	136	(8)
Quadratic Functions	144	(8)
Systems of Linear Equations	152	(11)
Nonlinear Systems	163	(3)
Applications of Systems of Equations	166	(10)
Review	176	(5)
Mathematical Snapshot: Wireless Phone Billing Plans	179	(2)
Exponential and Logarithmic Functions	181	(42)
Exponential Functions	182	(13)
Logarithmic Functions	195	(7)
Properties of Logarithms	202	(8)
Logarithmic and Exponential Equations	210	(6)
Review	216	(7)
Mathematical Snapshot: Drug Dosages	220	(3)
Matrix Algebra	223	(78)
Matrices	224	(7)
Matrix Addition and Scalar Multiplication	231	(8)
Matrix Multiplication	239	(13)
Method of Reduction	252	(10)
Method of Reduction (Continued)	262	(6)
Inverses	268	(9)
Determinants	277	(9)
Cramer's Rule	286	(5)
Input-Output Analysis with a Graphics Calculator	291	(4)
Review	295	(6)
Mathematical Snapshot: Insulin Requirements as a Linear Process	298	(3)
Linear Programming	301	(66)
Linear Inequalities in Two Variables	302	(5)
Linear Programming	307	(10)
Multiple Optimum Solutions	317	(2)
The Simplex Method	319	(13)
Degeneracy, Unbounded Solutions, and Multiple Optimum Solutions	332	(6)
Artificial Variables	338	(11)
Minimization	349	(5)
The Dual	354	(8)
Review	362	(5)
Mathematical Snapshot: Drug and Radiation Therapies	365	(2)
Mathematics of Finance	367	(30)
Compound Interest	368	(5)
Present Value	373	(5)
Annuities	378	(10)
Amortization of Loans	388	(5)
Review	393	(4)
Mathematical Snapshot: Treasury Securities	395	(2)
Introduction to Probability and Statistics	397	(82)
Basic Counting Principle and Permutations	398	(8)
Combinations and Other Counting Principles	406	(8)
Sample Spaces and Events	414	(9)
Probability	423	(12)
Conditional Probability and Stochastic Processes	435	(15)
Independent Events	450	(11)
Bayes's Formula	461	(10)
Review	471	(8)
Mathematical Snapshot: Probability and Cellular Automata	477	(2)
Additional Topics in Probability	479	(32)
Discrete Random Variables and Expected Value	480	(8)
The Binomial Distribution	488	(5)
Markov Chains	493	(12)
Review	505	(6)
Mathematical Snapshot: Markov Chains in Game Theory	508	(3)
Limits and Continuity	511	(44)
Limits	512	(11)
Limits (Continued)	523	(10)
Interest Compounded Continuously	533	(3)
Continuity	536	(8)
Continuity Applied to Inequalities	544	(4)
Review	548	(7)
Mathematical Snapshot: National Debt	552	(3)
Differentiation	555	(58)
The Derivative	556	(9)
Rules for Differentiation	565	(8)
The Derivative as a Rate of Change	573	(11)
Differentiability and Continuity	584	(2)
Product and Quotient Rules	586	(11)
The Chain Rule and the Power Rule	597	(9)
Review	606	(7)
Mathematical Snapshot: Marginal Propensity to Consume	611	(2)
Additional Differentiation Topics	613	(32)
Derivatives of Logarithmic Functions	614	(5)
Derivatives of Exponential Functions	619	(6)
Implicit Differentiation	625	(7)
Logarithmic Differentiation	632	(3)
Higher-Order Derivatives	635	(4)
Review	639	(6)
Mathematical Snapshot: Population Change over Time	642	(3)
Curve Sketching	645	(42)
Relative Extrema	646	(11)
Absolute Extrema on a Closed Interval	657	(3)
Concavity	660	(8)
The Second-Derivative Test	668	(2)
Asymptotes	670	(10)
Review	680	(7)
Mathematical Snapshot: Sketching the Phillips Curve	684	(3)
Applications of Differentiation	687	(36)
Applied Maxima and Minima	688	(13)
Differentials	701	(6)
Elasticity of Demand	707	(5)
Newton's Method	712	(5)
Review	717	(6)
Mathematical Snapshot: Economic Order Quantity	720	(3)
Integration	723	(74)
The Indefinite Integral	724	(7)
Integration with Initial Conditions	731	(5)
More Integration Formulas	736	(9)
Techniques of Integration	745	(6)
Summation	751	(3)
The Definite Integral	754	(9)
The Fundamental Theorem of Integral Calculus	763	(11)
Area	774	(4)
Area Between Curves	778	(8)
Consumers' and Producers' Surplus	786	(3)
Review	789	(8)
Mathematical Snapshot: Delivered Price	794	(3)
Methods and Applications of Integration	797	(54)
Integration by Parts	798	(5)
Integration by Partial Fractions	803	(7)
Integration by Tables	810	(6)
Average Value of a Function	816	(3)
Approximate Integration	819	(5)
Differential Equations	824	(8)
More Applications of Differential Equations	832	(8)
Improper Integrals	840	(4)
Review	844	(7)
Mathematical Snapshot: Dieting	848	(3)
Continuous Random Variables	851	(24)
Continuous Random Variables	852	(8)
The Normal Distribution	860	(6)
The Normal Approximation to the Binomial Distribution	866	(4)
Review	870	(5)
Mathematical Snapshot: Cumulative Distribution from Data	873	(2)
Multivariable Calculus	875	(68)
Functions of Several Variables	876	(6)
Partial Derivatives	882	(7)
Applications of Partial Derivatives	889	(7)
Implicit Partial Differentiation	896	(3)
Higher-Order Partial Derivatives	899	(3)
Chain Rule	902	(4)
Maxima and Minima for Functions of Two Variables	906	(10)
Lagrange Multipliers	916	(8)
Lines of Regression	924	(7)
A Comment on Homogeneous Functions	931	(2)
Multiple Integrals	933	(4)
Review	937	(6)
Mathematical Snapshot: Data Analysis to Model Cooling	941	(2)
Appendix A Concepts for Calculus	943	(56)
A.1 Interpreting Graphs	944	(6)
A.2 Modeling	950	(6)
A.3 Average Rate of Change	956	(6)
A.4 Instantaneous Rate of Change: The Derivative	962	(6)
A.5 Area Under a Curve	968	(5)
A.6 Sigma Notation	973	(4)
A.7 Areas and Integrals	977	(9)
A.8 Applications of Derivatives and Integrals	986	(8)
A.9 Review	994	(5)
Appendix B Compound Interest Tables	999	(16)
Appendix C Table of Selected Integrals	1015	(4)
Appendix D Areas Under the Standard Normal Curve	1019
Answers to Odd-Numbered Problems	An1
Index	I1
Photo Credits	I8