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

ISBN: 9780139157608 | 0139157603
Edition: 9th
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 7/1/1998

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SummaryTable of Contents
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 ... MORE
Prefacexi
0 Algebra Refresher
1(30)
0.1 Purpose
1(1)
... MORE
0.2 Sets and Real Numbers
1(2)
0.3 Some Properties of Real Numbers
3(4)
0.4 Operations with Real Numbers
7(2)
0.5 Exponents and Radicals
9(7)
0.6 Operations with Algebraic Expressions
16(5)
0.7 Factoring
21(2)
0.8 Fractions
23(8)
1 Equations
31(24)
1.1 Linear Equations
31(7)
1.2 Equations Leading to Linear Equations
38(4)
1.3 Quadratic Equations
42(7)
1.4 Supplement
49(1)
1.5 Review
50(2)
MATHEMATICAL SNAPSHOT: Real Growth of an Investment
52(3)
2 Applications of Equations and Inequalities
55(26)
2.1 Applications of Equations
55(8)
2.2 Linear Inequalities
63(5)
2.3 Applications of Inequalities
68(3)
2.4 Absolute Value
71(4)
2.5 Review
75(3)
MATHEMATICAL SNAPSHOT: Quality VCR Recording
78(3)
3 Functions and Graphs
81(38)
3.1 Functions
81(7)
3.2 Special Functions
88(4)
3.3 Combinations of Functions
92(4)
3.4 Graphs in Rectangular Coordinates
96(11)
3.5 Symmetry
107(4)
3.6 Translations and Reflections
111(3)
3.7 Review
114(3)
MATHEMATICAL SNAPSHOT: A Taxing Experience!
117(2)
4 Lines, Parabolas, and Systems
119(52)
4.1 Lines
119(8)
4.2 Applications and Linear Functions
127(7)
4.3 Quadratic Functions
134(8)
4.4 Systems of Linear Equations
142(11)
4.5 Nonlinear Systems
153(2)
4.6 Applications of Systems of Equations
155(9)
4.7 Review
164(3)
MATHEMATICAL SNAPSHOT: Anyone for Tennis?
167(4)
5 Exponential and Logarithmic Functions
171(38)
5.1 Exponential Functions
171(12)
5.2 Logarithmic Functions
183(7)
5.3 Properties of Logarithms
190(7)
5.4 Logarithmic and Exponential Equations
197(6)
5.5 Review
203(4)
MATHEMATICAL SNAPSHOT: Drug Dosages
207(2)
6 Matrix Algebra
209(76)
6.1 Matrices
209(7)
6.2 Matrix Addition and Scalar Multiplication
216(7)
6.3 Matrix Multiplication
223(13)
6.4 Method of Reduction
236(11)
6.5 Method of Reduction (Continued)
247(5)
6.6 Inverses
252(9)
6.7 Determinants
261(9)
6.8 Cramer's Rule
270(4)
6.9 Input-Output Analysis with a Graphics Calculator
274(4)
6.10 Review
278(4)
MATHEMATICAL SNAPSHOT: Insulin Requirements as a Linear Process
282(3)
7 Linear Programming
285(64)
7.1 Linear Inequalities in Two Variables
285(5)
7.2 Linear Programming
290(10)
7.3 Multiple Optimum Solutions
300(2)
7.4 The Simplex Method
302(12)
7.5 Degeneracy, Unbounded Solutions, Multiple Optimum Solutions
314(6)
7.6 Artificial Variables
320(10)
7.7 Minimization
330(5)
7.8 The Dual
335(8)
7.9 Review
343(4)
MATHEMATICAL SNAPSHOT: Drug and Radiation Therapies
347(2)
8 Mathematics of Finance
349(30)
8.1 Compound Interest
349(5)
8.2 Present Value
354(5)
8.3 Annuities
359(6)
8.4 Amortization of Loans
365(8)
8.5 Review
373(2)
MATHEMATICAL SNAPSHOT: The Rule of 78's
375(4)
9 Introduction to Probability and Statistics
379(76)
9.1 Basic Counting Principle and Permutations
379(7)
9.2 Combinations and Other Counting Principles
386(8)
9.3 Sample Spaces and Events
394(9)
9.4 Probability
403(11)
9.5 Conditional Probability and Stochastic Processes
414(14)
9.6 Independent Events
428(11)
9.7 Bayes' Formula
439(10)
9.8 Review
449(6)
10 Additional Topics in Probability
455(30)
10.1 Discrete Random Variables and Expected Value
455(8)
10.2 The Binomial Distribution
463(5)
10.3 Markov Chains
468(11)
10.4 Review
479(4)
MATHEMATICAL SNAPSHOT: Is the Price Right?
483(2)
11 Limits and Continvity
485(42)
11.1 Limits
485(10)
11.2 Limits (Continued)
495(10)
11.3 Interest Compounded Continuously
505(3)
11.4 Continuity
508(7)
11.5 Continuity Applied to Inequalities
515(5)
11.6 Review
520(4)
MATHEMATICAL SNAPSHOT: National Debt
524(3)
12 Differentiation
527(52)
12.1 The Derivative
527(9)
12.2 Rules for Differentiation
536(8)
12.3 The Derivative as a Rate of Change
544(11)
12.4 Differentiability and Continuity
555(1)
12.5 Product and Quotient Rules
556(10)
12.6 The Chain Rule and Power Rule
566(9)
12.7 Review
575(4)
13 Additional Differentiation Topics
579(26)
13.1 Derivatives of Logarithmic Functions
579(5)
13.2 Derivatives of Exponential Functions
584(6)
13.3 Implicit Differentiation
590(6)
13.4 Logarithmic Differentiation
596(3)
13.5 Higher-Order Derivatives
599(4)
13.6 Review
603(2)
14 Curve Sketching
605(38)
14.1 Relative Extrema
605(12)
14.2 Absolute Extrema on a Closed Interval
617(2)
14.3 Concavity
619(8)
14.4 The Second-Derivative Test
627(2)
14.5 Asymptotes
629(9)
14.6 Review
638(5)
15 Applications of Differentiation
643(32)
15.1 Applied Maxima and Minima
643(13)
15.2 Differentials
656(5)
15.3 Elasticity of Demand
661(6)
15.4 Newton's Method
667(4)
15.5 Review
671(4)
16 Integration
675(68)
16.1 The Indefinite Integral
675(6)
16.2 Integration with Initial Conditions
681(5)
16.3 More Integration Formulas
686(8)
16.4 Techniques of Integration
694(6)
16.5 Summation
700(3)
16.6 The Definite Integral
703(8)
16.7 The Fundamental Theorem of Integral Calculus
711(10)
16.8 Area
721(4)
16.9 Area Between Curves
725(8)
16.10 Consumers' and Producers' Surplus
733(3)
16.11 Review
736(5)
MATHEMATICAL SNAPSHOT: Delivered Price
741(2)
17 Methods and Applications of Integration
743(50)
17.1 Integration by Parts
743(5)
17.2 Integration by Partial Fractions
748(6)
17.3 Integration by Tables
754(6)
17.4 Average Value of a Function
760(2)
17.5 Approximate Integration
762(5)
17.6 Differential Equations
767(8)
17.7 More Applications of Differential Equations
775(7)
17.8 Improper Integrals
782(4)
17.9 Review
786(4)
MATHEMATICAL SNAPSHOT: Dieting
790(3)
18 Continuous Random Variables
793(20)
18.1 Continuous Random Variables
793(8)
18.2 The Normal Distribution
801(6)
18.3 The Normal Approximation to the Binomial Distribution
807(3)
18.4 Review
810(3)
19 Multivariable Calculus
813
19.1 Functions of Several Variables
813(6)
19.2 Partial Derivatives
819(7)
19.3 Applications of Partial Derivatives
826(6)
19.4 Implicit Partial Differentiation
832(3)
19.5 Higher-Order Partial Derivatives
835(2)
19.6 Chain Rule
837(4)
19.7 Maxima and Minima for Functions of Two Variables
841(10)
19.8 Lagrange Multipliers
851(8)
19.9 Lines of Regression
859(7)
19.10 A Comment on Homogeneous Functions
866(2)
19.11 Multiple Integrals
868(4)
19.12 Review
872(4)
MATHEMATICAL SNAPSHOT: Data Analysis to Model Cooling
876
Appendix A Concepts for CalculusA1(22)
A.1 Review: Slopes and Equations of LinesA1(2)
A.2 Secant Lines and Average Rate of ChangeA3(3)
A.3 Slope of a Curve and DerivativeA6(5)
A.4 Areas of Geometric ShapesA11(2)
A.5 Sigma NotationA13(2)
A.6 Riemann Sums and the Definite IntegralA15(5)
A.7 Area Under a Rate-of-Change CurveA20(3)
Appendix B Compound Interest TablesA23(15)
Appendix C Table of Selected IntegralsA38(4)
Appendix D Areas Under the Standard Normal CurveA42
Answers to Odd-Numbered ProblemsAn1
IndexI-1

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