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

ISBN: 9780131139480 | 0131139487
Edition: 12th
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2008

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SummaryTable of Contents
For courses in Mathematics for Business and Mathematical Methods in Business. This classic text continues to provide a mathematical foundation for students in business, economics, and the life and social sciences. Abundant applications cover such diverse areas as business, economics, biology, medicine, sociology, psychology, ecology, statistics, earth science, and archaeology. Its depth and completeness of coverage enables instructors to tailor their courses to students' needs. The authors frequently employ novel derivations that are not widesp... MORE
... MORE
Prefaceix
CHAPTER 0 Algebra Refresher1(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 Inequalities50(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 Graphs76(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 Systems122(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 Fine176(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 Finance216(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 Algebra248(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 Programming310(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 Statistics382(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 Probability466(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 Continuity496(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 Differentiation536(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 Topics590(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 Sketching632(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 Integration766(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 Variables812(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 Calculus834(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 Calculus901(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 Tables953(16)
Appendix C Table of Selected Integrals969(4)
Appendix D Areas Under the Standard Normal Curve973
Answers to Odd-Numbered ProblemsAN1
IndexI-1
Photo CreditsP-1

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