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Applied Mathematics for the Managerial, Life, and Social Sciences With Infotrac,9780534419769
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Applied Mathematics for the Managerial, Life, and Social Sciences With Infotrac

by
Edition:
3rd
ISBN13:

9780534419769

ISBN10:
0534419763
Format:
Paperback
Pub. Date:
7/11/2003
Publisher(s):
Brooks Cole
List Price: $166.00

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Summary

1. FUNDAMENTALS OF ALGEBRA. Real Numbers. Polynomials. Factoring Polynomials. Rational Expressions. Integer Exponents. Solving Equations. Rational Exponents and Radicals. Quadratic Equations. Inequalities and Absolute Value. Chapter1 Summary and Review Exercises. 2. FUNCTIONS AND THEIR GRAPHS. The Cartesian Coordinate System and Straight Lines. Equations of Lines. Using Technology. Functions and Their Graphs. The Algebra of Functions. Linear Functions. Portfolio: Carol Busa. Using Technology. Quadratic Functions. Chapter 2 Summary and Review Exercises. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Using Technology. Logarithmic Functions. Exponential Functions as Mathematical Models. Chapter 3 Summary and Review Exercises. 4. MATHEMATICS OF FINANCE. Compound Interest. Using Technology. Annuities. Using Technology. Amortization and Sinking Funds. Portfolio: John Decker. Using Technology. Arithmetic and Geometric Progressions (Optional). Chapter 4 Summary and Review Exercises. 5. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations Introduction. Solving Systems of Linear Equations: Unique Solutions. Using Technology. Solving Systems of Linear Equations: Undetermined and Overdetermined Systems. Using Technology. Matrices. Using Technology. Multiplication of Matrices. Using Technology. The Inverse of a Square Matrix. Using Technology. Chapter 5 Summary and Review Exercises. 6. LINEAR PROGRAMMING. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Portfolio: Leanne Jenkins. Graphical Solution of Linear Programming Problems. The Simplex Method: Standard Maximization Problems. Using Technology. Portfolio: Harley Lance Kaplan. The Simplex Method: Standard Minimization Problems. Using Technology. Chapter 6 Summary and Review Exercises. 7. SETS AND PROBABILITY. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Portfolio: John Higgins. Permutations and Combinations. Using Technology. Experiments, Sample Spaces, and Events. Probability. Rules of Probability. Chapter 7 Summary and Review Exercises. 8. ADDITIONAL TOPICS IN PROBABILITY. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes' Theorem. Distributions of Random Variables. Using Technology. Expected Value. Portfolio: Lilli Meiselman. Variance and Standard Deviation. Using Technology. Chapter 8 Summary and Review Exercises. 9. THE DERIVATIVE. Limits. Using Technology. Portfolio: James H. Chesebro, M.D. Continuity. Using Technology. The Derivative. Using Technology. Basic Rules of Differentiation. Using Technology. The Product and Quotient Rules: Higher-Order Derivatives. Using Technology. The Chain Rule. Using Technology. Differentiation of Exponential and Logarithmic Functions. Using Technology. Marginal Functions in Economics. Chapter 9 Summary and Review Exercises. 10. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Using Technology. Applications of the Second Derivative. Using Technology. Curve Sketching. Using Technology. Optimization I. Using Technology. Optimization II. Chapter 10 Summary and Review Exercises. 11. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology. Evaluating Definite Integrals. Using Technology. Area Between Two Curves. Using Technology. Applications of the Definite Integral to Business and Economics. Using Technology. Chapter 11 Summary and Review Exercises. 12. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Using Technology. Maxima and Minima of Functions of Several Variables. Chapter 12 Summary and Review Exercises. Answers to Selected Exercises. Index.

Table of Contents

Preface ix
CHAPTER 1 Fundamentals of Algebra 2(68)
1.1 Real Number's
3(6)
1.2 Polynomials
9(8)
1.3 Factoring Polynomials
17(5)
1.4 Rational Expressions
22(7)
1.5 Integral Exponents
29(4)
1.6 Solving Equations
33(6)
1.7 Rational Exponents and Radicals
39(9)
1.8 Quadratic Equations
48(9)
1.9 Inequalities and Absolute Value
57(13)
Chapter 1 Summary of Principal Formulas Terms
67(1)
Chapter 1 Review Exercises
68(2)
CHAPTER 2 Functions and Their Graphs 70(91)
2.1 The Cartesian Coordinate System and Straight Lines
71(7)
2.2 Equations of Lines
78(14)
Using Technology: Graphing a straight Line
88(4)
2.3 Functions and Their Graphs
92(18)
Using Technology: Graphing a Function
104(6)
2.4 The Algebra of Functions
110(9)
PORTFOLIO: Michael Marchlik
115(4)
2.5 Linear Functions
119(14)
PORTFOLIO: Carol Busa
123(5)
Using Technology: Linear Functions
128(5)
2.6 Quadratic Functions
133(11)
Using Technology: Finding the Points of Intersection of Two Graphs
142(2)
2.7 Functions and Mathematical Models
144(17)
Using Technology: Constructing Mathematical Models from Raw Data
154(4)
Chapter 2 Summary of Principal Formulas and Terms
158(1)
Chapter 2 Review Exercises
159(2)
CHAPTER 3 Exponential and Logarithmic Functions 161(31)
3.1 Exponential Functions
162(8)
Using Technology
168(2)
3.2 Logarithmic Functions
170(9)
3.3 Exponential Functions as Mathematical Models
179(13)
Using Technology: Analyzing Mathematical Models
188(2)
Chapter 3 Summary of Principal Formulas and Terms
190(1)
Chapter 3 Review Exercises
190(2)
CHAPTER 4 Mathematics of Finance 192(58)
4.1 Compound Interest
193(20)
Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment
208(5)
4.2 Annuities
213(12)
Using Technology: Finding the Amount of an Annuity
222(3)
4.3 Amortization and Sinking Funds
225(13)
PORTFOLIO: John Decker
230(4)
Using Technology: Amortizing a Loan
234(4)
4.4 Arithmetic and Geometric Progressions (Optional)
238(12)
Chapter 4 Summary of Principal Formulas and Terms
247(1)
Chapter 4 Review Exercises
247(3)
CHAPTER 5 Systems of Linear Equations and Matrices 250(87)
5.1 Systems of Linear Equations: An Introduction
251(8)
5.2 Systems of Linear Equations: Unique Solutions
259(17)
Using Technology: Systems of Linear Equations: Unique Solutions
272(4)
5.3 Systems of Linear Equations: Underdetermined and Overdetermined systems
276(12)
Using Technology: Systems of Linear Equations: Underdetermined and Overdetermined Systems
286(2)
5.4 Matrices
288(13)
Using Technology: Matrix Operations
296(5)
5.5 Multiplication of Matrices
301(16)
Using Technology: Matrix Multiplication
312(5)
5.6 The Inverse of a Square Matrix
317(20)
Using Technology: Finding the Inverse of a Square Matrix
330(4)
Chapter 5 Summary of Principal Formulas and Terms
334(1)
Chapter 5 Review Exercises
335(2)
CHAPTER 6 Linear Programming 337(80)
6.1 Graphing Systems of Linear Inequalities in Two Variables
338(8)
6.2 Linear Programming Problems
346(10)
PORTFOLIO: Leanne Jenkins
351(5)
6.3 Graphical Solution of Linear Programming Problems
356(13)
6.4 The Simplex Method: Standard Maximization Problems
369(28)
PORTFOLIO: Harley Lance Kaplan
385(5)
Using Technology: The Simplex Method: Solving Maximization Problems
390(7)
6.5 The Simplex Method: Standard Minimization Problems
397(20)
Using Technology: The Simplex Method: Solving Minimization Problems
408(6)
Chapter 6 Summary of Principal Terms
414(1)
Chapter 6 Review Exercises
415(2)
CHAPTER 7 Sets and Probability 417(73)
7.1 Sets and Set Operations
418(11)
7.2 The Number of Elements in a Finite Set
429(7)
7.3 The Multiplication Principle
436(7)
PORTFOLIO: John L. Higgins
440(3)
7.4 Permutations and Combinations
443(16)
Using Technology: Evaluating n!, P(n, r), and C(n, r)
454(5)
7.5 Experiments, Sample Spaces, and Events
459(9)
7.6 Probability
468(9)
7.7 Rules of Probability
477(13)
Chapter 7 Summary of Principal Formulas and Terms
485(2)
Chapter 7 Review Exercises
487(3)
CHAPTER 8 Additional Topics in Probability 490(72)
8.1 Use of Counting Techniques in Probability
491(8)
8.2 Conditional Probability and Independent Events
499(14)
8.3 Bayes' Theorem
513(9)
8.4 Distribution of Random Variables
522(12)
Using Technology: Graphing a Histogram
530(4)
8.5 Expected Value
534(11)
8.6 Variance and Standard Deviation
545(17)
PORTFOLIO: Lilli Meiselman
546(10)
Using Technology: Finding the Mean and Standard Deviation
556(3)
Chapter 8 Summary of Principal Formulas and Terms
559(1)
Chapter 8 Review Exercises
560(2)
CHAPTER 9 The Derivative 562(136)
9.1 Limits
563(22)
Using Technology: Finding the Limit of a Function
580(4)
PORTFOLIO: James H. Chesebro, M.D.
584(1)
9.2 Continuity
585(18)
Using Technology: Finding the Points of Discontinuity of a Function
598(5)
9.3 The Derivative
603(21)
Using Technology: Graphing a Function and Its Tangent Line
618(6)
9.4 Basic Rules of Differentiation
624(14)
Using Technology: Finding the Rate of Change of a Function
634(4)
9.5 The Product and Quotient Rules: Higher-Order Derivatives
638(18)
Using Technology: The Product and Quotient Rule; Finding the Second Derivative of a Function at a Given Point
652(4)
9.6 The Chain Rule
656(14)
Using Technology: Finding the Derivative of a Composite Function
668(2)
9.7 Differentiation of Exponential and Logarithmic Functions
670(13)
Using Technology
680(3)
9.8 Marginal Functions in Economics
683(15)
Chapter 9 Summary of Principal Formulas and Terms
693(2)
Chapter 9 Review Exercises
695(3)
CHAPTER 10 Applications of the Derivative 698(84)
10.1 Applications of the First Derivative
699(21)
Using Technology: Using the First Derivative to Analyze a Function
716(4)
10.2 Applications of the Second Derivative
720(17)
Using Technology: Finding the Inflection Points of a Function
734(3)
10.3 Curve sketching
737(15)
Using Technology: Analyzing the Properties of a Function
748(4)
10.4 Optimization I
752(16)
PORTFOLIO: Misato Nakazaki
760(4)
Using Technology: Finding the Absolute Extrema of a Function
764(4)
10.5 Optimization II
768(14)
Chapter 10 Summary of Principal Terms
779(1)
Chapter 10 Review Exercises
780(2)
CHAPTER 11 Integration 782(89)
11.1 Antiderivatives and the Rules of Integration
783(14)
11.2 Integration by Substitution
797(10)
11.3 Area and the Definite Integral
807(10)
11.4 The Fundamental Theorem of Calculus
817(10)
Using Technology: Evaluating Definite Integrals
826(1)
11.5 Evaluating Definite Integrals
827(12)
Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions
836(3)
11.6 Area between Two Curves
839(14)
Using Technology: Finding the Area between Two Curves
850(3)
11.7 Applications of the Definite Integral to Business and Economics
853(18)
Using Technology: Business and Economic Applications/Technology Exercises
866(1)
Chapter 11 Summary of Principal Formulas and Terms
867(1)
Chapter 11 Review Exercises
868(3)
CHAPTER 12 Calculus of Several Variables 871(39)
12.1 Functions of Several Variables
872(10)
12.2 Partial Derivatives
882(15)
Using Technology: Finding Partial Derivatives at a Given Point
894(3)
12.3 Maxima and Minima of Functions of Several Variables
897(13)
Chapter 12 Summary of Principal Terms
908(1)
Chapter 12 Review Exercises
908(2)
Answers to Odd-Numbered Exercises 910(55)
Index 965


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