Applied Mathematics for the Managerial, Life, and Social Sciences (with InfoTrac)

by Tan, S. T.

• ISBN13: 9780534419769
• ISBN10: 0534419763
• Edition: 3rd
• Format: Hardcover
• Copyright: 2003-07-11
• Publisher: Brooks Cole

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