Finite Mathematics and Calculus With Applications

by Lial, Margaret L.; Greenwell, Raymond N.; Miller, Charles D.

• ISBN13: 9780321016331
• ISBN10: 0321016335
• Edition: 5th
• Format: Hardcover
• Copyright: 1997-10-01
• Publisher: Pearson College Div

Summary

Widely known for incorporating interesting, relevant and realistic applications, this new edition offers many more real applications citing real data sources. It also allows for increased visualization and discovery through optional use of graphing calculators. A dedicated World Wide Web site rounds out the teaching and learning package, offering projects based on current events, and graphing calculator programs tied to the text.

Table of Contents

Preface	ix
Index of Applications	xv
Algebra Reference
Polynomials	xx
Factoring	xxiii
Rational Expressions	xxv
Equations	xxix
Inequalities	xxxv
Exponents	xl
Radicals	xliv
Linear Functions
Slope and Equations of a Line	2	(13)
Linear Functions	15	(12)
Linear Mathematical Models	27	(10)
Constructing a Mathematical Model	37	(19)
Review Exercises	49	(3)
Extended Application: Using Marginal Cost to Estimate the Cost of Educating Immigrants	52	(1)
Extended Application: Depreciation	53	(3)
Systems of Linear Equations and Matrices
Solution of Linear Systems by the Echelon Method	56	(10)
Solution of Linear Systems by the Gauss-Jordan Method	66	(13)
Addition and Subtraction of Matrices	79	(8)
Multiplication of Matrices	87	(11)
Matrix Inverses	98	(10)
Input-Output Models	108	(14)
Review Exercises	115	(5)
Extended Application:Contagion	120	(2)
Linear Programming:The Graphical Method
Graphing Linear Inequalities	122	(8)
Solving Linear Programming Problems Graphically	130	(6)
Applications of Linear Programming	136	(12)
Review Exercises	144	(4)
Linear Programming:The Simplex Method
Slack Variables and the Pivot	148	(8)
Maximization Problems	156	(10)
Minimization Problems; Duality	166	(11)
Nonstandard Problems	177	(15)
Review Exercises	186	(1)
Extended Application: A Minimum Cost Balanced Organic Fertilizer Mix	187	(5)
Mathematics of Finance
Simple and Compound Interest	192	(9)
Future Value of an Annuity	201	(9)
Present Value of an Annuity; Amortization	210	(18)
A Strategy for Solving Finance Problems	219	(1)
Review Exercises	220	(4)
Extended Application: Time, Money, and Polynomials	224	(4)
Sets and Probability
Sets	228	(9)
Applications of Venn Diagrams	237	(9)
Introduction to Probability	246	(8)
Basic Concepts of Probability	254	(11)
Conditional Probability; Independent Events	265	(16)
Bayes' Theorem	281	(17)
Probability Summary	288	(1)
Review Exercises	289	(6)
Extended Application: Medical Diagnosis	295	(3)
Counting Principles; Further Probability Topics
The Multiplication Principle; Permutations	298	(8)
Combinations	306	(9)
Probability Applications of Counting Principles	315	(10)
Binomial Probability	325	(7)
Probability Distributions; Expected Value	332	(18)
Review Exercises	343	(5)
Extended Application: Optimal Inventory for a Service Truck	348	(2)
Statistics
Frequency Distributions; Measures of Central Tendency	350	(12)
Measures of Variation	362	(8)
The Normal Distribution	370	(10)
Normal Approximation to the Binomial Distribution	380	(12)
Review Exercises	387	(5)
Markov Chains
Basic Properties of Markov Chains	392	(9)
Regular Markov Chains	401	(9)
Absorbing Markov Chains	410	(16)
Review Exercises	419	(4)
Extended Application: Cavities and Restoration	423	(3)
Game Theory
Strictly Determined Games	426	(8)
Mixed Strategies	434	(10)
Game Theory and Linear Programming	444	(14)
Review Exercises	451	(3)
Extended Application: Decision Making in the Military	454	(4)
Nonlinear Functions
Properties of Functions	458	(13)
Quadratic Functions	471	(8)
Translations and Reflections of Functions	479	(7)
Polynomial and Rational Functions	486	(14)
Exponential Functions	500	(11)
Logarithmic Functions	511	(14)
Applications: Growth and Decay; Mathematics of Finance	525	(23)
Review Exercises	538	(8)
Extended Application: Characteristics of the Monkeyface Prickleback	546	(2)
The Derivative
Limits	548	(17)
Continuity	565	(7)
Rates of Change	572	(14)
Definition of the Derivative	586	(18)
Graphical Differentiation	604	(12)
Review Exercises	610	(6)
Calculating the Derivative
Techniques for Finding Derivatives	616	(13)
Derivatives of Products and Quotients	629	(7)
The Chain Rule	636	(10)
Derivatives of Exponential Functions	646	(6)
Derivatives of Logarithmic Functions	652	(10)
Review Exercises	658	(4)
Graphs and the Derivative
Increasing and Decreasing Functions	662	(10)
Relative Extrema	672	(13)
Higher Derivatives, Concavity, and the Second Derivative Test	685	(14)
Curve Sketching	699	(13)
Review Exercises	707	(5)
Applications of the Derivative
Absolute Extrema	712	(8)
Applications of Extrema	720	(11)
Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand	731	(9)
Implicit Differentiation	740	(5)
Related Rates	745	(6)
Differentials: Linear Approximation	751	(13)
Review Exercises	757	(3)
Extended Application: A Total Cost Model for a Training Program	760	(1)
Extended Application: The Effect of Oil Price on the Optimal Speed of Ships	761	(3)
Integration
Antiderivatives	764	(11)
Substitution	775	(8)
Area and the Definite Integral	783	(13)
The Fundamental Theorem of Calculus	796	(10)
The Area Between Two Curves	806	(9)
Numerical Integration	815	(17)
Review Exercises	825	(4)
Extended Application: Estimating Depletion Dates for Minerals	829	(3)
Further Techniques and Applications of Integration
Integration by Parts; Tables of Integrals	832	(8)
Volume and Average Value	840	(6)
Continuous Money Flow	846	(8)
Improper Integrals	854	(5)
Solutions of Elementary and Separable Differential Equations	859	(19)
Review Exercises	871	(3)
Extended Application: How Much Does a Warranty Cost?	874	(4)
Multivariable Calculus
Functions of Several Variables	878	(11)
Partial Derivatives	889	(10)
Maxima and Minima	899	(9)
Lagrange Multipliers	908	(7)
Total Differentials and Approximations	915	(5)
Double Integrals	920	(20)
Review Exercises	932	(5)
Extended Application: Lagrange Multipliers for a Predator	937	(3)
Probability and Calculus
Continuous Probability Models	940	(7)
Expected Value and Variance of Continuous Random Variables	947	(6)
Special Probability Density Functions	953
Review Exercises	965	(3)
Extended Application: A Crop-Planting Model	968
Tables
Table 1: Formulas from Geometry	A-1
Table 2: Area Under a Normal Curve	A-3
Table 3: Integrals	A-5
Answers to Selected Exercises	A-7
Index	I-1