Fully worked solutions to odd-numbered exercises.
Raymond A. Barnett, a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern University; Charles Burke, City College of San Francisco; John Fuji, Merritt College; and Karl Byleen, Marquette University.
Michael R. Ziegler received his B.S. from Shippensburg StateCollege and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler has published over a dozen research articles in complex analysis and has co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen.
Karl E. Byleen received the B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.
Why We wrote This Book:
This text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible. We emphasize computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed. Graphing calculators and computers are playing an increasing role in mathematics education and in real-world applications of mathematics. This books deals with the mathematics that is required to use modern technology effectively as an OPTIONAL feature. In appropriate places in the text, there are clearly identified examples and exercises related to graphing calculators and computers, illustrations of applications of spreadsheets, and sample computer output. All of these may be omitted without loss of continuity.
PART 1 A LIBRARY OF ELEMENTARY FUNCTIONS
1 Linear Equations and Graphs
1-1 Linear Equations and Inequalities
1-2 Graphs and Lines
1-3 Linear Regression
Chapter 1 Review
Review Exercise
2 Functions and Graphs
2-1 Functions
2-2 Elementary Functions: Graphs and Transformations
2-3 Quadratic Functions
2-4 Exponential Functions
2-5 Logarithmic Functions
Chapter 2 Review
Review Exercise
PART 2 FINITE MATHEMATICS
3 Mathematics of Finance
3-1 Simple Interest
3-2 Compound and Continuous Compound Interest
3-3 Future Value of an Annuity; Sinking Funds
3-4 Present Value of an Annuity; Amortization
Chapter 3 Review
Review Exercise
4 Systems of Linear Equations; Matrices
4-1 Review: Systems of Linear Equations in Two Variables
4-2 Systems of Linear Equations and Augmented Matrices
4-3 Gauss—Jordan Elimination
4-4 Matrices: Basic Operations
4-5 Inverse of a Square Matrix
4-6 Matrix Equations and Systems of Linear Equations
4-7 Leontief Input—Output Analysis
Chapter 2 Review
Review Exercise
5 Linear Inequalities and Linear Programming
5-1 Inequalities in Two Variables
5-2 Systems of Linear Inequalities in Two Variables
5-3 Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Review
Review Exercise
6 Linear Programming: Simplex Method
6-1 A Geometric Introduction to the Simplex Method
6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≤
6-3 The Dual Problem; Minimization with Problem Constraints of the Form ≥
6-4 Maximization and Minimization with Mixed Problem Constraints
Chapter 6 Review
Review Exercise
7 Logic, Sets, and Counting
7-1 Logic
7-2 Sets
7-3 Basic Counting Principles
7-4 Permutations and Combinations
Chapter 7 Review
Review Exercise
8 Probability
8-1 Sample Spaces, Events, and Probability
8-2 Union, Intersection, and Complement of Events; Odds
8-3 Conditional Probability, Intersection, and Independence
8-4 Bayes’ Formula
8-5 Random Variable, Probability Distribution, and Expected Value
Chapter 8 Review
Review Exercise
9 Markov Chains
9-1 Properties of Markov Chains
9-2 Regular Markov Chains
9-3 Absorbing Markov Chains
Chapter 9 Review
Review Exercise
PART 3 CALCULUS
10 Limits and the Derivative
10-1 Introduction to Limits
10-2 Continuity
10-3 Infinite Limits and Limits at Infinity
10-4 The Derivative
10-5 Basic Differentiation Properties
10-6 Differentials
10-7 Marginal Analysis in Business and Economics
Chapter 10 Review
Review Exercise
11 Additional Derivative Topics
11-1 The Constant e and Continuous Compound Interest
11-2 Derivatives of Exponential and Logarithmic Functions
11-3 Derivatives of Products and Quotients
11-4 The Chain Rule
11-5 Implicit Differentiation
11-6 Related Rates
11-7 Elasticity of Demand
Chapter 11 Review
Review Exercise
12 Graphing and Optimization
12-1 First Derivative and Graphs
12-2 Second Derivative and Graphs
12-3 L’Hôpital’s Rule
12-4 Curve-Sketching Techniques
12-5 Absolute Maxima and Minima
12-6 Optimization
Chapter 12 Review
Review Exercise
13 Integration
13-1 Antiderivatives and Indefinite Integrals
13-2 Integration by Substitution
13-3 Differential Equations; Growth and Decay
13-4 The Definite Integral
13-5 The Fundamental Theorem of Calculus
Chapter 13 Review
Review Exercise
14 Additional Integration Topics
14-1 Area between Curves
14-2 Applications in Business and Economics
14-3 Integration by Parts
14-4 Integration Using Tables
Chapter 14 Review
Review Exercise
15 Multivariable Calculus
15-1 Functions of Several Variables
15-2 Partial Derivatives
15-3 Maxima and Minima
15-4 Maxima and Minima Using Lagrange Multipliers
15-5 Method of Least Squares
15-6 Double Integrals over Rectangular Regions
15-7 Double Integrals over More General Regions
Chapter 15 Review
Review Exercise
A Basic Algebra Review
Self-Test on Basic Algebra
A-1 Algebra and Real Numbers
A-2 Operations on Polynomials
A-3 Factoring Polynomials
A-4 Operations on Rational Expressions
A-5 Integer Exponents and Scientific Notation
A-6 Rational Exponents and Radicals
A-7 Quadratic Equations
B Special Topics
B-1 Sequences, Series, and Summation Notation
B-2 Arithmetic and Geometric Sequences
B-3 The Binomial Theorem
C Tables
Table I Basic Geometric Formulas
Table II Integration Formulas
Answers
Index
Applications Index
A Library of Elementary Functions