Mathematics with Applications

Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.   Thomas W. Hungerford received his bachelor’s degree from Holy Cross and his Ph.D. from the University of Chicago.  He taught for many years at the University of Washington (Seattle) before moving to Cleveland State University in 1980.  He has been at Saint Louis University since 2003.  He has written a number of research articles in algebra and several in mathematics education.  Dr. Hungerford is the author or coauthor of more than a dozen mathematics textbooks, ranging from high school to graduate level, several of which are published by Addison-Wesley.  He is active in promoting the effective use of technology in mathematics instruction.  Dr. Hungerford has also been a referee and reviewer for various mathematical journals and has served on National Science Foundation panels for selecting grant recipients.   John P. Holcomb, Jr.  received his bachelor's degree from St. Bonaventure University and his Ph.D. from the University at Albany, State University of New York.  He taught for five years at Youngstown State University prior to arriving at Cleveland State University in Fall 2000.  He is an associate professor and frequently collaborates with researchers in a variety of disciplines where he provides statistical analysis.  Dr. Holcomb has also authored several papers in statistical education and is very active in the American Statistical Association and the Mathematical Association of America.  He was named a Carnegie Scholar in 2000 by the Carnegie Foundation for the Advancement of Teaching and Learning and in 2003 received the Waller Award from the American Statistical Association for outstanding teaching of introductory statistics.                                                                        

Chapter 1         Algebra and Equations

                        1.1 The Real Numbers

                        1.2 Polynomials

                        1.3 Factoring

                        1.4 Rational Expressions

                        1.5 Exponents and Radicals

                        1.6 First-Degree Equations

                        1.7 Quadratic Equations

Case 1: Consumers Often Defy Common Sense

 

Chapter 2         Graphs, Lines, and Inequalities

                        2.1 Graphs

                        2.2 Equations of Lines

                        2.3 Linear Models

                        2.4 Linear Inequalities

                        2.5 Polynomial and Rational Inequalities

Case 2: Using Extrapolation to Predict Life Expectancy

  

Chapter 3         Functions and Graphs

                        3.1 Functions

                        3.2 Graphs of Functions

                        3.3 Applications of Linear Functions

                        3.4 Quadratic Functions

                        3.5 Applications of Quadratic Functions

                        3.6 Polynomial Functions

                        3.7 Rational Functions

Case 3: Architectural Arches

 

Chapter 4         Exponential and Logarithmic Functions

                        4.1 Exponential Functions

                        4.2 Applications of Exponential Functions

                        4.3 Logarithmic Functions

                        4.4 Logarithmic and Exponential Equations

Case 4: Characteristics of the Monkeyface Prickleback

  

Chapter 5         Mathematics of Finance

                        5.1 Simple Interest and Discount

                        5.2 Compound Interest

                        5.3 Future Value of an Annuity and Sinking Funds

                        5.4 Present Value of an Annuity and Amortization

Case 5: Time, Money, and Polynomials

 

Chapter 6         Systems of Linear Equations and Matrices

                        6.1 Systems of Linear Equations

                        6.2 The Gauss-Jordan Method

                        6.3 Basic Matrix Operations

                        6.4 Matrix Products and Inverses

                        6.5 Applications of Matrices

Case 6: Matrix Operations and Airline Route Maps      

 

 Chapter 7         Linear Programming

                        7.1 Graphing Linear Inequalities in Two Variables

                        7.2 Linear Programming: The Graphical Method

                        7.3 Applications of Linear Programming

                        7.4 The Simplex Method: Maximization

                        7.5 Maximization Applications

                        7.6 The Simplex Method: Duality and Minimization

                        7.7 The Simplex Method: Nonstandard Problems

Case 7: Cooking with Linear Programming

 

 Chapter 8         Sets and Probability

                        8.1 Sets

                        8.2 Applications of Venn Diagrams

                        8.3 Introduction to Probability

                        8.4 Basic Concepts of Probability

                        8.5 Conditional Probability and Independent Events

                        8.6 Bayes’ Formula

Case 8: Medical Diagnosis

        

 Chapter 9         Counting, Probability Distributions, and Further Topics in Probability

                        9.1 Probability Distributions and Expected Value

                        9.2 The Multiplication Principle, Permutations, and Combinations

                        9.3 Applications of Counting

                        9.4 Binomial Probability

                        9.5 Markov Chains

                        9.6 Decision Making

Case 9: Optimal Inventory for a Service Truck

  

Chapter 10       Introduction to Statistics

                        10.1 Frequency Distributions and Measures of Central Tendency

                        10.2 Measures of Variation

                        10.3 Normal Distributions

                        10.4 Normal Approximation to the Binomial Distribution

Case 10: Statistics in the Law—The Castaneda Decision

  

Chapter 11     Differential Calculus

                        11.1 Limits

                        11.2 One-sided Limits and Limits Involving Infinity

                        11.3 Rates of Change

                        11.4 Tangent Lines and Derivatives

                        11.5 Techniques for Finding Derivatives

                        11.6 Derivatives of Products and Quotients

                        11.7 The Chain Rule

                        11.8 Derivatives of Exponential and Logarithmic Functions

                        11.9 Continuity and Differentiability

Case 11: Price Elasticity of Demand

 

 Chapter 12     Applications of the Derivative

                        12.1 Derivatives and Graphs

                        12.2 The Second Derivative

                        12.3 Optimization Applications

                        12.4 Curve Sketching

Case 12: A Total Cost Model for a Training Program

 

Chapter 13     Integral Calculus

                        13.1 Antiderivatives

                        13.2 Integration by Substitution

                        13.3 Area and the Definite Integral

                        13.4 The Fundamental Theorem of Calculus

                        13.5 Applications of Integrals

                        13.6 Tables of Integrals (Optional)

                        13.7 Differential Equations

Case 13: Bounded Population Growth

 

 Chapter 14     Multivariate Calculus

                        14.1 Functions of Several Variables

                        14.2 Partial Derivatives

                        14.3 Extrema of Functions of Several Variables

Case 14: Global Warming and the Method of Least Squares