Higher Education

Finite Mathematics and Applied Calculus, 2nd Edition

  • Geoffrey C. Berresford Long Island University
  • Andrew M. Rockett Long Island University
  • ISBN-10: 1424057272  |  ISBN-13: 9781424057276
  • 1198 Pages
  • © 2009 | Published
  • College Bookstore Wholesale Price = $189.75



The Second Edition of this engaging text for the two-semester applied calculus and finite mathematics course uses intriguing, real-world applications to capture the interest of business, economics, life, and social science majors. This practical approach to mathematics, along with the integration of graphing calculators and Excel spreadsheet explorations, exposes students to the tools they will encounter in future careers.A wealth of pedagogy includes the following distinctive features: detailed Worked-out Examples with Annotations help students through more challenging concepts; Practice Problems are offered to help students check their understanding of concepts presented in the examples; Section Summaries briefly restate essential formulas and key concepts; Chapter Summary with Hints and Suggestions unify chapter themes, give specific reminders, and reference problems in the review exercises suitable for a practice test; and Cumulative Review Exercises appear at the end of groups of chapters to reinforce previously learned concepts and skills.

Features and Benefits

  • Graphing Calculator Examples and Exercises located throughout the text explore new topics, guide students through "messy" calculations, or show technology pitfalls. These may be omitted without disrupting the flow or cohesion of the text.
  • Application Previews place mathematics in a real-world context and motivate students' interest in the material.
  • Annotations beside many formulas and solution steps emphasize the importance of being able to "read mathematics" by restating much of the mathematics in words.
  • Eduspace is Houghton Mifflin's online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content.

Table of Contents

Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises.
1. Functions
Application Preview: World Record Mile Runs
1.1 Real Numbers, Inequalities, and Lines
1.2 Exponents
1.3 Functions
1.4 Functions, Continued
1.5 Exponential Functions
1.6 Logarithmic Functions
I. Finite Mathematics
2. Mathematics of Finance
Application Preview: Musical Instruments as Investments
2.1 Simple Interest
2.2 Compound Interest
2.3 Annuities
2.4 Amortization
3. Systems of Equations and Matrices
Application Preview: A "Taxing" Problem
3.1 Systems of Two Linear Equations in Two Variables
3.2 Matrices and Linear Equations in Two Variables
3.3 Systems of Linear Equations and the Gauss-Jordan Method
3.4 Matrix Arithmetic
3.5 Inverse Matrices and Systems of Linear Equations
3.6 Introduction to Modeling: Leontief Models and Least Squares
4. Linear Programming
Application Preview: Managing an Investment Portfolio
4.1 Linear Inequalities
4.2 Two-Variable Linear Programming Problems
4.3 The Simplex Method for Standard Maximum Problems
4.4 Standard Minimum Problems and Duality
4.5* Nonstandard Problems: The Dual Pivot Element and the Two-Stage Method
4.6* Nonstandard Problems: Artificial Variables and the Big-M Method
* These two sections provide alternate methods for solving the same types of problems. The choice of which to cover is left to the Instructor.
5. Probability
Application Preview: The Chevalier de Meré
5.1 Sets, Counting, and Venn Diagrams
5.2 Permutations and Combinations
5.3 Probability Spaces
5.4 Conditional Probability and Independence
5.5 Bayes'' Formula
5.6 Random Variables and Distributions
6. Statistics
Application Preview: Household Income
6.1 Random Samples and Data Organization
6.2 Measures of Central Tendency
6.3 Measures of Variation
6.4 Normal Distributions and Binomial Approximation
7. Markov Chains
Application Preview: Weather in Sri Lanka
7.1 States and Transitions
7.2 Regular Markov Chains
7.3 Absorbing Markov Chains
II. Calculus
8. Derivatives and Their Uses
Application Preview: Temperature, Superconductivity, and Limits
8.1 Limits and Continuity
8.2 Rates of Change, Slopes, and Derivatives
8.3 Some Differentiation Formulas
8.4 The Product and Quotient Rules
8.5 Higher-Order Derivatives
8.6 The Chain Rule and Generalized Power Rule
8.7 Nondifferentiable Functions
9. Further Applications of Derivatives
Application Preview: Stevens'' Law of Psychophysics
9.1 Graphing Using the First Derivative
9.2 Graphing Using the First and Second Derivatives
9.3 Optimization
9.4 Further Applications of Optimization
9.5 Optimizing Lot Size and Harvest Size
9.6 Implicit Differentiation and Related Rates
Cumulative Review for Chapters 1, 8-9
10. Exponential and Logarithmic Functions
Application Preview: Elasticity and Social Policy
10.1 Review of Exponential and Logarithmic Functions
10.2 Differentiation of Logarithmic and Exponential Functions
10.3 Two Applications to Economics: Related Rates and Elasticity of Demand
11. Integration and Its Applications
Application Preview: Cigarette Smoking
11.1 Antiderivatives and Indefinite Integrals
11.2 Integration Using Logarithmic and Exponential Functions
11.3 Definite Integrals and Areas
11.4 Further Applications of Definite Integrals: Average Value and Area Between Curves
11.5 Two Applications to Economics: Consumers'' Surplus and Income Distribution
11.6 Integration by Substitution
12. Integration Techniques and Differential Equations
Application Preview: Improper Integrals and Eternal Recognition
12.1 Integration by Parts
12.2 Integration Using Tables
12.3 Improper Integrals
12.4 Numerical Integration
12.5 Differential Equations
12.6 Further Applications of Differential Equations: Three Models of Growth
13. Calculus of Several Variables
Application Preview: Safe Cars, Unsafe Streets
13.1 Functions of Several Variables
13.2 Partial Derivatives
13.3 Optimizing Functions of Several Variables
13.4 Least Squares
13.5 Lagrange Multipliers and Constrained Optimization
13.6 Total Differentials and Approximate Changes
13.7 Multiple Integrals
Cumulative Review for Chapters 1, 8-13
Appendix: Normal Probabilities Using Tables
Answers to Selected Exercises
Available on the Web
G. Game Theory
Application Preview: Sherlock Holmes and James Moriarty
G.1 Two-Person Games and Saddle Points
G.2 Mixed Strategies
G.3 Games and Linear Programming
Chapter L Logic
L.1 Statements and Connectives
Application Preview: Grammar, Logic, and Rhetoric
L.2 Truth Tables
Application Preview: Circuits
L.3 Implications
Application Preview: "If..., then..." as a Computer Instruction
L.4 Valid Arguments
Application Preview: Fuzzy Logic and Artificial Intelligence
L.5 Quantifiers and Euler Diagrams
Application Preview: The Dog Walking Ordinance
Chapter Projects and Essays

Meet the Author

Author Bio

Geoffrey C. Berresford

Dr. Berresford received his Ph.D. from the Courant Institute of Mathematical Sciences at New York University and taught at the State University of New York at Purchase before joining the faculty at the C.W. Post campus of Long Island University. Besides co-authoring four textbooks with Dr. Rockett, he has published papers in differential equations, linear programming, logic, and probability, and has received several teaching awards and the Distinguished Service Award from The Metropolitan New York Section of the Mathematical Association of America.

Andrew M. Rockett

After completing his Ph.D. at Stony Brook University, Dr. Rockett joined the mathematics faculty at C.W. Post and began his collaborations with Dr. Berresford. His book with Peter Szusz on CONTINUED FRACTIONS (1992) was hailed by Ivan Niven as "an outstanding addition to the literature of mathematics," and he served the Kappa Mu Epsilon mathematics honor society as editor of the mathematics journal The Pentagon from 1989 to 1995. Dr. Rockett serves as a reviewer for several journals, including Mathematical Reviews for the American Mathematical Society.