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College Mathematics : Solving Problems in Finite Mathematics and Calculus

College Mathematics : Solving Problems in Finite Mathematics and Calculus - 03 edition

ISBN13: 978-0131602175

Cover of College Mathematics : Solving Problems in Finite Mathematics and Calculus 03 (ISBN 978-0131602175)
ISBN13: 978-0131602175
ISBN10: 0131602179
Edition: 03
Copyright: 2003
Publisher: Prentice Hall, Inc.
Published: 2003
International: No

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College Mathematics : Solving Problems in Finite Mathematics and Calculus - 03 edition

ISBN13: 978-0131602175

Bill Armstrong and Don Davis

ISBN13: 978-0131602175
ISBN10: 0131602179
Edition: 03
Copyright: 2003
Publisher: Prentice Hall, Inc.
Published: 2003
International: No

For courses in Mathematics for Business, Finite Mathematics, and Applied Calculus.

This text, modern in its writing style as well as in its applications, contains numerous exercises--both skill oriented and applications--, real data problems, and a problem solving method. Its exercises are based on data from the World Wide Web, and allow students to see for themselves how mathematics is used in everyday life.


  • Problem solving method--Occurs in worked out examples throughout the entire text in the steps entitled Understand the Situation and Interpret the Solution.
    • Provides students with the necessary preliminary thought processes needed when attacking a problem.
  • Real data modeling--Features problems based on data culled from the WWW.
    • Impresses upon students that mathematics can be used to solve a multitude of rich real world problems. Serves instructorswith an abundance of examples and exercises enabling students to see where they could use this mathematics in the real world.
  • Technology options--Follows worked examples for students and instructors who wish to use graphing calculator technology.
    • Shows students how the graphing calculator may be used to solve the example just presented.
  • Flashbacks--Revisits an example from a prior section and extends the content to introduce new topics.
    • Allows students to concentrate on a new topic using familiar applications. Enables instructorsto use students' prior knowledge and extend it naturally to new material.
  • From Your Toolbox boxes--Reviews a previously introduced key definition, theorem, or property required in the development of a new topic.
    • Allows students to stay on a task with the material being presented without having to flip back several pages.
  • Notes feature follows definitions, theorems, and properties.
    • Provides students with additional insight by clarifying the just presented mathematical idea verbally.
  • Checkpoints --Reinforce the topics, skill, or concept at hand.
    • Helps students take ownership of their learning and the course material, and gives them confidence in their ability to do so.
  • Interactive activities.
    • Gives students further mathematical insight by extending complete examples, solving worked examples using another method, discovering patterns, and exploring additional properties of recently introduced topics. Supplies instructorswith material for critical thinking exercises, classroom discussion, or collaborative learning.
  • Chapter openers--Includes photos, graphs, What We Know, and Where Do We Gosections.
    • Guides students through the text by highlighting what the have already learned and what they are about to cover.
  • Chapter-end narratives--Features Why We Learned It sections, extensive review exercises, and a chapter project.
    • Outlines the major chapter topics and how they are used in various careers, and offers students the chance to test their understanding of the material they have learned--and their understanding of it.

Table of Contents

College Mathematics

1. Linear Models and Systems of Linear Equations.

Problem Solving: Linear Equations. Linear Functions. Linear Models. Solving Systems of Linear Equations Graphically. Solving Systems of Linear Equations Algebraically.

2. Systems of Linear Equations and Matrices.

Matrices and Gauss-Jordan Elimination. Matrices and Operations. Matrix Multiplication. Matrix Inverses and Solving Systems of Linear Equations. Leontief Input-Output Models.

3. Linear Programming: The Graphical Method.

Problem Solving: Linear Inequalities. Graphing Systems of Linear Inequalities. Solving Linear Programming Problems Graphically. Applications of Linear Programming.

4. Linear Programming: The Simplex Method.

Introduction to The Simplex Method. Simplex Method: Standard Maximum Form Problems. Simplex Method: Standard Minimum Form Problems and Duality. Simplex Method: Nonstandard Problems.

5. Mathematics of Finance.

Simple Interest. Compound Interest. Future Value of an Annuity. Present Value of an Annuity.

6. Sets and the Fundamentals of Probability.

Problem Solving: Probability and Statistics. Sets and Set Operations. Principles of Counting. Introduction to Probability. Computing Probability using the Addition Rule. Computing Probability using the Multiplication Rule. Bayes' Theorem and Its Applications.

7. Graphical Data Description.

Graphing Qualitative Data. Graphing Quantitative Data. Measures of Centrality. Measures of Dispersion.

8. Probability Distributions.

Discrete Random Variables. Expected Value and Standard Deviation of a Discrete Random Variable. The Binomial Distribution. The Normal Distribution.

9. Markov Chains.

Introduction to Markov Chains. Regular Markov Chains. Absorbing Markov Chains.

10. Game Theory

Strictly Determined Games. Mixed Strategies. Game Theory and Linear Programming.

11. Functions, Modeling and Average Rate of Change.

Coordinate Systems and Functions. Introduction to Problem Solving. Linear Functions and Average Rate of Change. Quadratic Functions and Average Rate of Change on an Interval. Operations on Functions. Rational, Radical and Power Functions. Exponential Functions. Logarithmic Functions. Regression and Mathematical Models (Optional Section).

12. Limits, Instantaneous Rate of Change and the Derivative.

Limits. Limits and Asymptotes. Problem Solving: Rates of Change. The Derivative. Derivatives of Constants, Powers and Sums. Derivatives of Products and Quotients. Continuity and Nondifferentiability.

13. Applications of the Derivative.

The Differential and Linear Approximations. Marginal Analysis. Measuring Rates and Errors.

14. Additional Differentiation Techniques.

The Chain Rule. Derivatives Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation and Related Rates. Elasticity of Demand.

15. Further Applications of the Derivative.

First Derivatives and Graphs. Second Derivatives and Graphs. Graphical Analysis and Curve Sketching. Optimizing Functions on a Closed Interval. The Second Derivative Test and Optimization.

16. Integral Calculus.

The Indefinite Integral. Area and the Definite Integral. Fundamental Theorem of Calculus. Problem Solving: Integral Calculus and Total Accumulation. Integration by u-substitution. Integrals That Yield Logarithmic and Exponential Functions. Differential Equations: Separation of Variables. Differential Equations: Growth and Decay.

17. Applications of Integral Calculus.

Average Value of a Function and the Definite Integral in Finance. Area Between Curves and Applications. Economic Applications of Area between Curves. Integration by Parts. Numerical Integration. Improper Integrals.

18. Calculus of Several Variables.

Functions of Several Independent Variables. Level Curves, Contour Maps and Cross-Sectional Analysis. Partial Derivatives and Second-Order Partial Derivatives. Maxima and Minima. Lagrange Multipliers. Double Integrals.

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