College Mathematics: Solving Problems in Finite Mathematics and Calculus / Edition 1

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Overview

This book, 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. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews. For anyone who wants to see and understand how mathematics are used in everyday life.
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Product Details

  • ISBN-13: 9780130891310
  • Publisher: Pearson Education
  • Publication date: 11/1/2002
  • Edition number: 1
  • Pages: 1504
  • Product dimensions: 8.20 (w) x 10.30 (h) x 1.90 (d)

Meet the Author

Bill Armstrong

Bill Armstrong. Bill is a native of Ohio and became a hard-core Buckeyes fan after earning both his Bachelors and Masters degrees in Mathematics at The Ohio State University.


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Table of Contents

Finite 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. MarkovChains.
Introduction to Markov Chains. Regular Markov Chains. Absorbing Markov Chains. Chapter 10 Game Theory. Strictly Determined Games. Mixed Strategies. Game Theory and Linear Programming.

APPENDICES.


Appendix A. Prerequisites for Finite Mathematics.
Percents, Decimals and Fractions. Evaluating Expressions and Order of Operations. Properties of Integer Exponents. Rational Exponents and Radicals.

Appendix B. Algebra Review.
Multiplying Polynomial Expressions. Factoring Trinomials. Solving Linear Equations. Solving Quadratic Equations. Properties of Logarithms. Geometric Sequence and Series.

Appendix C. Calculator Programs.
Appendix D. Standard Normal Table.

Brief Calculus 1. 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).

2. 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.

3. Applications of the Derivative.
The Differential and Linear Approximations. Marginal Analysis. Measuring Rates and Errors.

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

5. 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.

6. 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.

7. 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.

8. 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.

Appendix A. Essentials of Algebra.
Appendix B. Calculator Programs.
Appendix C. Selected Proofs.

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.

Finite Mathematics

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Introduction

Audience

In preparing to write the two components that comprise this text, we talked with many colleagues who teach finite mathematics and a brief or applied calculus course to find out if they experienced the same difficulties in teaching these subjects that we have encountered. What we learned is that while there is very little similarity in the topics covered or in how much time is spent on each area, there is remarkable uniformity in the needs of students who enroll in these diverse courses. Professors at Community Colleges, Universities, and Liberal Arts Colleges all told us that their students are generally unmotivated, unsure of their algebra skills, uncomfortable with translating English into mathematics, and unschooled in how to set up problems for solution. Armed with this knowledge, we prepared College Mathematics: Solving Problems in Finite Mathematics and Calculus to address these fundamental needs.

As with other college mathematics textbooks, our text is designed for a two-term course for students majoring in economics, business, social or behavioral sciences. The book is organized into two parts. The first ten chapters cover the topics most frequently taught in a finite mathematics course. The second part of the book consists of eight chapters of applied calculus. We have organized the topics for maximum flexibility within each part so that the text may be adapted to any college or university's curriculum. However, that is where the similarity ends. We have crafted this book around six key principles designed to address student's needs:

  • Present the mathematics in language that students can read and understand
  • Teachgood problem solving techniques and provide ample practice
  • Use real data applications to keep it interesting
  • Provide timely reinforcement of algebra and other essential skills
  • Let Instructor's decide whether to incorporate technology
  • Present Probability and Statistics with clarity and precision
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