College Mathematics
Solving Problems in Finite Mathematics and Calculus
Published on 12. June 2003
Book
Hardback
1504 pages
978-0-13-089131-0 (ISBN)
Description
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.
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.
More details
Language
English
Place of publication
United States
Publishing group
Pearson Education (US)
Target group
Professional and scholarly
Dimensions
Height: 262 mm
Width: 215 mm
Thickness: 48 mm
Weight
2822 gr
ISBN-13
978-0-13-089131-0 (9780130891310)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
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.
Bill taught at numerous colleges including Ohio State and Phoenix College, before taking his current position at Lakeland Community College near Cleveland, Ohio. Bill enjoys working with students at all levels and teaches courses ranging from Algebra to Differential Equations. He employs various teaching strategies to interest and motivate students including using humor to lighten the subject matter and inviting comments from students. His enjoyment of teaching and constant interaction with students has earned him a reputation as an innovative, enthusiastic, and effective teacher.
When Bill is not teaching, tutoring during office hours, or writing, he enjoys playing pool and golf, coaching his sons' little league baseball teams, and hanging out at home with his wife... not necessarily in that order!
Don Davis. Also a native of Ohio, Don earned a Bachelor of Science degree in Education, specializing in Political Science, Economics, and Mathematics from Bowling Green State University in Bowling Green, Ohio. After teaching at the high school level, Don received his Master of Science degree in Mathematics from Ohio University. He taught at Ohio State University - Newark before joining the Lakeland Community College faculty. With his background in Economics, Don is always searching for ways to apply mathematics to the "real world" and to connect mathematical concepts to the various courses his students are taking. By using technology, along with interesting, practical applications, Don brings his many mathematics classes to life for students. Like Bill, one typically finds Don in his office helping students understand the concepts of his courses. His dedication to his students makes him a sought-after teacher.
In his free time, Don is often found playing with his three children or scurrying after one of the many pets currently in residence at his home including a rat, two parakeets, a turtle, a lizard, a dog, and two cats. Occasionally, he enjoys a quiet night at home.
Bill taught at numerous colleges including Ohio State and Phoenix College, before taking his current position at Lakeland Community College near Cleveland, Ohio. Bill enjoys working with students at all levels and teaches courses ranging from Algebra to Differential Equations. He employs various teaching strategies to interest and motivate students including using humor to lighten the subject matter and inviting comments from students. His enjoyment of teaching and constant interaction with students has earned him a reputation as an innovative, enthusiastic, and effective teacher.
When Bill is not teaching, tutoring during office hours, or writing, he enjoys playing pool and golf, coaching his sons' little league baseball teams, and hanging out at home with his wife... not necessarily in that order!
Don Davis. Also a native of Ohio, Don earned a Bachelor of Science degree in Education, specializing in Political Science, Economics, and Mathematics from Bowling Green State University in Bowling Green, Ohio. After teaching at the high school level, Don received his Master of Science degree in Mathematics from Ohio University. He taught at Ohio State University - Newark before joining the Lakeland Community College faculty. With his background in Economics, Don is always searching for ways to apply mathematics to the "real world" and to connect mathematical concepts to the various courses his students are taking. By using technology, along with interesting, practical applications, Don brings his many mathematics classes to life for students. Like Bill, one typically finds Don in his office helping students understand the concepts of his courses. His dedication to his students makes him a sought-after teacher.
In his free time, Don is often found playing with his three children or scurrying after one of the many pets currently in residence at his home including a rat, two parakeets, a turtle, a lizard, a dog, and two cats. Occasionally, he enjoys a quiet night at home.
Content
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. Markov Chains.
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.
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. 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.