by Bill Armstrong and Don Davis
List price: $128.00
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.
Features
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.
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.
Features
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.