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Capturing student interest with a wealth of relevant, real world applications, Stefan Waner and Steven Costenoble's FINITE MATHEMATICS AND APPLIED CALCULUS, 4th Edition makes the material come alive for students! Providing maximum flexibility with the use of technology, the book integrates the use of spreadsheets and graphing calculators with instructions for Microsoft Excel and the TI-83. This technology material is clearly delineated so instructors can use as much or as little as they would like for their course. The popular accompanying website also provides a wealth of interactive tutorials, exercises, and online support. Connecting with all types of teaching and learning styles, Waner/Costenoble supports a wide range of instructional paradigms: from traditional lecture to a hybrid course to distance learning.
0. ALGEBRA REVIEW. Real Numbers. Exponents and Radicals. Multiplying and Factoring Algebraic Equations. Rational Expressions. Solving Polynomial Equations. Solving Miscellaneous Equations. 1. FUNCTIONS AND LINEAR MODELS. Functions from the Numerical and Algebraic Viewpoints. Functions from the Graphical Viewpoint. Linear Functions. Linear Models. Linear Regression. Key Concepts. Review Exercises. Case Study: Modeling Spending on Internet Advertising. Technology Guides. Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Two Equations in Two Unknowns. Using Matrices to Solve Systems of Equations. Applications of Systems of Linear Equations. Key Concepts. Review Exercises. Case Study: The Impact of Regulating Sulfur Emissions. Technology Guides. 3. MATRIX ALGEBRA AND APPLICATIONS. Matrix Addition and Scalar Multiplication. Matrix Multiplication. Matrix Inversion. Matrices in Practice: Game Theory. Matrices in Practice: Input-Output Models. Key Concepts. Review Exercises. Case Study: The Japanese Economy. Technology Guides. 4. LINEAR PROGRAMMING. Graphing Linear Inequalities. Solving Linear Programming Problems Graphically. The Simplex Method: Solving Standard Maximization Problems. The Simplex Method: Solving General Linear Programming Problems. The Simplex Method and Duality (Optional). Key Concepts. Review Exercises. Case Study: Airline Scheduling. Technology Guides. 5. THE MATHEMATICS OF FINANCE. Simple Interest. Compound Interest. Annuities, Loans, and Bonds. Key Concepts. Review Exercises. Case Study: Saving for College. Technology Guides. 6. SETS AND COUNTING. Sets and Set Operations. Cardinality. The Addition and Multiplication Principles. Permutations and Combinations. Key Concepts. Review Exercises. Case Study: Designing a Puzzle. Technology Guides. 7. PROBABILITY. Sample Spaces and Events. Estimated Probability. Theoretical Probability and Probability Distributions. Probability and Counting Techniques (optional). Conditional Probability and Independence. Bayes' Theorem and Applications. Probability in Practice: Markov Systems. Key Concepts. Review Exercises. Case Study: The Monty Hall Problem. Technology Guides. 8. RANDOM VARIABLES AND STATISTICS. Random Variables and Distributions. Bernoulli Trials and Binomial Random Variables. Measures of Central Tendency. Measures of Dispersion. Normal Distributions. Key Concepts. Review Exercises. Case Study: Spotting Tax Fraud with Benford's Law. Technology Guides. Optional Internet Topics: Sampling Distributions and the Central Limit Theorem. Confidence Intervals. Hypothesis Testing. 9. NONLINEAR MODELS. Quadratic Functions and Models. Exponential Functions and Models. Logarithmic Functions and Models. Logistic Functions and Models. Key Concepts. Review Exercises. Case Study: Checking up on Malthus. Technology Guides. Optional Internet Topics: Inverse Functions. Using and Deriving Algebraic Properties of Logarithms. 10. INTRODUCTION TO THE DERIVATIVE. Limits: Numerical and Graphical Approaches. Limits and Continuity. Limits: Algebraic Approach. Average Rate of Change. Derivatives: Numerical and Graphical Viewpoints. Derivatives: Algebraic Viewpoint. Derivatives of Powers, Sums, and Constant Multiples. A First Application: Marginal Analysis. Key Concepts. Review Exercises. Case Study: Reducing Sulfur Emissions. Technology Guides. Optional Internet Topics: Sketching the Graph of the Derivative. Proof of the Power Rule. Continuity and Differentiability. 11. TECHNIQUES OF DIFFERENTIATION. The Product and Quotient Rules. The Chain Rule. Derivatives of Logarithmic and Exponential Functions. Implicit Differentiation. Key Concepts. Review Exercises. Case Study: Projecting Market Growth. Technology Guides. Optional Internet Topic: Linear Approximation and Error Estimation. 12. APPLICATIONS OF THE DERIVATIVE. Maxima and Minima. Applications of Maxima and Minima. The Second Derivative and Analyzing Graphs. Related Rates. Elasticity. Key Concepts. Review Exercises. Case Study: Production Lot Size Management. Technology Guides. 13. THE INTEGRAL. The Indefinite Integral. Substitution. The Definite Integral: Numerical and Graphical Approaches. The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus. Key Concepts. Review Exercises. Case Study: Wage Inflation. Technology Guides. Optional Internet Topic: Numerical Integration. 14. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL. Integration by Parts. Area Between Two Curves and Applications. Averages and Moving Averages. Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams. Improper Integrals and Applications. Differential Equations and Applications. Key Concepts. Review Exercises. Case Study: Estimating Tax Revenues. Technology Guides. Optional Internet Topic: Taylor Polynomials. 15. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables from the Numerical and Algebraic Viewpoints. Three Dimensional Space and the Graph of a Function of Two Variables. Partial Derivatives. Maxima and Minima. Constrained Maxima and Minima and Applications. Double Integrals and Applications. Key Concepts. Review Exercises. Case Study: Modeling Household Income. Technology Guides. Optional Internet Topic: The Chain Rule for Functions of Several Variables. 16. TRIGONOMETRIC MODELS. Trigonometric Functions, Models, and Regression. Derivatives of Trigonometric Functions and Applications. Integrals of Trigonometric Functions and Applications. Key Concepts. Review Exercises. Case Study: Predicting Cocoa Inventories. Technology Guides. Appendix A: Logic. Appendix B Table: Area Under A Normal Curve. Answers To Selected Exercises. Index. OPTIONAL INTERNET TOPIC. S. CALCULUS APPLIED TO PROBABILITY AND STATISTICS. Introduction. Continuous Random Variables and Histograms. Probability Density Functions: Uniform, Exponential, Normal, and Beta. Mean, Median, Variance and Standard Deviation. Case Study: Creating a Family Trust.
Posted January 14, 2011
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