Finite Mathematics With Calculus A Modeling Approach

This text uses a modeling approach to unify the traditional topics of finite mathematics and calculus. Use of graphing calculators is carefully integrated to support the modeling approach. The authors apply graphical, numerical, and symbolic techniques to motivate understanding.

  

1. MATHEMATICAL MODELS The Modeling Process / Modeling with Equalities / Modeling with Proportionality / Modeling with Graphs / Linear Equations and Straight Lines / Graphing Systems of Equations / Chapter 1 Keys 2. LINEAR MODELS Elementary Row Operations / Gaussian Elimination / Modeling Data with Straight Lines / Matrices / Matrix Inversion / Chapter 2 Keys 3. LINEAR PROGRAMMING MODELS Modeling with Inequalities / Graphing Linear Inequalities / Optimizing with Graphs / Initializing the Simplex Method / The Basic Simplex Algorithm / The Enhanced Simplex Algorithm / Chapter 3 Keys 4. FINANCIAL MODELS Interest / Present Value / Annuities / Present Value of an Annuity / Chapter 4 Keys 5. PRESENTATION MODELS Sets and Venn Diagrams / Pie Charts and Bar Graphs / Standard Measures for Numerical Data / Tree Diagrams / Chapter 5 Keys 6. PROBABILITY MODELS Equally Likely Outcomes / The Laws of Probability / Conditional Probability and Independent Events / The Bayesean Method / Combinatorics / Bernoulli Trials / Expected Value / Chapter 6 Keys 7. MARKOV CHAIN MODELS Markov Chains / Distribution Vectors / Absorbing States / Chapter 7 Keys 8. PROBABILITY DISTRIBUTION MODELS Random Number Generators / Uniform Distributions / Sampling / Normal Distributions / Exponential Distributions / Chapter 8 Keys 9. MODELING WITH FUNCTIONS Functions / Polynomial, Rational, and Power Functions / Exponential Functions / The Natural Logarithm / Trigonometric Functions / Chapter 9 Keys 10. MODELING CHANGE Rates of Change / Limits and Continuity / The Derivative / More Rules of Differentiation / The Chain Rule / Differentiable Functions / Chapter 10 Keys 11. OPTIMIZATION MODELS Critical Points / Design Problems / Production Problems / Related Rates / Second Derivative and Local Optima / Chapter 11 Keys 12. MODELING WITH INTEGRALS Antiderivatives and Indefinite Integrals / Applications of the Indefinite Integral / Substitution of Variables / The Definite Integral / Applications of the Definite Integral / Probability Density Functions / Chapter 12 Keys 13. MULTIVARIABLE MODELS Functions of Many Variables / Partial Derivatives / Optimization / Iterated Integrals / Chapter 13 Keys / APPENDIX A: EXPONENTS / APPENDIX B: POLYNOMIALS / APPENDIX C: FACTORING / APPENDIX D: ROOTS AND THE QUADRATIC FORMULA / APPENDIX E: COMMON LOGARITHMS / APPENDIX F: SIGMA NOTATION / APPENDIX G: LEONTIEF MODELS / ANSWERS TO SELECTED PROBLEMS / INDEX / PHOTO CREDITS