Finite Mathematics with Calculus

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