Finite Mathematics and Applied Calculus Book

Note: Each chapter concludes with Review Exercises and a Make It Real project. 1. Functions and Linear Models Functions Linear Functions Linear Models 2. Systems of Linear Equations Systems of Linear Equations Using Matrices to Solve Linear Systems of Equations Linear System Applications 3. Matrix Algebra and Applications Matrix Addition and Scalar Multiplication Matrix Multiplication and Inverses Solving Matrix Equations Leontief Input-Output Models 4. Linear Programming Graphing Linear Inequalities Solving Linear Programming Problems Graphically Solving Standard Maximization Problems with the Simplex Method Solving Standard Minimization Problems and the Dual Solving General Linear Programming Problems with the Simplex Method 5. Nonlinear Models Quadratic Function Models Higher-Order Polynomial Function Models Exponential Function Models Logarithmic Function Models Choosing a Mathematical Model 6. Mathematics of Finance Solving Exponential Equations Simple and Compound Interest Future Value of an Increasing Annuity Present Value of a Decreasing Annuity 7. Sets and Probability Introduction to Sets Cardinality and the Addition and Multiplication Principles Permutations and Combinations Introduction to Probability Basic Probability Concepts 8. Advanced Probability and Statistics Conditional Probability Bayes' Theorem and Applications Markov Chains Random Variables and Expected Value Measures of Central Tendency and Dispersion Normal Distributions 9. The Derivative Average Rates of Change Limits and Instantaneous Rates of Change The Derivative as a Slope: Graphical Method The Derivative as a Function: Algebraic Method Interpreting the Derivative 10. Differentiation Techniques Basic Derivative Rules The Product and Quotient Rules The Chain Rule Exponential and Logarithmic Rules Implicit Differentiation 11. Derivative Applications Maxima and Minima Applications of Maxima and Minima Concavity and the Second Derivative Related Rates 12. The Integral Indefinite Integrals Integration by Substitution Using Sums to Approximate Area The Definite Integral The Fundamental Theorem of Calculus 13. Advanced Integration Techniques and Applications Integration by Parts Area Between Two Curves Differential Equations and Applications Differential Equations: Limited Growth and Logistic Models 14. Multivariable Functions and Partial Derivatives Multivariable Functions Partial Derivatives Multivariable Maxima and Minima Constrained Maxima and Minima and Applications