College Mathematics for the Managerial, Life, and Social Sciences

1. STRAIGHT LINES AND LINEAR FUNCTIONS. The Cartesian Coordinate System. Straight Lines. Linear Functions and Mathematical Models. Intersection of Straight Lines. The Method of Least Squares. 2. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations: An Introduction. Systems of Linear Equations: Unique Solutions. Systems of Linear Equations: Underdetermined and Overdetermined Systems. Matrices. Multiplication of Matrices. The Inverse of a Square Matrix. Leontief Input-Output Model. 3. LINEAR PROGRAMMING: A GEOMETRIC APPROACH. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. 4. LINEAR PROGRAMMING: AN ALGEBRAIC APPROACH. The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. 5. MATHEMATICS OF FINANCE. Compound Interest. Annuities. Amortization and Sinking Funds. Arithmetic and Geometric Progressions (Optional). 6. SETS AND COUNTING. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations. 7. PROBABILITY. Experiments, Sample Spaces, and Events. Definition of a Probability. Rules of a Probability. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes' Theorem. Markov Chains (Optional). 8. PROBABILITY DISTRIBUTIONS AND STATISTICS. Distributions of Random Variables. Expected Value. Variance and Standard Deviation. The Binomial Distribution. The Normal Distribution. Applications of the Normal Distribution. 9. PRECALCULUS REVIEW. Exponents and Radicals. Algebraic Expressions. Algebraic Fractions. Inequalities and Absolute Value. 10. FUNCTIONS, LIMITS, AND THE DERIVATIVE. Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Limits. One-Sided Limits and Continuity. The Derivative. 11. DIFFERENTIATION. Basic Rules of Differentiation. The Product and Quotient Rules. The Chain Rule. Marginal Functions in Economics. Higher Order Derivatives. Implicit Differentiation and Related Rates. Differentials. 12. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. 13. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. 14. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Evaluating Definite Integrals. Area Between Two Curves. Applications of the Definite Integral to Business and Economics. 15. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Numerical Integration. Improper Integrals. Applications of Calculus to Probability. 16. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Appendix A. Appendix B.Tan, Soo T. is the author of 'College Mathematics for the Managerial, Life, and Social Sciences', published 2005 under ISBN 9780534408039 and ISBN 0534408036.