Applied Mathematics for the Managerial, Life, and Social Sciences

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1. FUNDAMENTALS OF ALGEBRA. Real Numbers. Polynomials. Factoring Polynomials. Rational Expressions. Integral Exponents. Solving Equations. Rational Exponents and Radicals. Quadratic Equations. Inequalities and Absolute Value. 2. FUNCTIONS AND THEIR GRAPHS. The Cartesian Coordinate System and Straight Lines. Equations of Lines. Functions and Their Graphs. The Algebra of Functions. Linear Functions. Quadratic Functions. Functions and Mathematical Models. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Exponential Functions as Mathematical Models. 4. MATHEMATICS OF FINANCE. Compound Interest. Annuities. Amortization and Sinking Funds. Arithmetic and Geometric Progressions (Optional). 5. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations: An Introduction. Systems of Linear Equations: Unique Solutions. Systems of Linear Equations: Undetermined and Overdetermined Systems. Matrices. Multiplication of Matrices. The Inverse of a Square Matrix. 6. LINEAR PROGRAMMING. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. 7. SETS AND PROBABILITY. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations. Experiments, Sample Spaces, and Events. Probability. Rules of Probability. 8. ADDITIONAL TOPICS IN PROBABILITY. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes" Theorem. Distributions of Random Variables. Expected Value. Variance and Standard Deviation. 9. THE DERIVATIVE. Limits. Continuity. The Derivative. Basic Rules of Differentiation. The Product and Quotient Rules: Higher-Order Derivatives. The Chain Rule. Differentiation of Exponential and Logarithmic Functions. Marginal Functions in Economics. 10. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. 11. 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. 12. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. Linear Inequalities in Two Variables. Linear Programming Problems. Graphical Solution of Linear Programming Problems. The Simplex Method: Standard Maximization Problems. The Simplex Method: Standard Minimization Problems. 7. SETS AND PROBABILITY. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Permutations and Combinations. Experiments, Sample Spaces, and Events. Probability. Rules of Probability. 8. ADDITIONAL TOPICS IN PROBABILITY. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes" Theorem. Distributions of Random Variables. Expected Value. Variance and Standard Deviation. 9. THE DERIVATIVE. Limits. Continuity. The Derivative. Basic Rules of Differentiation. The Product and Quotient Rules: Higher-Order Derivatives. The Chain Rule. Differentiation of Exponential and Logarithmic Functions. Marginal Functions in Economics. 10. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II. 11. 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. 12. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables.

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