Applied Calculus for the Managerial, Life, and Social Sciences – Soo T. Tan – 6th Edition

1. PRELIMINARIES. Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines.

2. 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.

3. 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.

4. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Applications of the Second Derivative. Curve Sketching. Optimization I. Optimization II.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Logarithmic Functions. Compound Interest. Differentiation of Exponential Functions. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models.

6. 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. Volumes of Solids of Revolution.

7. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals.

8. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Total Differentials. Double Integrals. Applications of Double Integrals.

9. DIFFERENTIAL EQUATIONS. Differential Equations. Separation of Variables. Applications of Separable Differential Equations. Approximate Solutions of Differential Equations.

10. PROBABILITY AND CALCULUS. Probability Distributions of Random Variables. Expected Value and Standard Deviation. Normal Distributions.

11. TAYLOR POLYNOMIALS AND INFINITE SERIES. Taylor Polynomials. Infinite Sequences. Infinite Series. Series with Positive Terms. Power Series and Taylor Series. More on Taylor Series. The Newton-Raphson Method.

12. TRIGONOMETRIC FUNCTIONS. Measurement of Angles. The Trigonometric Functions. Differentiation of Trigonometric Functions. Integration of Trigonometric Functions.