Table of Contents

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.
7. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Volumes of Solids of Revolution.
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 Numbers. Power Series and Taylor Series. More on Taylor Series. Newton's Method.
12. TRIGONOMETRIC FUNCTIONS.
Measurement of Angles. The Trigonometric Functions. Differentiation of Trigonometric Functions. Integration of Trigonometric Functions
APPENDIX A.
The Inverse of a Function. The Graphs of Inverse Functions. Functions That Have Inverses. Finding the Inverse of a Function.
APPENDIX B.
Indeterminate Forms and l'Hôpital's Rule. The Indeterminate Forms 0/0 and infinity/infinity.
APPENDIX C.
The Standard Normal Distribution.
Answers to Odd-Numbered Exercises.
Index.

About the Author

Soo T. Tan has published numerous papers in Optimal Control Theory and Numerical Analysis. He received his S.B. degree from Massachusetts Institute of Technology, his M.S. degree from the University of Wisconsin-Madison, and his Ph.D. from the University of California at Los Angeles. One of the most important lessons I learned from my early experience teaching these courses is that many of the students come into these courses with some degree of apprehension. This awareness led to the intuitive approach I have adopted in all of my texts.""