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. Applications of Calculus
to Probability.
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.
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.""
Ask a Question About this Product More... |