Synopses & Reviews
In the market-leading CALCULUS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Soo T. Tan provides an accurate, accessible presentation of mathematics combined with just the right balance of applications, pedagogy, and technology to help students succeed in the course. The new Sixth Edition includes highly interesting current applications and exercises to help stimulate student motivation. An exciting new array of supplements provides students with extensive learning support so instructors will have more time to focus on teaching the core concepts.
Review
"I've like using Tan for the following reason: It doesn't get in the way! The book allows me to teach the course the way I want to."
Review
"Tan's clarity and conciseness make the text easier for students to follow. The clean presentation of examples and showing small algebra steps seem well suited for our students."
Review
"Tan makes the material easy for students to learn without simplifying the content or lowering the level. Even students with somewhat weak algebra skills manage to learn the calculus and simultaneously sharpen their algebra skills."
Review
"The variety of exercises is also very good. They expose students to most of the classic computational problems they will run into, and the application problems run the gamut of uses of calculus in different fields."
Synopsis
An introductory calculus course for non-math students. Coverage begins with precalculus, and moves on to such topics functions, limits, the derivative, differentiation, integration, and multivariable calculus.
About the Author
Soo T. Tan, Professor of Mathematics at Stonehill College, 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. "By the time I started writing the first of what turned out to be a series of textbooks in mathematics for students in the managerial, life, and social sciences, I had quite a few years of experience teaching mathematics to non-mathematics majors. 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. As you will see, I try to introduce each abstract mathematical concept through an example drawn from a common, real-life experience. Once the idea has been conveyed, I then proceed to make it precise, thereby assuring that no mathematical rigor is lost in this intuitive treatment of the subject. Another lesson I learned from my students is that they have a much greater appreciation of the material if the applications are drawn from their fields of interest and from situations that occur in the real world. This is one reason why you will see so many exercises in my texts that are modeled on data gathered from newspapers, magazines, journals, and other media. Whether it be the ups and downs of the stock market, the growth of HMOs in the U.S., the solvency of the Social Security system, the budget deficit, the AIDS epidemic, or the growth of the Internet, I weave topics of current interest into my examples and exercises, to keep the book relevant to all of my readers."
Table of Contents
1. PRELIMINARIES. Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines. Summary of Principal Formulas and Terms. Review Exercises. 2. FUNCTIONS, LIMITS, AND THE DERIVATIVE. Functions and Their Graphs. Using Technology: Graphing a Function. The Algebra of Functions. Portfolio: Michael Marchlik. Functions and Mathematical Models. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Summary of Principal Formulas and Terms. Review Exercises. 3. DIFFERENTIATION. Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Portfolio: John Decker. Using Technology: Finding the Differential of a Function. Summary of Principal Formulas and Terms. Review Exercises. 4. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Function. Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Summary of Principal Terms. Review Exercises. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Using Technology. Logarithmic Functions. Compound Interest. Portfolio: Misato Nakazaki. Differentiation of Exponential Functions. Using Technology. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Using Technology: Analyzing Mathematical Models. Summary of Principal Formulas and Terms. Review Exercises. 6. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Definite Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Consumers' Surplus and Producers' Surplus. Summary of Principal Formulas and Terms. Review Exercises. 7. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Portfolio: James H. Chesebro, M.D. Improper Integrals. Applications of Probability to Calculus. Summary of Principal Formulas and Terms. Review Exercises. 8. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of a Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Summary of Principal Terms. Review Exercises. Answers to Odd-Numbered Exercises. Index.