Larry J. Goldstein ,
Villanova University
David C. Lay , the University of Maryland
David I. Schneider , the University of Maryland
Published July 1998 by
Engineering/Science/Mathematics
Copyright 1999, 520 pp.
Cloth ISBN 0-13-079767-7
Once again, these extremely
readable, highly regarded, and widely adopted texts present innovative ways for applying
calculus to real-world situations in the business, economics, life science, and social
science disciplines. The texts' straightforward, engaging approach fosters the growth of
both the student's mathematical maturity and his/her appreciation for the usefulness of
mathematics. The authors' "tried and true" formula - pairing substantial amounts of
graphical analysis and informal geometric proofs with an abundance of hands-on exercises
- has proven to be tremendously successful with both students and instructors.
What would the benefit to
your students be of using a text which blends practical applications with mathematical
concepts?
Reinforces class lessons with
carefully designed exercise sets, and challenges students to make their own
connections.
Gets students going with practice
problems that provide supported tasks.
Minimizes prerequisites,
allowing those who have forgotten much of their high school mathematics to start anew with
this self-contained material.
Includes many real-life
applications/scenarios as well as the Index of Applications, which demonstrates to
students the relevance of their studies.
Provides easy-to-understand
instructions for using calculators, eliminating the need for a manual.
Makes available up-to-date, customized
calculus software for instructors interested in the use of computers.
Early introduction to the
derivative and its applications. (Chs. 1 & 2)
(NOTE: Calculus and Its
Applications, 8/E consists of Chs. 0-12. Brief Calculus and Its
Applications, 8/E consists of Chs. 0-8.)
Index of Applications.
Preface.
Introduction.
0. Functions.
Functions and Their Graphs. Some Important Functions. The Algebra of Functions. Zeros of
Functions - The Quadratic Formula and Factoring. Exponents and Power Functions.
Functions and Graphs in Applications.
1. The Derivative.
The Slope of a Straight Line.
The Slope of a Curve at a Point. The Derivative. Limits and the Derivative.
Differentiability and Continuity. Some Rules for Differentiation. More About Derivatives.
The Derivative as a Rate of Change.
2. Applications of the Derivative.
Describing Graphs of Functions. The First and Second Derivative Rules. Curve Sketching
(Introduction.) Curve Sketching (Conclusion.) Optimization Problems. Further Optimization
Problems. Applications of Calculus to Business and Economics.
3. Techniques of Differentiation.
The Product and Quotient Rules. The Chain Rule and the General Power Rule. Implicit
Differentiation and Related Rates.
4. The Exponential and Natural Logarithm Functions.
Exponential Functions. The Exponential Function e x. Differentiation of
Exponential Functions. The Natural Logarithm Function. The Derivative of ln x.
Properties of the Natural Logarithm Function.
5. Applications of the Exponential and Natural Logarithm Functions.
Exponential Growth and Decay. Compound Interest. Applications of the Natural Logarithm
Function to Economics. Further Exponential Models.
6. The Definite Integral.
Antidifferentiation. Areas and Reimann Sums. Definite Integrals and the Fundamental
Theorem. Areas in the xy-Plane. Applications of the Definite Integral.
7. Functions of Several Variables.
Examples of Functions of Several Variables. Partial Derivatives. Maxima and Minima of
Functions of Several Variables. Lagrange Multipliers and Constrained Optimization. The
Method of Least Squares. Double Integrals.
8. The Trigonometric Functions.
Radian Measure of Angles. The Sine and the Cosine. Differentiation of sin t and cos
t. The Tangent and Other Trigonometric Functions.
9. Techniques of Integration.
Integration by Substitution. Integration by Parts. Evaluation of Definite Integrals.
Approximation of Definite Integrals. Some Applications of the Integral. Improper
Integrals.
10. Differential Equations.
Solutions of Differential
Equations. Separation of Variables. Numerical Solution of Differential Equations.
Qualitative Theory of Differential Equations. Applications of Differential Equations.
11. Taylor Polynomials and Infinite Series.
Taylor Polynomials. The Newton-Raphson Algorithm. Infinite Series. Series with Positive
Terms. Taylor Series.
12. Probability and Calculus.
Discrete Random Variables. Continuous Random Variables. Expected Value and Variance.
Exponential and Normal Random Variables. Poisson and Geometric Random Variables.
Appendices.
A. Calculus and the TI-82 Calculator.
B. Calculus and the TI-83 Calculator.
C. Calculus and the TI-85 Calculator.
D. Calculus and the TI-86 Calculator.
E. Areas Under the Standard Normal Curve.
Answers to Exercises.
Index.
