Brief Calculus and Its Applications, 8/e
Larry J. Goldstein, Villanova University
David C. Lay, the University of Maryland
David I. Schneider, the University of Maryland
Published July, 1998 by Prentice Hall Engineering/Science/Mathematics
Copyright 1999, 520 pp.
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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.
NEW Details the ways in which technology
can be used to foster understanding of several topics while it facilitates
NEW Ends each chapter with a Review of Fundamental
Concepts, helping students focus on the chapter's key points.
NEW Places greater emphasis on the significance
of differential equations in applications involving exponential functions.
NEW Customized calculus software is available
through the study guide.
NEW Companion website supports and extends
the materials presented in the text.
NEW All graphs of functions have been redrawn
Reinforces class lessons with carefully designed exercise
sets, and challenges students to make their own connections.
Gets students going with practice problems that provide
Minimizes prerequisites, allowing those who have forgotten
much of their high school mathematics to start anew with this self-contained
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.)
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
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 egif/super_k.gifx. 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
Exponential Growth and Decay. Compound Interest. Applications
of the Natural Logarithm Function to Economics. Further Exponential
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
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
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.
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.
@COURSECODE = MM0503:
@COURSENAME = Applied Calculus
@CGPAGE = Course Guide Page 334