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Brief Calculus and Its Applications,9780130466181
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Brief Calculus and Its Applications

by ; ;
Edition:
10th
ISBN13:

9780130466181

ISBN10:
0130466182
Format:
Hardcover
Pub. Date:
1/1/2004
Publisher(s):
Prentice Hall
List Price: $113.35
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Summary

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 formulapairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exerciseshas proven to be tremendously successful with both students and instructors.

Table of Contents

Preface ix
Introduction 1(2)
Functions
3(63)
Functions and Their Graphs
3(15)
Some Important Functions
18(9)
The Algebra of Functions
27(5)
Zeros of Functions---The Quadratic Formula and Factoring
32(8)
Exponents and Power Functions
40(8)
Functions and Graphs in Applications
48(18)
Graphing Functions Using Technology
60(6)
The Derivative
66(71)
The Slope of a Straight Line
68(11)
The Slope of a Curve at a Point
79(6)
The Derivative
85(9)
Limits and the Derivative
94(10)
Differentiability and Continuity
104(6)
Some Rules for Differentiation
110(7)
More About Derivatives
117(4)
The Derivative as a Rate of Change
121(16)
Applications of the Derivative
137(72)
Describing Graphs of Functions
137(12)
The First and Second Derivative Rules
149(10)
Curve Sketching (Introduction)
159(7)
Curve Sketching (Conclusion)
166(7)
Optimization Problems
173(10)
Further Optimization Problems
183(10)
Applications of Derivatives to Business and Economics
193(16)
Techniques of Differentiation
209(29)
The Product and Quotient Rules
209(9)
The Chain Rule and the General Power Rule
218(6)
Implicit Differentiation and Related Rates
224(14)
Logarithm Functions
238(30)
Exponential Functions
238(4)
The Exponential Function ex
242(5)
Differentiation of Exponential Functions
247(6)
The Natural Logarithm Function
253(5)
The Derivative of In x
258(4)
Properties of the Natural Logarithm Function
262(6)
Applications of the Exponential and Natural Logarithm Functions
268(40)
Exponential Growth and Decay
268(11)
Compound Interest
279(7)
Applications of the Natural Logarithm Function to Economics
286(8)
Further Exponential Models
294(14)
The Definite Integral
308(77)
Antidifferentiation
309(9)
Areas and Riemann Sums
318(9)
Definite Integrals and the Fundamental Theorem
327(12)
Areas in the xy-Plane
339(10)
Applications of the Definite Integral
349(9)
Techniques of Integration
358(9)
Improper Integrals
367(7)
Applications of Calculus to Probability
374(11)
Functions of Several Variables
385(63)
Examples of Functions of Several Variables
385(7)
Partial Derivatives
392(9)
Maxima and Minima of Functions of Several Variables
401(9)
Lagrange Multipliers and Constrained Optimization
410(10)
The Method of Least Squares
420(7)
Nonlinear Regression
427(13)
Double Integrals
440(8)
The Trigonometric Functions
448
Radian Measure of Angles
448(4)
The Sine and the Cosine
452(8)
Differentiation and Integration of sin t and cos t
460(10)
The Tangent and Other Trigonometric Functions
470
Appendix A: Calculus and the TI-82 Calculator 1(5)
Appendix B: Calculus and the TI-83/TI-83 Plus Calculators 6(5)
Appendix C: Calculus and the TI-85 Calculator 11(5)
Appendix D: Calculus and the TI-86 Calculator 16(5)
Answers to Exercises 21
Index 1


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