9780130873040

Calculus and Its Applications

by ; ;
  • ISBN13:

    9780130873040

  • ISBN10:

    0130873047

  • Edition: 9 PCK SUB
  • Format: Hardcover
  • Copyright: 7/1/2000
  • Publisher: Pearson College Div
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Summary

For Applied Calculus courses. 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(67)
Functions and Their Graphs
3(15)
Some Important Functions
18(9)
The Algebra of Functions
27(7)
Zeros of Functions---The Quadratic Formula and Factoring
34(8)
Exponents and Power Functions
42(7)
Functions and Graphs in Applications
49(21)
Graphing Functions Using Technology
62(6)
Chapter Project
68(2)
The Derivative
70(74)
The Slope of a Straight Line
72(11)
The Slope of a Curve at a Point
83(6)
The Derivative
89(12)
Limits and the Derivative
101(10)
Differentiability and Continuity
111(5)
Some Rules for Differentiation
116(7)
More About Derivatives
123(5)
The Derivative as a Rate of Change
128(16)
Chapter Project
143(1)
Applications of the Derivative
144(70)
Describing Graphs of Functions
144(12)
The First and Second Derivative Rules
156(10)
Curve Sketching (Introduction)
166(7)
Curve Sketching (Conclusion)
173(7)
Optimization Problems
180(9)
Further Optimization Problems
189(9)
Applications of Derivatives to Business and Economics
198(16)
Chapter Project
213(1)
Techniques of Differentiation
214(29)
The Product and Quotient Rules
214(8)
The Chain Rule and the General Power Rule
222(6)
Implicit Differentiation and Related Rates
228(15)
Chapter Project
242(1)
The Exponential and Natural Logarithm Functions
243(31)
Exponential Functions
243(4)
The Exponential Function ex
247(5)
Differentiation of Exponential Functions
252(5)
The Natural Logarithm Function
257(5)
The Derivative of In x
262(4)
Properties of the Natural Logarithm Function
266(8)
Chapter Project
272(2)
Applications of the Exponential and Natural Logarithm Functions
274(39)
Exponential Growth and Decay
274(10)
Compound Interest
284(8)
Applications of the Natural Logarithm Function to Economics
292(6)
Further Exponential Models
298(15)
Chapter Project
312(1)
The Definite Integral
313(54)
Antidifferentiation
314(9)
Areas and Riemann Sums
323(9)
Definite Integrals and the Fundamental Theorem
332(12)
Areas in the xy-Plane
344(10)
Applications of the Definite Integral
354(13)
Chapter Project
366(1)
Functions of Several Variables
367(63)
Examples of Functions of Several Variables
367(7)
Partial Derivatives
374(9)
Maxima and Minima of Functions of Several Variables
383(8)
Lagrange Multipliers and Constrained Optimization
391(11)
The Method of Least Squares
402(7)
Nonlinear Regression
409(12)
Double Integrals
421(9)
Chapter Project
429(1)
The Trigonometric Functions
430(30)
Radian Measure of Angles
430(4)
The Sine and the Cosine
434(8)
Differentiation and Integration of sin t and cos t
442(10)
The Tangent and Other Trigonometric Functions
452(8)
Chapter Project
459(1)
Techniques of Integration
460(43)
Integration by Substitution
461(7)
Integration by Parts
468(4)
Evaluation of Definite Integrals
472(5)
Approximation of Definite Integrals
477(11)
Some Applications of the Integral
488(5)
Improper Integrals
493(10)
Chapter Project
502(1)
Differential Equations
503(45)
Solutions of Differential Equations
503(7)
Separation of Variables
510(9)
Numerical Solution of Differential Equations
519(6)
Graphing Solutions of Differential Equations
525(10)
Applications of Differential Equations
535(13)
Chapter Project
547(1)
Taylor Polynomials and Infinite Series
548(45)
Taylor Polynomials
548(8)
The Newton-Raphson Algorithm
556(9)
Infinite Series
565(10)
Series with Positive Terms
575(6)
Taylor Series
581(12)
Chapter Project
592(1)
Probability and Calculus
593(46)
Discrete Random Variables
593(8)
Continuous Random Variables
601(9)
Expected Value and Variance
610(6)
Exponential and Normal Random Variables
616(10)
Poisson and Geometric Random Variables
626(13)
Chapter Project
639
Appendix A: Calculus and the TI-82 Calculator 1
Appendix B: Calculus and the TI-83/TI-83 Plus Calculators 6
Appendix C: Calculus and the TI-85 Calculator 11
Appendix D: Calculus and the TI-86 Calculator 16
Appendix E: Areas under the Standard Normal Curve 22
Answers to Exercises 23
Index 1

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