Calculus , Alternate Version, 2nd Edition,9780471361138

Calculus , Alternate Version, 2nd Edition

by ; ; ; ; ; ;
Edition: 2nd
ISBN13: 9780471361138
ISBN10: 0471361135
Format: Paperback
Pub. Date: 2000-01-01
Publisher(s): Wiley
List Price: $127.80

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Summary

A revision of the best selling innovative Calculus text on the market. Functions are presented graphically, numerically, algebraically, and verbally to give readers the benefit of alternate interpretations. The text is problem driven with exceptional exercises based on real world applications from engineering, physics, life sciences, and economics. Revised edition features new sections on limits and continuity, limits, l'Hopital's Rule, and relative growth rates, and hyperbolic functions.

Table of Contents

Functions
1(42)
Functions and Growth
2(8)
New Functions from Old
10(9)
Families of Functions and Modeling
19(7)
Introduction to Continuity
26(17)
Review Problems
29(2)
Projects and Computer Algebra Investigations
31(2)
Focus on Theory
33(1)
Underpinnings of Calculus
33(1)
The Binomial Theorem
34(4)
Completeness of the Real Numbers
38(5)
Key Concept: The Derivative
43(58)
How do We Measure Speed?
44(7)
The Derivative at a Point
51(10)
The Derivative Function
61(7)
Interpretations of the Derivative
68(4)
The Second Derivative
72(29)
Review Problems
78(4)
Projects and Computer Algebra Investigations
82(2)
Focus on Theory
84(1)
Limits and Continuity
84(9)
Differentiability and Linear Approximation
93(8)
Short-Cuts To Differentiation
101(52)
Powers and Polynomials
102(7)
The Exponential Function
109(5)
The Product and Quotient Rules
114(6)
The Chain Rule
120(5)
The Trigonometric Functions
125(6)
Applications of the Chain Rule
131(5)
Implicit Functions
136(3)
Linear Approximations and Limits
139(14)
Review Problems
145(3)
Projects and Computer Algebra Investigations
148(2)
Focus on Practice
150(1)
Differentiation
150(3)
Using the Derivative
153(56)
Using First and Second Derivatives
154(10)
Families of Curves: a Qualitative Study
164(4)
Optimization
168(8)
Applications to Marginality
176(8)
More Optimization: Introduction to Modeling
184(7)
Hyperbolic Functions
191(18)
Review Problems
195(3)
Projects and Computer Algebra Investigations
198(3)
Focus on Theory
201(1)
Theorems about Continuous and Differentiable Functions
201(8)
Key Concept: the Definite Integral
209(44)
How do we Measure Distance Traveled?
210(7)
The Definite Integral
217(7)
Interpretations of the Definite Integral
224(7)
Theorems about Definite Integrals
231(22)
Review Problems
239(5)
Projects and Computer Algebra Investigations
244(2)
Focus on Theory
246(1)
The Definite Integral
246(7)
Constructing Antiderivatives
253(28)
Antiderivatives Graphically and Numerically
254(4)
Constructing Antiderivatives Analytically
258(6)
Differential Equations
264(5)
Second Fundamental Theorem of Calculus
269(12)
Review Problems
273(3)
Projects and Computer Algebra Investigations
276(2)
Focus on Modeling
278(1)
The Equations of Motion
278(3)
Integration
281(56)
Integration by Substitution: Part I
282(6)
Integration by Substitution: Part II
288(5)
Integration by Parts
293(6)
Tables of Integrals
299(5)
Approximating Definite Integrals
304(6)
Approximation Errors and Simpson's Rule
310(6)
Improper Integrals
316(8)
More on Improper Integrals
324(13)
Review Problems
329(2)
Projects and Computer Algebra Investigations
331(3)
Focus on Practice
334(1)
Integration
334(3)
Using the Definite Integral
337(50)
Applications to Geometry
338(8)
Density and Center of Mass
346(6)
Applications to Physics
352(8)
Applications to Economics
360(27)
Review Problems
367(3)
Projects and Computer Algebra Investigations
370(2)
Focus on Modeling
372(1)
Distribution Functions
372(7)
Probability and more on Distributions
379(8)
Approximations and Series
387(64)
Taylor Polynomials and Series
388(9)
Convergence of Series
397(10)
Finding and Using Taylor Series
407(6)
Geometric Series
413(7)
Fourier Series
420(31)
Review Problems
432(3)
Projects and Computer Algebra Investigations
435(3)
Focus on Theory
438(1)
Convergence Theorems
438(7)
The Error in Taylor Approximations
445(6)
Differential Equations
451(92)
What is a Differential Equation?
452(4)
Slope Fields
456(7)
Euler's Method
463(4)
Separation of Variables
467(5)
Growth and Decay
472(10)
Applications and Modeling
482(10)
Models of Population Growth
492(12)
Second-order Differential Equations: Oscillations
504(8)
Linear Second-Order Differential Equations
512(31)
Review Problems
520(3)
Projects and Computer Algebra Investigations
523(4)
Focus on Modeling
527(1)
Systems of Differential Equations
527(9)
Analyzing the Phase Plane
536(7)
APPENDIX 543(44)
A Roots, Accuracy, and Bounds
544(9)
B Compound Interest
553(5)
C Polar Coordinates
558(1)
D Complex Numbers
559(5)
E Newton's Method
564(4)
F Parametric Equations
568(6)
G Parametric Equations and Calculus
574(4)
H Projects
578(9)
Ready Reference 587(18)
Answers to Odd Numbered Problems 605(14)
Index 619

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