Calculus , Alternate Version, 2nd Edition

by Deborah Hughes-Hallett (Harvard Univ.); Andrew M. Gleason (Harvard Univ.); Daniel E. Flath (Univ. of South Alabama); Patti Frazer Lock (St. Lawrence Univ.); Sheldon P. Gordon (Suffolk County Community College); David O. Lomen (Univ. of Arizona); Dav

• ISBN13: 9780471361138
• ISBN10: 0471361135
• Edition: 2nd
• Format: Paperback
• Copyright: 2000-01-01
• Publisher: Wiley

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