Calculus: Single Variable

by Hughes-Hallett, Deborah; Gleason, Andrew M.

• ISBN13: 9780471164432
• ISBN10: 0471164437
• Edition: 2nd
• Format: Hardcover
• Copyright: 1998-11-01
• Publisher: John Wiley & Sons Inc

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, l2Hopital2s Rule, and relative growth rates, and hyperbolic functions.

Table of Contents

A Library of Functions	1	(86)
What's A Function?	2	(5)
Linear Functions	7	(6)
Exponential Functions	13	(11)
Power Functions	24	(7)
Notes on Inverse Functions	31	(4)
Logarithms	35	(5)
The Number e And Natural Logarithms	40	(6)
New Functions From Old	46	(6)
The Trigonometric Functions	52	(8)
Polynomials And Rational Functions	60	(7)
Introduction to Continuity	67	(20)
Review Problems	70	(6)
Projects	76	(1)
Focus on Theory	77	(1)
Underpinnings of Calculus	77	(1)
The Binomial Theorem	78	(4)
Completeness of The Real Numbers	82	(5)
Key Concept: The Derivative	87	(58)
How Do We Measure Speed?	88	(7)
The Derivative At A Point	95	(10)
The Derivative Function	105	(7)
Interpretations of The Derivative	112	(4)
The Second Derivative	116	(29)
Review Problems	122	(4)
Projects	126	(1)
Focus on Theory	127	(1)
Limits And Continuity	127	(9)
Differentiability And Linear Approximation	136	(9)
Key Concept: The Definite Integral	145	(44)
How Do We Measure Distance Traveled?	146	(7)
The Definite Integral	153	(7)
Interpretations of The Definite Integral	160	(7)
Theorems About Definite Integrals	167	(22)
Review Problems	175	(5)
Projects	180	(1)
Focus on Theory	181	(1)
The Definite Integral	181	(8)
Short-Cuts to Differentiation	189	(50)
Powers And Polynomials	190	(7)
The Exponential Function	197	(5)
The Product and Quotient Rules	202	(6)
The Chain Rule	208	(5)
The Trigonometric Functions	213	(6)
Applications of The Chain Rule	219	(5)
Implicit Functions	224	(3)
Linear Approximations And Limits	227	(12)
Review Problems	233	(3)
Projects	236	(1)
Focus on Practice	237	(1)
Differentiation	237	(2)
Using The Derivative	239	(54)
Using First And Second Derivatives	240	(10)
Families of Curves: A Qualitative Study	250	(4)
Optimization	254	(8)
Applications to Marginality	262	(8)
More Optimization: Introduction to Modeling	270	(7)
Hyperbolic Functions	277	(16)
Review Problems	281	(3)
Projects	284	(2)
Focus on Theory	286	(1)
Theorems About Continuous And Differentiable Functions	286	(7)
Constructing Antiderivatives	293	(28)
Antiderivatives Graphically And Numerically	294	(4)
Constructing Antiderivatives Analytically	298	(6)
Differential Equations	304	(5)
Second Fundamental Theorem of Calculus	309	(12)
Review Problems	313	(3)
Projects	316	(1)
Focus on Modeling	317	(1)
The Equations of Motion	317	(4)
Integration	321	(54)
Integration By Substitution: Part I	322	(6)
Integration By Substitution: Part II	328	(5)
Integration By Parts	333	(6)
Tables of Integrals	339	(5)
Approximating Definite Integrals	344	(6)
Approximation Errors And Simpson's Rule	350	(6)
Improper Integrals	356	(8)
More on Improper Integrals	364	(11)
Review Problems	369	(2)
Projects	371	(2)
Focus on Practice	373	(1)
Integration	373	(2)
Using The Definite Integral	375	(50)
Applications to Geometry	376	(8)
Density And Center of Mass	384	(6)
Applications to Physics	390	(8)
Applications to Economics	398	(27)
Review Problems	405	(3)
Projects	408	(1)
Focus on Modeling	409	(1)
Distribution Functions	409	(7)
Probability And More on Distributions	416	(9)
Approximations And Series	425	(64)
Taylor Polynomials And Series	426	(9)
Convergence of Series	435	(9)
Finding And Using Taylor Series	444	(7)
Geometric Series	451	(7)
Fourier Series	458	(31)
Review Problems	471	(3)
Projects	474	(2)
Focus on Theory	476	(1)
Convergence Theorems	476	(5)
The Error in Taylor Approximations	481	(8)
Differential Equations	489	(90)
What is A Differential Equation?	490	(4)
Slope Fields	494	(7)
Euler's Method	501	(4)
Separation of Variables	505	(5)
Growth And Decay	510	(10)
Applications And Modeling	520	(10)
Models of Population Growth	530	(12)
Second-Order Differential Equations: Oscillations	542	(8)
Linear Second-Order Differential Equations	550	(29)
Review Problems	558	(3)
Projects	561	(2)
Focus on Modeling	563	(1)
Systems of Differential Equations	563	(9)
Analyzing The Phase Plane	572	(7)
APPENDIX	579	(44)
A Roots, Accuracy, And Bounds	580	(9)
B Compound Interest	589	(4)
C Polar Coordinates	593	(2)
D Complex Numbers	595	(5)
E Newton's Method	600	(4)
F Parametric Equations	604	(6)
G Parametric Equations And Calculus	610	(4)
H Projects	614	(9)
Answers to Odd Numbered Problems	623	(16)
Index	639