Single Variable Calculus, Volume 2

by Stewart, James

• ISBN13: 9780534496777
• ISBN10: 0534496776
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-06-21
• Publisher: Brooks Cole

Summary

Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS, VOLUME 2, 5th Edition guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.

Table of Contents

Preface	xii
To the Student	xxiv
Integrals	314	(60)
Areas and Distances	315	(11)
The Definite Integral	326	(14)
Discovery Project: Area Functions	339	(1)
The Fundamental Theorem of Calculus	340	(10)
Indefinite Integrals and the Net Change Theorem	350	(10)
Writing Project: Newton, Leibniz, and the Invention of Calculus	359	(1)
The Substitution Rule	360	(14)
Review	368	(4)
Problems Plus	372	(2)
Applications of Integration	374	(38)
Areas between Curves	375	(7)
Volumes	382	(11)
Volumes by Cylindrical Shells	393	(5)
Work	398	(4)
Average Value of a Function	402	(10)
Review	406	(2)
Problems Plus	408	(4)
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions	412	(98)
Inverse Functions	413	(8)
Exponential Functions and Their Derivatives	421	(13)
Logarithmic Functions	434	(7)
Derivatives of Logarithmic Functions	441	(10)
The Natural Logarithmic Function	451	(9)
The Natural Exponential Function	460	(7)
General Logarithmic and Exponential Functions	467	(10)
Inverse Trigonometric Functions	477	(9)
Applied Project: Where to Sit at the Movies	485	(1)
Hyperbolic Functions	486	(7)
Indeterminate Forms and L'Hospital's Rule	493	(17)
Writing Project: The Origins of L'Hospital's Rule	504	(1)
Review	504	(4)
Problems Plus	508	(2)
Techniques of Integration	510	(72)
Integration by Parts	511	(7)
Trigonometric Integrals	518	(7)
Trigonometric Substitution	525	(7)
Integration of Rational Functions by Partial Fractions	532	(9)
Strategy for Integration	541	(6)
Integration Using Tables and Computer Algebra Systems	547	(7)
Discovery Project: Patterns in Integrals	553	(1)
Approximate Integration	554	(12)
Improper Integrals	566	(16)
Review	576	(3)
Problems Plus	579	(3)
Further Applications of Integration	582	(40)
Arc Length	583	(7)
Discovery Project: Arc Length Contest	590	(1)
Area of a Surface of Revolution	590	(7)
Discovery Project: Rotating on a Slant	596	(1)
Applications to Physics and Engineering	597	(10)
Applications to Economics and Biology	607	(4)
Probability	611	(11)
Review	618	(2)
Problems Plus	620	(2)
Differential Equations	622	(64)
Modeling with Differential Equations	623	(5)
Direction Fields and Euler's Method	628	(9)
Separable Equations	637	(10)
Applied Project: How Fast Does a Tank Drain?	645	(1)
Applied Project: Which Is Faster, Going Up or Coming Down?	646	(1)
Exponential Growth and Decay	647	(12)
Applied Project: Calculus and Baseball	658	(1)
The Logistic Equation	659	(9)
Linear Equations	668	(6)
Predator-Prey Systems	674	(12)
Review	680	(4)
Problems Plus	684	(2)
Parametric Equations and Polar Coordinates	686	(50)
Curves Defined by Parametric Equations	687	(9)
Laboratory Project: Running Circles around Circles	695	(1)
Calculus with Parametric Curves	696	(9)
Laboratory Project: Bezier Curves	705	(1)
Polar Coordinates	705	(10)
Areas and Lengths in Polar Coordinates	715	(5)
Conic Sections	720	(8)
Conic Sections in Polar Coordinates	728	(8)
Review	732	(3)
Problems Plus	735	(1)
Infinite Sequences and Series	736
Sequences	737	(12)
Laboratory Project: Logistic Sequences	749	(1)
Series	749	(10)
The Integral Test and Estimates of Sums	759	(7)
The Comparison Tests	766	(5)
Alternating Series	771	(5)
Absolute Convergence and the Ratio and Root Tests	776	(7)
Strategy for Testing Series	783	(2)
Power Series	785	(5)
Representations of Functions as Power Series	790	(6)
Taylor and Maclaurin Series	796	(12)
Laboratory Project: An Elusive Limit	808	(1)
The Binomial Series	808	(4)
Writing Project: How Newton Discovered the Binomial Series	812	(1)
Applications of Taylor Polynomials	812
Applied Project: Radiation from the Stars	821	(1)
Review	822	(3)
Problems Plus	825
Appendixes	1	(82)
A. Numbers, Inequalities, and Absolute Values	2	(8)
B. Coordinate Geometry and Lines	10	(6)
C. Graphs of Second-Degree Equations	16	(8)
D. Trigonometry	24	(10)
E. Sigma Notation	34	(5)
F. Proofs of Theorems	39	(2)
G. Complex Numbers	41	(8)
H. Answers to Odd-Numbered Exercises	49	(34)
Index	83