Single Variable Calculus Early Transcendentals

by STEWART

• ISBN13: 9780534393335
• ISBN10: 0534393330
• Edition: 5th
• Format: Paperback
• Copyright: 2003-06-20
• Publisher: Brooks Cole

Table of Contents

Functions and Models	1	(32)
Four Ways to Represent a Function	1	(4)
Mathematical Models: A Catalog of Essential Functions	5	(3)
New Functions from Old Functions	8	(6)
Graphing Calculators and Computers	14	(4)
Exponential Functions	18	(3)
Inverse Functions and Logarithms	21	(12)
Review	25	(6)
Principles of Problem Solving	31	(2)
Limits and Derivatives	33	(44)
The Tangent and Velocity Problems	33	(2)
The Limit of a Function	35	(4)
Calculating Limits Using the Limit Laws	39	(4)
The Precise Definition of a Limit	43	(3)
Continuity	46	(5)
Limits at Infinity; Horizontal Asymptotes	51	(7)
Tangents, Velocities, and Other Rates of Change	58	(3)
Derivatives	61	(3)
The Derivative as a Function	64	(13)
Review	69	(6)
Problems Plus	75	(2)
Differentiation Rules	77	(56)
Derivatives of Polynomials and Exponential Functions	77	(4)
The Product and Quotient Rules	81	(3)
Rates of Change in the Natural and Social Sciences	84	(4)
Derivatives of Trigonometric Functions	88	(2)
The Chain Rule	90	(5)
Implicit Differentiation	95	(6)
Higher Derivatives	101	(4)
Derivatives of Logarithmic Functions	105	(3)
Hyperbolic Functions	108	(3)
Related Rates	111	(4)
Linear Approximations and Differentials	115	(18)
Review	118	(9)
Problems Plus	127	(6)
Applications of Differentiation	133	(88)
Maximum and Minimum Values	133	(5)
The Mean Value Theorem	138	(3)
How Derivatives Affect the Shape of a Graph	141	(11)
Indeterminate Forms and L'Hospital's Rule	152	(5)
Summary of Curve Sketching	157	(13)
Graphing with Calculus and Calculators	170	(10)
Optimization Problems	180	(10)
Applications to Business and Economics	190	(2)
Newton's Method	192	(5)
Antiderivatives	197	(24)
Review	202	(13)
Problems Plus	215	(6)
Integrals	221	(30)
Areas and Distances	221	(5)
The Definite Integral	226	(5)
The Fundamental Theorem of Calculus	231	(4)
Indefinite Integrals and the Net Change Theorem	235	(3)
The Substitution Rule	238	(4)
The Logarithm Defined as an Integral	242	(9)
Review	243	(6)
Problems Plus	249	(2)
Applications of Integration	251	(32)
Areas between Curves	251	(7)
Volumes	258	(8)
Volumes by Cylindrical Shells	266	(5)
Work	271	(2)
Average Value of a Function	273	(10)
Review	274	(5)
Problems Plus	279	(4)
Techniques of Integration	283	(56)
Integration by Parts	283	(4)
Trigonometric Integrals	287	(4)
Trigonometric Substitution	291	(5)
Integration of Rational Functions by Partial Fractions	296	(7)
Strategy for Integration	303	(5)
Integration Using Tables and Computer Algebra Systems	308	(4)
Approximate Integration	312	(7)
Improper Integrals	319	(20)
Review	326	(9)
Problems Plus	335	(4)
Further Applications of Integration	339	(26)
Arc Length	339	(3)
Area of a Surface of Revolution	342	(4)
Applications to Physics and Engineering	346	(7)
Applications to Economics and Biology	353	(2)
Probability	355	(10)
Review	357	(4)
Problems Plus	361	(4)
Differential Equations	365	(32)
Modeling with Differential Equations	365	(1)
Direction Fields and Euler's Method	366	(4)
Separable Equations	370	(5)
Exponential Growth and Decay	375	(2)
The Logistic Equation	377	(4)
Linear Equations	381	(4)
Predator-Prey Systems	385	(12)
Review	387	(6)
Problems Plus	393	(4)
Parametric Equations and Polar Coordinates	397	(46)
Curves Defined by Parametric Equations	397	(5)
Calculus with Parametric Curves	402	(8)
Polar Coordinates	410	(9)
Areas and Lengths in Polar Coordinates	419	(7)
Conic Sections	426	(4)
Conic Sections in Polar Coordinates	430	(13)
Review	433	(8)
Problems Plus	441	(2)
Infinite Sequences and Series	443	(78)
Sequences	443	(5)
Series	448	(6)
The Integral Test and Estimates of Sums	454	(4)
The Comparison Tests	458	(2)
Alternating Series	460	(3)
Absolute Convergence and the Ratio and Root Tests	463	(3)
Strategy for Testing Series	466	(2)
Power Series	468	(3)
Representations of Functions as Power Series	471	(5)
Taylor and Maclaurin Series	476	(7)
The Binomial Series	483	(4)
Applications of Taylor Polynomials	487	(20)
Review	494	(7)
Problems Plus	501	(6)
APPENDIXES
A Numbers, Inequalities, and Absolute Values	507	(2)
B Coordinate Geometry and Lines	509	(3)
C Graphs of Second-Degree Equations	512	(2)
D Trigonometry	514	(5)
E Sigma Notation	519	(2)
G Complex Numbers	521