Single Variable Calculus

by STEWART

• ISBN13: 9780534393311
• ISBN10: 0534393314
• Edition: 5th
• Format: Paperback
• Copyright: 2003-01-06
• Publisher: Brooks Cole

Table of Contents

Functions and Models
Four Ways to Represent a Function	2	(9)
Mathematical Models	11	(6)
New Functions from Old Functions	17	(4)
Graphing Calculators and Computers	21	(2)
Exponential Functions	23	(4)
Inverse Functions and Logarithms	27	(9)
Technology Plus	33	(3)
Limits and Rates of Change
The Tangent and Velocity Problems	36	(3)
The Limit of a Function	39	(8)
Calculating Limits Using the Limit Laws	47	(7)
The Precise Definition of a Limit	54	(5)
Continuity	59	(4)
Limits at Infinity; Horizontal Asymptotes	63	(6)
Tangents, Velocities, and Other Rates of Change	69	(3)
Derivatives	72	(5)
The Derivative as a Function	77	(11)
Technology Plus	83	(5)
Derivatives
Derivatives of Polynomials and Exponential Functions	88	(3)
The Product and Quotient Rules	91	(2)
Rates of Change in the Natural and Social Sciences	93	(3)
Derivatives of Trigonometric Functions	96	(3)
The Chain Rule	99	(4)
Implicit Differentiation	103	(7)
Higher Derivatives	110	(3)
Derivatives of Logarithmic Functions	113	(3)
Hyperbolic Functions	116	(4)
Related Rates	120	(6)
Linear Approximations and Differentials	126	(8)
Technology Plus	130	(4)
Applications of Differentiation
Maximum and Minimum Values	134	(6)
The Mean Value Theorem	140	(4)
How Derivatives Affect the Shape of a Graph	144	(8)
Indeterminante Forms and L' Hospital's Rule	152	(4)
Summary of Curve Sketching	156	(5)
Graphing with Calculus and Calculators	161	(2)
Optimization Problems	163	(3)
Applications to Business and Economics	166	(2)
Newton's Method	168	(2)
Antiderivatives	170	(8)
Technology Plus	173	(5)
Integrals
Areas and Distances	178	(6)
The Definite Integral	184	(6)
The Fundamental Theorem of Calculus	190	(2)
Indefinite Integrals and the Net Change Theorem	192	(4)
The Substitution Rule	196	(6)
The Logarithm Defined as an Integral	202	(8)
Technology Plus	207	(3)
Applications of Integration
Areas between Curves	210	(5)
Volumes	215	(4)
Volumes by Cylindrical Shells	219	(2)
Work	221	(2)
Average Value of a Function	223	(6)
Technology Plus	226	(3)
Techniques of Integration
Integration by Parts	229	(3)
Trigonometric Integrals	232	(4)
Trigonometric Substitution	236	(4)
Integration of Rational Functions by Partial Fractions	240	(5)
Strategy for Integration	245	(2)
Using Tables of Integrals and Computer Algebra Systems	247	(2)
Approximate Integration	249	(5)
Improper Integrals	254	(8)
Technology Plus	258	(4)
Further Applications of Integration
Arc Length	262	(5)
Area of a Surface of Revolution	267	(2)
Applications to Physics and Engineering	269	(4)
Applications to Economics and Biology	273	(2)
Probability	275	(5)
Technology Plus	278	(2)
Differential Equations
Modeling with Differential Equations	280	(2)
Direction Fields and Euler's Method	282	(3)
Separable Equations	285	(3)
Exponential Growth and Decay	288	(3)
The Logistic Equation	291	(2)
Linear Equations	293	(2)
Predator-Prey Systems	295	(5)
Technology Plus	297	(3)
Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations	300	(4)
Calculus with Parametric Curves	304	(6)
Polar Coordinates	310	(7)
Areas and Lengths in Polar Coordinates	317	(3)
Conic Sections	320	(4)
Conic Section in Polar Coordinates	324	(6)
Technology Plus	327	(3)
Infinite Sequences and Series
Sequences	330	(5)
Series	335	(4)
The Integral Test and Estimates of Sums	339	(3)
The Comparison Tests	342	(3)
Alternating Series	345	(3)
Absolute Convergence and the Ratio and Root Tests	348	(5)
Strategy for Testing Series	353	(2)
Power Series	355	(3)
Representations of Functions as Power Series	358	(4)
Taylor and Maclaurin Series	362	(7)
The Binomial Series	369	(2)
Applications of Taylor Polynomials	371	(8)
Technology Plus	375	(4)
On Your Own
Chapter 1 On Your Own	379	(6)
Chapter 2 On Your Own	385	(9)
Chapter 3 On Your Own	394	(11)
Chapter 4 On Your Own	405	(11)
Chapter 5 On Your Own	416	(6)
Chapter 6 On Your Own	422	(5)
Chapter 7 On Your Own	427	(8)
Chapter 8 On Your Own	435	(5)
Chapter 9 On Your Own	440	(7)
Chapter 10 On Your Own	447	(6)
Chapter 11 On Your Own	453	(12)
Answers to On Your Own	465