Study Guide for Single Variable Calculus, Early Transcendentals

by Stewart, James

• ISBN13: 9780534368203
• ISBN10: 0534368204
• Format: Paperback
• Copyright: 1999-08-23
• Publisher: Brooks Cole

Summary

Reinforces student understanding of calculus with additional explanations, worked-out examples, and practice problems.

Table of Contents

Functions and Models
Four Ways to Represent a Function	2	(7)
Mathematical Models	9	(6)
New Functions from Old Functions	15	(4)
Graphing Calculators and Computers	19	(2)
Exponential Functions	21	(4)
Inverse Functions and Logarithms	25	(9)
Technology Plus	31	(3)
Limits and Rates of Change
The Tangent and Velocity Problems	34	(3)
The Limit of a Function	37	(8)
Calculating Limits Using the Limit Laws	45	(7)
The Precise Definition of a Limit	52	(5)
Continuity	57	(4)
Limits at Infinity; Horizontal Asymptotes	61	(6)
Tangents, Velocities, and Other Rates of Change	67	(3)
Derivatives	70	(5)
The Derivative as a Function	75	(11)
Technology Plus	81	(5)
Derivatives
Derivatives of Polynomials and Exponential Functions	86	(3)
The Product and Quotient Rules	89	(2)
Rates of Change in the Natural and Social Sciences	91	(3)
Derivatives of Trigonometric Functions	94	(3)
The Chain Rule	97	(4)
Implicit Differentiation	101	(7)
Higher Derivatives	108	(3)
Derivatives of Logarithmic Functions	111	(3)
Hyperbolic Functions	114	(4)
Related Rates	118	(5)
Linear Approximations and Differentials	123	(7)
Technology Plus	126	(4)
Applications of Differentiation
Maximum and Minimum Values	130	(6)
The Mean Value Theorem	136	(4)
How Derivatives Affect the Shape of a Graph	140	(8)
Indeterminante Forms and L'Hospital's Rule	148	(4)
Summary of Curve Sketching	152	(5)
Graphing with Calculus and Calculators	157	(2)
Optimization Problems	159	(3)
Applications to Economics	162	(2)
Newton's Method	164	(2)
Antiderivatives	166	(8)
Technology Plus	169	(5)
Integrals
Areas and Distances	174	(6)
The Definite Integral	180	(6)
The Fundamental Theorem of Calculus	186	(2)
Indefinite Integrals and the Total Change Theorem	188	(4)
The Substitution Rule	192	(6)
The Logarithm Defined as an Integral	198	(8)
Technology Plus	203	(3)
Applications of Integration
Areas between Curves	206	(5)
Volumes	211	(4)
Volumes by Cylindrical Shells	215	(2)
Work	217	(2)
Average Value of a Function	219	(6)
Technology Plus	222	(3)
Techniques of Integration
Integration by Parts	225	(3)
Trigonometric Integrals	228	(4)
Trigonometric Substitution	232	(4)
Integration of Rational Functions by Partial Fractions	236	(5)
Strategy for Integration	241	(2)
Using Tables of Integrals and Computer Algebra Systems	243	(2)
Approximate Integration	245	(5)
Improper Integrals	250	(8)
Technology Plus	254	(4)
Further Applications of Integration
Arc Length	258	(5)
Area of a Surface of Revolution	263	(2)
Applications to Physics and Engineering	265	(4)
Applications to Economics and Biology	269	(2)
Probability	271	(5)
Technology Plus	274	(2)
Differential Equations
Modeling with Differential Equations	276	(2)
Direction Fields and Euler's Method	278	(3)
Separable Equations	281	(3)
Exponential Growth and Decay	284	(3)
The Logistic Equation	287	(2)
Linear Equations	289	(2)
Predator-Prey Systems	291	(5)
Technology Plus	293	(3)
Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations	296	(4)
Tangents and Areas	300	(4)
Arc Length and Surface Area	304	(3)
Polar Coordinates	307	(7)
Areas and Lengths in Polar Coordinates	314	(3)
Conic Sections	317	(4)
Conic Sections in Polar Coordinates	321	(7)
Technology Plus	324	(4)
Infinite Sequences and Series
Sequences	328	(5)
Series	333	(4)
The Integral Test and Estimates of Sums	337	(3)
The Comparison Tests	340	(3)
Alternating Series	343	(3)
Absolute Convergence and the Ratio and Root Tests	346	(5)
Strategy for Testing Series	351	(2)
Power Series	353	(3)
Representations of Functions as Power Series	356	(4)
Taylor and Maclaurin Series	360	(7)
The Binomial Series	367	(2)
Applications of Taylor Polynomials	369	(8)
Technology Plus	373	(4)
On Your Own
Chapter 1 On Your Own	377	(6)
Chapter 2 On Your Own	383	(9)
Chapter 3 On Your Own	392	(11)
Chapter 4 On Your Own	403	(11)
Chapter 5 On Your Own	414	(6)
Chapter 6 On Your Own	420	(5)
Chapter 7 On Your Own	425	(8)
Chapter 8 On Your Own	433	(5)
Chapter 9 On Your Own	438	(7)
Chapter 10 On Your Own	445	(7)
Chapter 11 On Your Own	452	(12)
Answers to On Your Own	464