Calculus : Concepts and Contexts

by Stewart, James

• ISBN13: 9780534377182
• ISBN10: 0534377181
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-12-13
• Publisher: Brooks Cole

Summary

James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

Table of Contents

A Preview of Calculus	2	(8)
Functions and Models	10	(84)
Four Ways to Represent a Function	11	(13)
Mathematical Models	24	(14)
New Functions from Old Functions	38	(11)
Graphing Calculators and Computers	49	(7)
Exponential Functions	56	(8)
Inverse Functions and Logarithms	64	(11)
Parametric Curves	75	(19)
Laboratory Project Running Circles around Circles	83	(1)
Review	84	(4)
Priciples of Problem Solving	88	(6)
Limits and Derivatives	94	(94)
The Tangent and Velocity Problems	95	(5)
The Limit of a Function	100	(10)
Calculating Limits Using the Limit Laws	110	(9)
Continuity	119	(11)
Limits Involving Infinity	130	(12)
Tangents, Velocities, and Other Rates of Change	142	(8)
Derivatives	150	(7)
Writing Project Early Methods for Finding Tangents	157	(1)
The Derivative as a Function	157	(14)
Linear Approximations	171	(4)
What Does f' Say about f?	175	(13)
Review	181	(4)
Focus on Problem Solving	185	(3)
Differentiation Rules	188	(76)
Derivatives of Polynomials and Exponential Functions	189	(10)
Applied Project Building a Better Roller Coaster	198	(1)
The Product and Quotient Rules	199	(7)
Rates of Change in the Natural and Social Sciences	206	(12)
Derivatives of Trigonometric Functions	218	(7)
The Chain Rule	225	(12)
Laboratory Project Bezier Curves	236	(1)
Applied Project Where Should a Pilot Start Descent?	237	(1)
Implicit Differentiation	237	(8)
Derivatives of Logarithmic Functions	245	(7)
Discovery Project Hyperbolic Functions	251	(1)
Linear Approximations and Differentials	252	(12)
Laboratory Project Taylor Polynomials	257	(1)
Review	258	(3)
Focus on Problem Solving	261	(3)
Applications of Differentiation	264	(80)
Related Rates	265	(6)
Maximum and Minimum Values	271	(9)
Applied Project The Calculus of Rainbows	279	(1)
Derivatives and the Shapes of Curves	280	(11)
Graphing with Calculus and Calculators	291	(7)
Indeterminate Forms and 1'Hospital's Rule	298	(9)
Writing Project The Origins of l'Hospital's Rule	307	(1)
Optimization Problems	307	(12)
Applied Project The Shape of a Can	318	(1)
Applications to Economics	319	(5)
Newton's Method	324	(5)
Antiderivatives	329	(15)
Review	336	(4)
Focus on Problem Solving	340	(4)
Integrals	344	(102)
Areas and Distances	345	(12)
The Definite Integral	357	(12)
Evaluating Definite Integrals	369	(11)
Discovery Project Area Functions	379	(1)
The Fundamental Theorem of Calculus	380	(9)
Writing Project Newton, Leibniz, and the Invention of Calculus	388	(1)
The Substitution Rule	389	(7)
Integration by Parts	396	(7)
Additional Techniques of Integration	403	(6)
Integration Using Tables and Computer Algebra Systems	409	(7)
Discovery Project Patterns in Integrals	415	(1)
Approximate Integration	416	(12)
Improper Integrals	428	(18)
Review	438	(4)
Focus on Problem Solving	442	(4)
Applications of Integration	446	(60)
More about Areas	447	(6)
Volumes	453	(14)
Discovery Project Rotating on a Slant	466	(1)
Arc Length	467	(6)
Discovery Project Arc Length Contest	472	(1)
Average Value of a Function	473	(3)
Applied Project Where to Sit at the Movies	476	(1)
Applications to Physics and Engineering	476	(11)
Applications to Economics and Biology	487	(5)
Probability	492	(14)
Review	499	(3)
Focus on Problem Solving	502	(4)
Differential Equations	506	(56)
Modeling with Differential Equations	507	(5)
Direction Fields and Euler's Method	512	(10)
Separable Equations	522	(9)
Applied Project Which Is Faster, Going Up or Coming Down?	530	(1)
Exponential Growth and Decay	531	(10)
Applied Project Calculus and Baseball	540	(1)
The Logistic Equation	541	(9)
Predator-Prey Systems	550	(12)
Review	557	(3)
Focus on Problem Solving	560	(2)
Infinite Sequences and Series	562	(84)
Sequences	563	(10)
Laboratory Project Logistic Sequences	573	(1)
Series	573	(10)
The Integral and Comparison Tests; Estimating Sums	583	(9)
Other Convergence Tests	592	(8)
Power Series	600	(5)
Representations of Functions as Power Series	605	(6)
Taylor and Maclaurin Series	611	(11)
The Binomial Series	622	(4)
Writing Project How Newton Discovered the Binomial Series	626	(1)
Applications of Taylor Polynomials	626	(9)
Applied Project Radiation from the Stars	634	(1)
Using Series to Solve Differential Equations	635	(11)
Review	640	(3)
Focus on Problem Solving	643	(3)
Vectors and the Geometry of Space	646	(58)
Three-Dimensional Coordinate Systems	647	(5)
Vectors	652	(9)
The Dot Product	661	(6)
The Cross Product	667	(9)
Discovery Project The Geometry of a Tetrahedron	675	(1)
Equations of Lines and Planes	676	(9)
Functions and Surfaces	685	(9)
Cylindrical and Spherical Coordinates	694	(10)
Laboratory Project Families of Surfaces	699	(1)
Review	700	(3)
Focus on Problem Solving	703	(1)
Vector Functions	704	(44)
Vector Functions and Space Curves	705	(6)
Derivatives and Integrals of Vector Functions	711	(6)
Arc Length and Curvature	717	(8)
Motion in Space	725	(11)
Applied Project Kepler's Laws	735	(1)
Parametric Surfaces	736	(12)
Review	742	(3)
Focus on Problem Solving	745	(3)
Partial Derivatives	748	(90)
Functions of Several Variables	749	(11)
Limits and Continuity	760	(6)
Partial Derivatives	766	(13)
Tangent Planes and Linear Approximations	779	(11)
The Chain Rule	790	(8)
Directional Derivatives and the Gradient Vector	798	(13)
Maximum and Minimum Values	811	(11)
Applied Project Designing a Dumpster	820	(1)
Discovery Project Quadratic Approximations and Critical Points	821	(1)
Lagrange Multipliers	822	(16)
Applied Project Rocket Science	829	(1)
Applied Project Hydro-Turbine Optimization	830	(1)
Review	831	(5)
Focus on Problem Solving	836	(2)
Multiple Integrals	838	(78)
Double Integrals over Rectangles	839	(10)
Iterated Integrals	849	(5)
Double Integrals over General Regions	854	(9)
Double Integrals in Polar Coordinates	863	(5)
Applications of Double Integrals	868	(10)
Surface Area	878	(5)
Triple Integrals	883	(10)
Discovery Project Volumes of Hyperspheres	893	(1)
Triple Integrals in Cylindrical and Spherical Coordinates	893	(8)
Applied Project Roller Derby	900	(1)
Discovery Project The Intersection of Three Cylinders	901	(1)
Change of Variables in Multiple Integrals	901	(15)
Review	910	(4)
Focus on Problem Solving	914	(2)
Vector Calculus	916
Vector Fields	917
Line Integrals	924
The Fundamental Theorem for Line Integrals	936
Green's Theorem	945
Curl and Divergence	952
Surface Integrals	960
Stokes' Theorem	971
Writing Project Three Men and Two Theorems	977
The Divergence Theorem	978
Summary	985
Review	986
Focus on Problem Solving	989
Appendixes	A1
A Intervals, Inequalities, and Absolute Values	A2
B Coordinate Geometry	A7
C Trigonometry	A18
D Precise Definitions of Limits	A29
E A Few Proofs	A39
F Sigma Notation	A44
G Integration of Rational Functions by Partial Fractions	A50
H Polar Coordinates	A58
I Complex Numbers	A74
J Answers to Odd-Numbered Exercises	A83
Index	A135