Calculus Concepts and Contexts

by Stewart, James

• ISBN13: 9780534410032
• ISBN10: 0534410030
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-11-04
• Publisher: Brooks Cole

Table of Contents

A Preview of Calculus	2	(8)
Functions and Models	10	(82)
Four Ways to Represent a Function	11	(14)
Mathematical Models: A Catalog of Essential Functions	25	(13)
New Functions from Old Functions	38	(11)
Graphing Calculators and Computers	49	(6)
Exponential Functions	55	(8)
Inverse Functions and Logarithms	63	(11)
Parametric Curves	74	(18)
Laboratory Project: Running Circles around Circles	82	(1)
Review	83	(3)
Principles of Problem Solving	86	(6)
Limits and Derivatives	92	(90)
The Tangent and Velocity Problems	93	(5)
The Limit of a Function	98	(10)
Calculating Limits Using the Limit Laws	108	(9)
Continuity	117	(11)
Limits Involving Infinity	128	(11)
Tangents, Velocities, and Other Rates of Change	139	(9)
Derivatives	148	(7)
Writing Project: Early Methods for Finding Tangents	155	(1)
The Derivative as a Function	155	(13)
What Does f' Say about f?	168	(14)
Review	175	(4)
Focus on Problem Solving	179	(3)
Differentiation Rules	182	(80)
Derivatives of Polynomials and Exponential Functions	183	(10)
Applied Project: Building a Better Roller Coaster	192	(1)
The Product and Quotient Rules	193	(7)
Rates of Change in the Natural and Social Sciences	200	(13)
Derivatives of Trigonometric Functions	213	(7)
The Chain Rule	220	(12)
Laboratory Project: Bezier Curves	231	(1)
Applied Project: Where Should a Pilot Start Descent?	232	(1)
Implicit Differentiation	232	(8)
Derivatives of Logarithmic Functions	240	(7)
Discovery Project: Hyperbolic Functions	246	(1)
Linear Approximations and Differentials	247	(15)
Laboratory Project: Taylor Polynomials	254	(1)
Review	255	(3)
Focus on Problem Solving	258	(4)
Applications of Differentiation	262	(80)
Related Rates	263	(6)
Maximum and Minimum Values	269	(9)
Applied Project: The Calculus of Rainbows	277	(1)
Derivatives and the Shapes of Curves	278	(11)
Graphing with Calculus and Calculators	289	(8)
Indeterminate Forms and I'Hospital's Rule	297	(9)
Writing Project: The Origins of I'Hospital's Rule	305	(1)
Optimization Problems	306	(11)
Applied Project: The Shape of a Can	316	(1)
Applications to Business and Economics	317	(5)
Newton's Method	322	(5)
Antiderivatives	327	(15)
Review	335	(4)
Focus on Problem Solving	339	(3)
Integrals	342	(98)
Areas and Distances	343	(11)
The Definite Integral	354	(12)
Evaluating Definite Integrals	366	(11)
Discovery Project: Area Functions	376	(1)
The Fundamental Theorem of Calculus	377	(9)
Writing Project: Newton, Leibniz, and the Invention of Calculus	385	(1)
The Substitution Rule	386	(7)
Integration by Parts	393	(7)
Additional Techniques of Integration	400	(5)
Integration Using Tables and Computer Algebra Systems	405	(7)
Discovery Project: Patterns in Integrals	411	(1)
Approximate Integration	412	(11)
Improper Integrals	423	(17)
Review	433	(4)
Focus on Problem Solving	437	(3)
Applications of Integration	440	(58)
More about Areas	441	(6)
Volumes	447	(14)
Discovery Project: Rotating on a Slant	460	(1)
Arc Length	461	(6)
Discovery Project: Arc Length Contest	466	(1)
Average Value of a Function	467	(4)
Applied Project: Where to Sit at the Movies	470	(1)
Applications to Physics and Engineering	471	(11)
Applications to Economics and Biology	482	(4)
Probability	486	(12)
Review	493	(3)
Focus on Problem Solving	496	(2)
Differential Equations	498	(58)
Modeling with Differential Equations	499	(5)
Direction Fields and Euler's Method	504	(9)
Separable Equations	513	(11)
Applied Project: How Fast Does a Tank Drain?	521	(2)
Applied Project: Which Is Faster, Going Up or Coming Down?	523	(1)
Exponential Growth and Decay	524	(11)
Applied Project: Calculus and Baseball	534	(1)
The Logistic Equation	535	(9)
Predator-Prey Systems	544	(12)
Review	551	(3)
Focus on Problem Solving	554	(2)
Infinite Sequences and Series	556	(80)
Sequences	557	(10)
Laboratory Project: Logistic Sequences	567	(1)
Series	567	(10)
The Integral and Comparison Tests; Estimating Sums	577	(9)
Other Convergence Tests	586	(8)
Power Series	594	(5)
Representations of Functions as Power Series	599	(6)
Taylor and Maclaurin Series	605	(12)
Laboratory Project: An Elusive Limit	617	(1)
The Binomial Series	617	(4)
Writing Project: How Newton Discovered the Binomial Series	621	(1)
Applications of Taylor Polynomials	621	(15)
Applied Project: Radiation from the Stars	630	(1)
Review	631	(3)
Focus on Problem Solving	634	(2)
Vectors and the Geometry of Space	636	(58)
Three-Dimensional Coordinate Systems	637	(5)
Vectors	642	(9)
The Dot Product	651	(6)
The Cross Product	657	(9)
Discovery Project: The Geometry of a Tetrahedron	665	(1)
Equations of Lines and Planes	666	(10)
Laboratory Project: Putting 3D in Perspective	675	(1)
Functions and Surfaces	676	(9)
Cylindrical and Spherical Coordinates	685	(9)
Laboratory Project: Families of Surfaces	690	(1)
Review	690	(3)
Focus on Problem Solving	693	(1)
Vector Functions	694	(44)
Vector Functions and Space Curves	695	(7)
Derivatives and Integrals of Vector Functions	702	(6)
Are Length and Curvature	708	(8)
Motion in Space: Velocity and Acceleration	716	(12)
Applied Project: Kepler's Laws	727	(1)
Parametric Surfaces	728	(10)
Review	734	(2)
Focus on Problem Solving	736	(2)
Partial Derivatives	738	(90)
Functions of Several Variables	739	(11)
Limits and Continuity	750	(6)
Partial Derivatives	756	(13)
Tangent Planes and Linear Approximations	769	(11)
The Chain Rule	780	(8)
Directional Derivatives and the Gradient Vector	788	(13)
Maximum and Minimum Values	801	(12)
Applied Project: Designing a Dumpster	811	(1)
Discovery Project: Quadratic Approximations and Critical Points	812	(1)
Lagrange Multipliers	813	(15)
Applied Project: Rocket Science	820	(1)
Applied Project: Hydro-Turbine Optimization	821	(1)
Review	822	(4)
Focus on Problem Solving	826	(2)
Multiple Integrals	828	(76)
Double Integrals over Rectangles	829	(8)
Iterated Integrals	837	(6)
Double Integrals over General Regions	843	(8)
Double Integrals in Polar Coordinates	851	(6)
Applications of Double Integrals	857	(10)
Surface Area	867	(5)
Triple Integrals	872	(10)
Discovery Project: Volumes of Hyperspheres	881	(1)
Triple Integrals in Cylindrical and Spherical Coordinates	882	(7)
Applied Project: Roller Derby	888	(1)
Discovery Project: The Intersection of Three Cylinders	889	(1)
Change of Variables in Multiple Integrals	889	(15)
Review	898	(4)
Focus on Problem Solving	902	(2)
Vector Calculus	904
Vector Fields	905	(7)
Line Integrals	912	(12)
The Fundamental Theorem for Line Integrals	924	(9)
Green's Theorem	933	(7)
Curl and Divergence	940	(8)
Surface Integrals	948	(11)
Stokes' Theorem	959	(7)
Writing Project: Three Men and Two Theorems	965	(1)
The Divergence Theorem	966	(7)
Summary	973
Review	974	(3)
Focus on Problem Solving	977
Appendixes	1	(134)
A Intervals, Inequalities, and Absolute Values	2	(5)
B Coordinate Geometry	7	(11)
C Trigonometry	18	(11)
D Precise Definitions of Limits	29	(10)
E A Few Proofs	39	(5)
F Sigma Notation	44	(6)
G Integration of Rational Functions by Partial Fractions	50	(8)
H Polar Coordinates	58	(16)
I Complex Numbers	74	(9)
J Answers to Odd-Numbered Exercises	83	(52)
Index	135