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Calculus : Concepts and Contexts

ISBN: 9780534410032 | 0534410030
Edition: 3rd
Format: Hardcover
Publisher: Cengage Learning
Pub. Date: 11/4/2004

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Table of Contents
A Preview of Calculus2(8)
Functions and Models
10(82)
Four Ways to Represent a Function
11(14)
... MORE
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)
Index135

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