Calculus: Single and Multivariable, Update , 3rd Edition,9780471448747

Calculus: Single and Multivariable, Update , 3rd Edition

by ; ; ; ; ;
Edition: 3rd
ISBN13: 9780471448747
ISBN10: 0471448745
Format: Paperback
Pub. Date: 2003-02-01
Publisher(s): WILEY
List Price: $187.90

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Summary

Work more effectively and check solutions as you go along with the text! This Student Solutions Manual is designed to accompany Hughes-Hallett's Calculus: Single & Multivariable, 4th Edition. It contains solutions to every other odd-numbered problem in the text for chapters 1-20. Striking a balance between concepts, modeling, and skills, Calculus: Single & Multivariable, 4th Edition is a highly acclaimed book that arms readers with an accessible introduction to calculus. It builds on the strengths from previous editions, presenting key concepts graphically, numerically, symbolically, and verbally. Guided by this innovative Rule of Four approach, the fourth edition examines new topics while providing readers with a strong conceptual understanding of the material.

Table of Contents

A Library of Functions
1(54)
Functions and Change
2(7)
Exponential Functions
9(8)
New Functions from Old
17(6)
Logarithmic Functions
23(6)
Trigonometric Functions
29(8)
Powers, Polynomials, and Rational Functions
37(8)
Introduction to Continuity
45(10)
Review Problems
48(4)
Check Your Understanding
52(2)
Projects
54(1)
Key Concept: The Derivative
55(50)
How Do We Measure Speed?
56(6)
Limits
62(8)
The Derivative at a Point
70(8)
The Derivative Function
78(7)
Interpretations of the Derivative
85(4)
The Second Derivative
89(6)
Continuity and Differentiability
95(10)
Review Problems
99(4)
Check Your Understanding
103(1)
Projects
104(1)
Short-Cuts to Differentiation
105(60)
Powers and Polynomials
106(7)
The Exponential Function
113(5)
The Product and Quotient Rules
118(5)
The Chain Rule
123(5)
The Trigonometric Functions
128(5)
Applications of the Chain Rule
133(5)
Implicit Functions
138(3)
Parametric Equations
141(9)
Linear Approximation and the Derivative
150(4)
Using Local Linearity to Find Limits
154(11)
Review Problems
159(3)
Check Your Understanding
162(1)
Projects
163(2)
Using the Derivative
165(56)
Using First and Second Derivatives
166(10)
Families of Curves
176(4)
Optimization
180(9)
Applications to Marginality
189(7)
Optimization and Modeling
196(7)
Hyperbolic Functions
203(4)
Theorems About Continuous and Differentiable Functions
207(14)
Review Problems
212(4)
Check Your Understanding
216(1)
Projects
217(4)
Key Concept: The Definite Integral
221(40)
How Do We Measure Distance Traveled?
222(7)
The Definite Integral
229(7)
Interpretations of the Definite Integral
236(8)
Theorems About Definite Integrals
244(17)
Review Problems
252(5)
Check Your Understanding
257(1)
Projects
258(3)
Constructing Antiderivatives
261(28)
Antiderivatives Graphically and Numerically
262(6)
Constructing Antiderivatives Analytically
268(5)
Differential Equations
273(5)
Second Fundamental Theorem of Calculus
278(4)
The Equations of Motion
282(7)
Review Problems
284(3)
Check Your Understanding
287(1)
Projects
288(1)
Integration
289(56)
Integration by Substitution
290(8)
Integration by Parts
298(6)
Tables of Integrals
304(5)
Algebraic Identities and Trigonometric Substitutions
309(8)
Approximating Definite Integrals
317(5)
Approximation Errors and Simpson's Rule
322(4)
Improper Integrals
326(8)
Comparison of Improper Integrals
334(11)
Review Problems
338(4)
Check Your Understanding
342(1)
Projects
343(2)
Using the Definite Integral
345(60)
Areas and Volumes
346(6)
Applications to Geometry
352(8)
Density and Center of Mass
360(8)
Applications to Physics
368(9)
Applications to Economics
377(6)
Distribution Functions
383(7)
Probability, Mean, and Median
390(15)
Review Problems
397(4)
Check Your Understanding
401(1)
Projects
402(3)
Series
405(28)
Geometric Series
406(6)
Convergence of Sequences and Series
412(5)
Tests for Convergence
417(6)
Power Series
423(10)
Review Problems
429(2)
Check Your Understanding
431(1)
Projects
431(2)
Approximating Functions
433(44)
Taylor Polynomials
434(7)
Taylor Series
441(5)
Finding and Using Taylor Series
446(7)
The Error in Taylor Polynomial Approximations
453(4)
Fourier Series
457(20)
Review Problems
470(3)
Check Your Understanding
473(1)
Projects
474(3)
Differential Equations
477(82)
What is a Differential Equation?
478(4)
Slope Fields
482(6)
Euler's Method
488(4)
Separation of Variables
492(5)
Growth and Decay
497(9)
Applications and Modeling
506(8)
Models of Population Growth
514(9)
Systems of Differential Equations
523(9)
Analyzing the Phase Plane
532(5)
Second-Order Differential Equations: Oscillations
537(7)
Linear Second-Order Differential Equations
544(15)
Review Problems
552(3)
Check Your Understanding
555(1)
Projects
556(3)
Functions of Several Variables
559(46)
Functions of Two Variables
560(7)
Graphs of Functions of Two Variables
567(8)
Contour Diagrams
575(10)
Linear Functions
585(6)
Functions of Three Variables
591(4)
Limits and Continuity
595(10)
Review Problems
600(2)
Check Your Understanding
602(1)
Projects
603(2)
A Fundamental Tool: Vectors
605(34)
Displacement Vectors
606(8)
Vectors in General
614(6)
The Dot Product
620(9)
The Cross Product
629(10)
Review Problems
635(2)
Check Your Understanding
637(1)
Projects
638(1)
Differentiating Functions of Several Variables
639(62)
The Partial Derivative
640(7)
Computing Partial Derivatives Algebraically
647(4)
Local Linearity and the Differential
651(7)
Gradients and Directional Derivatives in the Plane
658(8)
Gradients and Directional Derivatives in Space
666(6)
The Chain Rule
672(9)
Second-Order Partial Derivatives
681(8)
Differentiability
689(12)
Review Problems
695(3)
Check Your Understanding
698(1)
Projects
699(2)
Optimization: Local and Global Extrema
701(34)
Local Extrema
702(8)
Optimization
710(8)
Constrained Optimization: Lagrange Multipliers
718(17)
Review Problems
728(4)
Check Your Understanding
732(1)
Projects
732(3)
Integrating Functions of Several Variables
735(48)
The Definite Integral of a Function of Two Variables
736(7)
Interated Integrals
743(8)
Triple Integrals
751(5)
Double Integrals in Polar Coordinates
756(4)
Integrals in Cylindrical and Spherical Coordinates
760(9)
Applications of Integration to Probability
769(5)
Change of Variables in a Multiple Integral
774(9)
Review Problems
777(3)
Check Your Understanding
780(1)
Projects
781(2)
Parameterization and Vector Fields
783(42)
Parameterized Curves
784(7)
Motion, Velocity, and Acceleration
791(8)
Vector Fields
799(5)
The Flow of a Vector Field
804(5)
Parameterized Surfaces
809(16)
Review Problems
819(3)
Check Your Understanding
822(1)
Projects
823(2)
Line Integrals
825(38)
The Idea of a Line Integral
826(8)
Computing Line Integrals Over Parameterized Curves
834(5)
Gradient Fields and Path-Independent Fields
839(9)
Path-Dependent Vector Fields and Green's Theorem
848(15)
Review Problems
857(3)
Check Your Understanding
860(1)
Projects
861(2)
Flux Integrals
863(24)
The Idea of a Flux Integral
864(8)
Flux Integrals for Graphs, Cylinders, and Spheres
872(7)
Flux Integrals Over Parameterized Surfaces
879(8)
Review Problems
882(2)
Check Your Understanding
884(1)
Projects
884(3)
Calculus of Vector Fields
887(40)
The Divergence of a Vector Field
888(7)
The Divergence Theorem
895(6)
The Curl of a Vector Field
901(8)
Stokes' Theorem
909(6)
The Three Fundamental Theorems
915(12)
Review Problems
919(4)
Check Your Understanding
923(1)
Projects
924(3)
APPENDIX
927(24)
A Roots, Accuracy, and Bounds
928(8)
B Polar Coordinates
936(2)
C Complex Numbers
938(7)
D Newton's Method
945(3)
E Determinants
948(3)
Ready Reference 951(16)
Answers to Odd Numbered Problems 967(26)
Index 993

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