Thomas' Calculus, Alternate Edition,9780321193636

Thomas' Calculus, Alternate Edition

by ;
Edition: 9th
ISBN13: 9780321193636
ISBN10: 0321193636
Format: Hardcover
Pub. Date: 1996-01-01
Publisher(s): Addison Wesley
List Price: $155.48

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Summary

George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs.

Table of Contents

To the Instructor viii
To the Student xvii
P Preliminaries
1 Real Numbers and the Real Line
1(7)
2 Coordinates, Lines, and Increments
8(9)
3 Functions
17(10)
4 Shifting Graphs
27(8)
5 Trigonometric Functions
35(12)
QUESTIONS TO GUIDE YOUR REVIEW
47(1)
PRACTICE EXERCISES
48(1)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
49(2)
1 Limits and Continuity
1.1 Rates of Change and Limits
51(10)
1.2 Rules for Finding Limits
61(5)
1.3 Target Values and Formal Definitions of Limits
66(12)
1.4 Extensions of the Limit Concept
78(9)
1.5 Continuity
87(10)
1.6 Tangent Lines
97(6)
QUESTIONS TO GUIDE YOUR REVIEW
103(1)
PRACTICE EXERCISES
104(1)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
105(4)
2 Derivatives
2.1 The Derivative of a Function
109(12)
2.2 Differentiation Rules
121(10)
2.3 Rates of Change
131(12)
2.4 Derivatives of Trigonometric Functions
143(11)
2.5 The Chain Rule
154(10)
2.6 Implicit Differentiation and Rational Exponents
164(8)
2.7 Related Rates of Change
172(8)
QUESTIONS TO GUIDE YOUR REVIEW
180(1)
PRACTICE EXERCISES
181(4)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
185(4)
3 Applications of Derivatives
3.1 Extreme Values of Functions
189(7)
3.2 The Mean Value Theorem
196(9)
3.3 The First Derivative Test for Local Extreme Values
205(4)
3.4 Graphing with y' and y"
209(11)
3.5 Limits as x -> ± oo, Asymptotes, and Dominant Terms
220(13)
3.6 Optimization
233(15)
3.7 Linearization and Differentials
248(12)
3.8 Newton's Method
260(8)
QUESTIONS TO GUIDE YOUR REVIEW
268(1)
PRACTICE EXERCISES
269(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
272(3)
4 Integration
4.1 Indefinite Integrals
275(7)
4.2 Differential Equations, Initial Value Problems, and Mathematical Modeling
282(8)
4.3 Integration by Substitution-Running the Chain Rule Backward
290(8)
4.4 Estimating with Finite Sums
298(11)
4.5 Riemann Sums and Definite Integrals
309(14)
4.6 Properties, Area, and the Mean Value Theorem
323(9)
4.7 The Fundamental Theorem
332(10)
4.8 Substitution in Definite Integrals
342(4)
4.9 Numerical Integration
346(10)
QUESTIONS TO GUIDE YOUR REVIEW
356(1)
PRACTICE EXERCISES
357(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
360(5)
5 Applications of Integrals
5.1 Areas Between Curves
365(9)
5.2 Finding Volumes by Slicing
374(5)
5.3 Volumes of Solids of Revolution-Disks and Washers
379(8)
5.4 Cylindrical Shells
387(6)
5.5 Lengths of Plane Curves
393(7)
5.6 Areas of Surfaces of Revolution
400(7)
5.7 Moments and Centers of Mass
407(11)
5.8 Work
418(9)
5.9 Fluid Pressures and Forces
427(7)
5.10 The Basic Pattern and Other Modeling Applications
434(10)
QUESTIONS TO GUIDE YOUR REVIEW
444(1)
PRACTICE EXERCISES
444(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
447(2)
6 Transcendental Functions
6.1 Inverse Functions and Their Derivatives
449(9)
6.2 Natural Logarithms
458(9)
6.3 The Exponential Function
467(7)
6.4 aX and log ax
474(8)
6.5 Growth and Decay
482(9)
6.6 L'Hôpital's Rule
491(7)
6.7 Relative Rates of Growth
498(6)
6.8 Inverse Trigonometric Functions
504(9)
6.9 Derivatives of Inverse Trigonometric Functions; Integrals
513(7)
6.10 Hyperbolic Functions
520(9)
6.11 First Order Differential Equations
529(12)
6.12 Euler's Numerical Method; Slope Fields
541(6)
QUESTIONS TO GUIDE YOUR REVIEW
547(1)
PRACTICE EXERCISES
548(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
551(4)
7 Techniques of Integration
7.1 Basic Integration Formulas
555(7)
7.2 Integration by Parts
562(7)
7.3 Partial Fractions
569(9)
7.4 Trigonometric Substitutions
578(5)
7.5 Integral Tables and CAS
583(11)
7.6 Improper Integrals
594(12)
QUESTIONS TO GUIDE YOUR REVIEW
606(1)
PRACTICE EXERCISES
606(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
609(4)
8 Infinite Series
8.1 Limits of Sequences of Numbers
613(9)
8.2 Theorems for Calculating Limits of Sequences
622(8)
8.3 Infinite Series
630(10)
8.4 The Integral Test for Series of Nonnegative Terms
640(4)
8.5 Comparison Tests for Series of Nonnegative Terms
644(5)
8.6 The Ratio and Root Tests for Series of Nonnegative Terms
649(6)
8.7 Alternating Series, Absolute and Conditional Convergence
655(8)
8.8 Power Series
663(9)
8.9 Taylor and Maclaurin Series
672(6)
8.10 Convergence of Taylor Series; Error Estimates
678(10)
8.11 Applications of Power Series
688(11)
QUESTIONS TO GUIDE YOUR REVIEW
699(1)
PRACTICE EXERCISES
700(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
703(6)
9 Conic Sections, Parametrized Curves, and Polar Coordinates
9.1 Conic Sections and Quadratic Equations
709(14)
9.2 Classifying Conic Sections by Eccentricity
723(5)
9.3 Quadratic Equations and Rotations
728(6)
9.4 Parametrizations of Plane Curves
734(10)
9.5 Calculus with Parametrized Curves
744(7)
9.6 Polar Coordinates
751(5)
9.7 Graphing in Polar Coordinates
756(8)
9.8 Polar Equations for Conic Sections
764(6)
9.9 Integration in Polar Coordinates
770(7)
QUESTIONS TO GUIDE YOUR REVIEW
777(1)
PRACTICE EXERCISES
778(5)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
783(4)
10 Vectors and Analytic Geometry in Space
10.1 Vectors in the Plane
787(8)
10.2 Cartesian (Rectangular) Coordinates and Vectors in Space
795(11)
10.3 Dot Products
806(9)
10.4 Cross Products
815(7)
10.5 Lines and Planes in Space
822(7)
10.6 Cylinders and Quadric Surfaces
829(12)
10.7 Cylindrical and Spherical Coordinates
841(6)
QUESTIONS TO GUIDE YOUR REVIEW
847(1)
PRACTICE EXERCISES
848(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
851(4)
11 Vector-Valued Functions and Motion in Space
11.1 Vector-Valued Functions and Space Curves
855(13)
11.2 Modeling Projectile Motion
868(8)
11.3 Arc Length and the Unit Tangent Vector T
876(5)
11.4 Curvature, Torsion, and the TNB Frame
881(12)
11.5 Planetary Motion and Satellites
893(9)
QUESTIONS TO GUIDE YOUR REVIEW
902(1)
PRACTICE EXERCISES
902(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
905(4)
12 Multivariable Functions and Partial Derivatives
12.1 Functions of Several Variables
909(8)
12.2 Limits and Continuity
917(7)
12.3 Partial Derivatives
924(9)
12.4 Differentiability, Linearization, and Differentials
933(11)
12.5 The Chain Rule
944(8)
12.6 Partial Derivatives with Constrained Variables
952(5)
12.7 Directional Derivatives, Gradient Vectors, and Tangent Planes
957(13)
12.8 Extreme Values and Saddle Points
970(10)
12.9 Lagrange Multipliers
980(9)
12.10 Taylor's Formula
989(4)
QUESTIONS TO GUIDE YOUR REVIEW
993(1)
PRACTICE EXERCISES
994(4)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
998(3)
13 Multiple Integrals
13.1 Double Integrals
1001(11)
13.2 Areas, Moments, and Centers of Mass
1012(8)
13.3 Double Integrals in Polar Form
1020(6)
13.4 Triple Integrals in Rectangular Coordinates
1026(8)
13.5 Masses and Moments in Three Dimensions
1034(5)
13.6 Triple Integrals in Cylindrical and Spherical Coordinates
1039(9)
13.7 Substitutions in Multiple Integrals
1048(7)
QUESTIONS TO GUIDE YOUR REVIEW
1055(1)
PRACTICE EXERCISES
1056(2)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
1058(3)
14 Integration in Vector Fields
14.1 Line Integrals
1061(6)
14.2 Vector Fields, Work, Circulation, and Flux
1067(9)
14.3 Path Independence, Potential Functions, and Conservative Fields
1076(8)
14.4 Green's Theorem in the Plane
1084(12)
14.5 Surface Area and Surface Integrals
1096(10)
14.6 Parametrized Surfaces
1106(8)
14.7 Stoker's Theorem
1114(9)
14.8 The Divergence Theorem and a Unified Theory
1123(11)
QUESTIONS TO GUIDE YOUR REVIEW
1134(1)
PRACTICE EXERCISES
1134(3)
ADDITIONAL EXERCISES-THEORY, EXAMPLES, APPLICATIONS
1137
Appendices
A.1 Mathematical Induction
A-1
A.2 Proofs of Limit Theorems in Section 1.2
A-4
A.3 Complex Numbers
A-7
A.4 Simpson's One-Third Rule
A-17
A.5 Cauchy's Mean Value Theorem and the Stronger Form of l'Hôpital's Rule
A-18
A.6 Limits That Arise Frequently
A-20
A.7 The Distributive Law for Vector Cross Products
A-21
A.8 Determinants and Cramer's Rule
A-22
A.9 Euler's Theorem and the Increment Theorem
A-29
Answers A-35
Index I-1

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