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Thomas' Calculus : Early Transcendentals,9780201662092
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Thomas' Calculus : Early Transcendentals

by ; ; ;
Edition:
10th
ISBN13:

9780201662092

ISBN10:
0201662094
Format:
Hardcover w/CD
Pub. Date:
1/1/2001
Publisher(s):
Addison Wesley

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Summary

The tenth edition of this clear, precise calculus text with superior applications sets the standard in calculus. The tenth edition of this proven text was carefully revised to give students the solid base they need to succeed in math, science and engineering programs. Through a comprehensive technology package, this edition now includes more opportunity to incorporate optional, but meaningful technology into the course.

Table of Contents

To the Instructor xiii
To the Student xxv
Preliminaries 1(1)
Lines
1(9)
Functions and Graphs
10(14)
Exponential Functions
24(7)
Inverse Functions and Logarithms
31(13)
Trigonometric Functions and Their Inverses
44(16)
Parametric Equations
60(7)
Modeling Change
67(18)
Questions to Guide Your Review
76(1)
Practice Exercises
77(3)
Additional Exercises: Theory, Examples, Applications
80(5)
Limits and Continuity
85(62)
Rates of Change and Limits
85(14)
Finding Limits and One-Sided Limits
99(13)
Limits Involving Infinity
112(11)
Continuity
123(11)
Tangent Lines
134(13)
Questions to Guide Your Review
141(1)
Practice Exercises
142(1)
Additional Exercises: Theory, Examples, Applications
143(4)
Derivatives
147(94)
The Derivative as a Function
147(13)
The Derivative as a Rate of Change
160(13)
Derivatives of Products, Quotients, and Negative Powers
173(6)
Derivatives of Trigonometric Functions
179(8)
The Chain Rule
187(11)
Implicit Differentiation
198(9)
Related Rates
207(9)
Derivatives of Inverse Trigonometric Functions
216(6)
Derivatives of Exponential and Logarithmic Functions
222(19)
Questions to Guide Your Review
232(1)
Practice Exercises
233(5)
Additional Exercises: Theory, Examples, Applications
238(3)
Applications of Derivatives
241(92)
Extreme Values of Functions
241(13)
The Mean Value Theorem and Differential Equations
254(9)
The Shape of a Graph
263(13)
Graphical Solutions of Autonomous Differential Equations
276(9)
Modeling and Optimization
285(18)
Linearization and Differentials
303(13)
Newton's Method
316(17)
Questions to Guide Your Review
325(1)
Practice Exercises
326(4)
Additional Exercises: Theory, Examples, Applications
330(3)
Integration
333(82)
Indefinite Integrals, Differential Equations, and Modeling
333(10)
Integral Rules; Integration by Substitution
343(8)
Estimating with Finite Sums
351(12)
Riemann Sums and Definite Integrals
363(11)
The Mean Value and Fundamental Theorems
374(12)
Substitution in Definite Integrals
386(9)
Numerical Integration
395(20)
Questions to Guide Your Review
407(1)
Practice Exercises
408(4)
Additional Exercises: Theory, Examples, Applications
412(3)
Applications of Integrals
415(74)
Volumes by Slicing and Rotation About an Axis
415(13)
Modeling Volume Using Cylindrical Shells
428(7)
Lengths of Plane Curves
435(8)
First-Order Separable Differential Equations
443(10)
Springs, Pumping, and Lifting
453(11)
Fluid Forces
464(7)
Moments and Centers of Mass
471(18)
Questions to Guide Your Review
483(1)
Practice Exercises
484(3)
Additional Exercises: Theory, Examples, Applications
487(2)
Transcendental Functions and Differential Equations
489(50)
Logarithms
489(7)
Exponential Functions
496(7)
Linear First-Order Differential Equations
503(9)
Euler's Method; Population Models
512(12)
Hyperbolic Functions
524(15)
Questions to Guide Your Review
534(1)
Practice Exercises
534(2)
Additional Exercises: Theory, Examples, Applications
536(3)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
539(68)
Basic Integration Formulas
539(7)
Integration by Parts
546(9)
Partial Fractions
555(10)
Trigonometric Substitutions
565(5)
Integral Tables, Computer Algebra Systems, and Monte Carlo Integration
570(8)
L'Hopital's Rule
578(8)
Improper Integrals
586(21)
Questions to Guide Your Review
600(4)
Practice Exercises
601(2)
Additional Exercises: Theory, Examples, Applications
603(4)
Infinite Series
607(110)
Limits of Sequences of Numbers
608(11)
Subsequences, Bounded Sequences, and Picard's Method
619(8)
Infinite Series
627(12)
Series of Nonnegative Terms
639(12)
Alternating Series, Absolute and Conditional Convergence
651(9)
Power Series
660(9)
Taylor and Maclaurin Series
669(14)
Applications of Power Series
683(8)
Fourier Series
691(7)
Fourier Cosine and Sine Series
698(19)
Questions to Guide Your Review
707(1)
Practice Exercises
708(3)
Additional Exercises: Theory, Examples, Applications
711(6)
Vectors in the Plane and Polar Functions
717(70)
Vectors in the Plane
717(11)
Dot Products
728(10)
Vector-Valued Functions
738(11)
Modeling Projectile Motion
749(12)
Polar Coordinates and Graphs
761(9)
Calculus of Polar Curves
770(17)
Questions to Guide Your Review
780(1)
Practice Exercises
780(4)
Additional Exercises: Theory, Examples, Applications
784(3)
Vectors and Motion in Space
787(86)
Cartesian (Rectangular) Coordinates and Vectors in Space
787(9)
Dot and Cross Products
796(11)
Lines and Planes in Space
807(9)
Cylinders and Quadric Surfaces
816(9)
Vector-Valued Functions and Space Curves
825(13)
Arc Length and the Unit Tangent Vector T
838(9)
The TNB Frame; Tangential and Normal Components of Acceleration
847(10)
Planetary Motion and Satellites
857(16)
Questions to Guide Your Review
866(1)
Practice Exercises
867(3)
Additional Exercises: Theory, Examples, Applications
870(3)
Multivariable Functions and Their Derivatives
873(102)
Functions of Several Variables
873(9)
Limits and Continuity in Higher Dimensions
882(8)
Partial Derivatives
890(12)
The Chain Rule
902(9)
Directional Derivatives, Gradient Vectors, and Tangent Planes
911(14)
Linerization and Differentials
925(11)
Extreme Values and Saddle Points
936(11)
Lagrange Multipliers
947(11)
*Partial Derivatives with Constrained Variables
958(5)
Taylor's Formula for Two Variables
963(12)
Questions to Guide Your Review
968(1)
Practice Exercises
968(4)
Additional Exercises: Theory, Examples, Applications
972(3)
Multiple Integrals
975(78)
Double Integrals
975(12)
Areas, Moments and Centers of Mass*
987(13)
Double Integrals in Polar Form
1000(7)
Triple Integrals in Rectangular Coordinates
1007(10)
Masses and Moments in Three Dimensions
1017(7)
Triple Integrals in Cylindrical and Spherical Coordinates
1024(13)
Substitutions in Multiple Integrals
1037(16)
Questions to Guide Your Review
1046(1)
Practice Exercises
1047(2)
Additional Exercises: Theory, Examples, Applications
1049(4)
Integration in Vector Fields
1053(90)
Line Integrals
1053(6)
Vector Fields, Work, Circulation, and Flux
1059(11)
Path Independence, Potential Functions, and Conservative Fields
1070(10)
Green's Theorem in the Plane
1080(12)
Surface Area and Surface Integrals
1092(11)
Parametrized Surfaces
1103(10)
Stokes' Theorem
1113(11)
Divergence Theorem and a Unified Theory
1124(19)
Questions to Guide Your Review
1136(1)
Practice Exercises
1136(3)
Additional Exercises: Theory, Examples, Applications
1139(4)
Appendices 1143(40)
A.1 Mathematical Induction
1143(3)
A.2 Proofs of Limit Theorems in Section 1.2
1146(4)
A.3 Proof of the Chain Rule
1150(1)
A.4 Complex Numbers
1151(11)
A.5 Simpson's One-Third Rule
1162(1)
A.6 Cauchy's Mean Value Theorem and the Stronger Form of L'Hopital's Rule
1163(1)
A.7 Limits That Arise Frequently
1164(2)
A.8 Proof of Taylor's Theorem
1166(1)
A.9 The Distributive Law for Vector Cross Products
1167(2)
A.10 Determinants and Cramer's Rule
1169(7)
A.11 The Mixed Derivative Theorem and the Increment Theorem
1176(5)
A.12 The Area of a Parallelogram's Projection on a Plane
1181(2)
Answers 1183
Index I-1
A Brief Table of Integrals T-1


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