Thomas' Calculus, Updated,9780201755275

Thomas' Calculus, Updated

by ; ; ;
Edition: 10th
ISBN13: 9780201755275
ISBN10: 0201755270
Format: Package
Pub. Date: 2003-01-01
Publisher(s): Addison Wesley
List Price: $192.00

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Summary

The updated tenth edition of this clear, precise calculus text with superior applications sets the standard in calculus. 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
P Preliminaries 1(1142)
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(78)
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 and Parametric Equations
187(11)
Implicit Differentiation
198(9)
Related Rates
207(18)
Questions To Guide Your Review
216(1)
Practice Exercises
217(4)
Additional Exercises: Theory, Examples, Applications
221(4)
Applications of Derivatives
225(88)
Extreme Values of Functions
225(12)
The Mean Value Theorem and Differential Equations
237(8)
The Shape of a Graph
245(12)
Graphical Solutions of Autonomous Differential Equations
257(9)
Modeling and Optimization
266(17)
Linearization and Differentials
283(14)
Newton's Method
297(16)
Questions to Guide Your Review
305(1)
Practice Exercises
305(4)
Additional Exercises: Theory, Examples, Applications
309(4)
Integration
313(80)
Indefinite Integrals, Differential Equations, and Modeling
313(9)
Integral Rules; Integration by Substitution
322(7)
Estimating with Finite Sums
329(11)
Riemann Sums and Definite Integrals
340(11)
The Mean Value and Fundamental Theorems
351(13)
Substitution in Definite Integrals
364(9)
Numerical Integration
373(20)
Questions to Guide Your Review
384(1)
Practice Exercises
385(4)
Additional Exercises: Theory, Examples, Applications
389(4)
Applications of Integrals
393(64)
Volumes by Slicing and Rotation About an Axis
393(13)
Modeling Volume Using Cylindrical Shells
406(7)
Lengths of Plane Curves
413(8)
Springs, Pumping, and Lifting
421(11)
Fluid Forces
432(7)
Moments and Centers of Mass
439(18)
Questions to Guide Your Review
451(1)
Practice Exercises
451(3)
Additional Exercises: Theory, Examples, Applications
454(3)
Transcendental Functions and Differential Equations
457(82)
Logarithms
457(9)
Exponential Functions
466(11)
Derivatives of Inverse Trigonometric Functions; Integrals
477(8)
First-Order Separable Differential Equations
485(14)
Linear First-Order Differential Equations
499(8)
Euler's Method; Population Models
507(13)
Hyperbolic Functions
520(19)
Questions to Guide Your Review
530(1)
Practice Exercises
531(4)
Additional Exercises: Theory, Examples, Applications
535(4)
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(1)
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)
Linearization 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
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)
A.13 Conic Sections
1183
Answers 1(1)
Index 1(1)
A Brief Table of Integrals 1

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