University Calculus, Part Two (Multivariable, Chap 8-14)

by Hass, Joel; Weir, Maurice D.; Thomas, George B.

• ISBN13: 9780321454218
• ISBN10: 0321454219
• Edition: 1st
• Format: Paperback
• Copyright: 2007-01-01
• Publisher: Addison Wesley

Summary

University Calculus: Alternate Edition Part One, Single Variable answers the demand for a more streamlined, less expensive version of the highly acclaimed Thomas' Calculus, Eleventh Edition.& The text retains the same quality and quantity of exercises as the eleventh edition while using a faster-paced presentation. This text focuses on the thinking behind calculus and uses the same precise, accurate exposition for which the Thomas series is well known. The elegant art program helps today's readers visualize important concepts.KEY TOPICS Functions; Limits and Continuity; Differentiation; Applications of Derivatives; Integration; Applications of Definite Integrals; Transcendental Functions; Techniques of Integration; Infinite Sequences and Series; Polar Coordinates and Conics. MARKET For all readers interested in Calculus.

Table of Contents

Preface	p. vii
Infinite Sequences and Series	p. 502
Sequences	p. 502
Infinite Series	p. 515
The Integral Test	p. 523
Comparison Tests	p. 529
The Ratio and Root Tests	p. 533
Alternating Series, Absolute and Conditional Convergence	p. 537
Power Series	p. 543
Taylor and Maclaurin Series	p. 553
Convergence of Taylor Series	p. 559
The Binomial Series	p. 569
Questions to Guide Your Review	p. 572
Practice Exercises	p. 573
Additional and Advanced Exercises	p. 575
Polar Coordinates and Conics	p. 577
Polar Coordinates	p. 577
Graphing in Polar Coordinates	p. 582
Areas and Lengths in Polar Coordinates	p. 586
Conic Sections	p. 590
Conics in Polar Coordinates	p. 599
Conics and Parametric Equations; The Cycloid	p. 606
Questions to Guide Your Review	p. 610
Practice Exercises	p. 610
Additional and Advanced Exercises	p. 612
Vectors and the Geometry of Space	p. 614
Three-Dimensional Coordinate Systems	p. 614
Vectors	p. 619
The Dot Product	p. 628
The Cross Product	p. 636
Lines and Planes in Space	p. 642
Cylinders and Quadric Surfaces	p. 652
Questions to Guide Your Review	p. 657
Practice Exercises	p. 658
Additional and Advanced Exercises	p. 660
Vector-Valued Functions and Motion in Space	p. 663
Vector Functions and Their Derivatives	p. 663
Integrals of Vector Functions	p. 672
Arc Length in Space	p. 678
Curvature of a Curve	p. 683
Tangential and Normal Components of Acceleration	p. 689
Velocity and Acceleration in Polar Coordinates	p. 694
Questions to Guide Your Review	p. 698
Practice Exercises	p. 698
Additional and Advanced Exercises	p. 700
Partial Derivatives	p. 702
Functions of Several Variables	p. 702
Limits and Continuity in Higher Dimensions	p. 711
Partial Derivatives	p. 719
The Chain Rule	p. 731
Directional Derivatives and Gradient Vectors	p. 739
Tangent Planes and Differentials	p. 747
Extreme Values and Saddle Points	p. 756
Lagrange Multipliers	p. 765
Taylor's Formula for Two Variables	p. 775
Questions to Guide Your Review	p. 779
Practice Exercises	p. 780
Additional and Advanced Exercises	p. 783
Multiple Integrals	p. 785
Double and Iterated Integrals over Rectangles	p. 785
Double Integrals over General Regions	p. 790
Area by Double Integration	p. 799
Double Integrals in Polar Form	p. 802
Triple Integrals in Rectangular Coordinates	p. 807
Moments and Centers of Mass	p. 816
Triple Integrals in Cylindrical and Spherical Coordinates	p. 825
Substitutions in Multiple Integrals	p. 837
Questions to Guide Your Review	p. 846
Practice Exercises	p. 846
Additional and Advanced Exercises	p. 848
Integration in Vector Fields	p. 851
Line Integrals	p. 851
Vector Fields, Work, Circulation, and Flux	p. 856
Path Independence, Potential Functions, and Conservative Fields	p. 867
Green's Theorem in the Plane	p. 877
Surfaces and Area	p. 887
Surface Integrals and Flux	p. 896
Stokes' Theorem	p. 905
The Divergence Theorem and a Unified Theory	p. 914
Questions to Guide Your Review	p. 925
Practice Exercises	p. 925
Additional and Advanced Exercises	p. 928
First-Order Differential Equations (online)
Solutions, Slope Fields, and Picard's Theorem
First-Order Linear Equations
Applications
Euler's Method
Graphical Solutions of Autonomous Equations
Systems of Equations and Phase Planes
Second-Order Differential Equations (online)
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications
Euler Equations
Power Series Solutions
Appendices	p. AP-1
Real Numbers and the Real Line	p. AP-1
Mathematical Induction	p. AP-7
Lines, Circles, and Parabolas	p. AP-10
Trigonometry Formulas	p. AP-19
Proofs of Limit Theorems	p. AP-21
Commonly Occurring Limits	p. AP-25
Theory of the Real Numbers	p. AP-26
The Distributive Law for Vector Cross Products	p. AP-29
The Mixed Derivative Theorem and the Increment Theorem	p. AP-30
Answers	p. A-1
Index	p. I-1
A Brief Table of Integrals	p. T-1
Credits	p. C-1
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