Basic Multi-Variable Calculus,9780716724438

Basic Multi-Variable Calculus

by ; ;
Edition: 3rd
ISBN13: 9780716724438
ISBN10: 071672443X
Format: Hardcover
Pub. Date: 1993-03-15
Publisher(s): W. H. Freeman
List Price: $106.13

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Table of Contents

Preface vii
Algebra and Geometry of Euclidean Space
1(90)
Vectors in the Plane and Space
2(20)
The Inner Product and Distance
22(17)
2 x 2 and 3 x 3 Matrices and Determinants
39(7)
The Cross Product and Planes
46(14)
n-Dimensional Euclidean Space
60(13)
Curves in the Plane and in Space
73(18)
Review Exercises
83(8)
Differentiation
91(80)
Graphs and Level Surfaces
92(17)
Partial Derivatives and Continuity
109(15)
Differentiability, the Derivative Matrix, and Tangent Planes
124(9)
The Chain Rule
133(13)
Gradients and Directional Derivatives
146(14)
Implicit Differentiation
160(11)
Review Exercises
166(5)
Higher Derivatives and Extrema
171(56)
Higher Order Partial Derivatives
172(10)
Taylor's Theorem
182(8)
Maxima and Minima
190(11)
Second Derivative Test
201(10)
Constrained Extrema and Lagrange Multipliers
211(16)
Review Exercises
221(6)
Vector-Valued Functions
227(42)
Acceleration
228(7)
Arc Length
235(6)
Vector Fields
241(8)
Divergence and Curl
249(20)
Review Exercises
263(6)
Multiple Integrals
269(86)
Volume and Cavalieri's Principle
270(10)
The Double Integral Over a Rectangle
280(11)
The Double Integral Over Regions
291(15)
Triple Integrals
306(12)
Change of Variables, Cylindrical and Spherical Coordinates
318(21)
Applications of Multiple Integrals
339(16)
Review Exercises
350(5)
Integrals Over Curves and Surfaces
355(60)
Line Integrals
356(18)
Parametrized Surfaces
374(8)
Area of a Surface
382(16)
Surface Integrals
398(17)
Review Exercises
411(4)
The Integral Theorems of Vector Analysis
415(64)
Green's Theorem
416(13)
Stokes' Theorem
429(17)
Gauss' Theorem
446(12)
Path Independence and the Fundamental Theorems of Calculus
458(21)
Review Exercises
473(6)
Epilogue 479(2)
Practice Examination 1 481(4)
Practice Examination 2 485(4)
Answers to Odd-Numbered Exercises 489(32)
Index 521

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