Ebook: Calculus of Several Variables

The present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.

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This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.

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This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Vectors....Pages 3-48
Differentiation of Vectors....Pages 49-65
Functions of Several Variables....Pages 66-86
The Chain Rule and the Gradient....Pages 87-120
Front Matter....Pages 121-121
Maximum and Minimum....Pages 123-142
Higher Derivatives....Pages 143-179
Front Matter....Pages 181-181
Potential Functions....Pages 183-205
Curve Integrals....Pages 206-232
Double Integrals....Pages 233-268
Green’s Theorem....Pages 269-290
Front Matter....Pages 291-291
Triple Integrals....Pages 293-317
Surface Integrals....Pages 318-364
Front Matter....Pages 365-365
Matrices....Pages 367-384
Linear Mappings....Pages 385-411
Determinants....Pages 412-433
Applications to Functions of Several Variables....Pages 434-452
The Change of Variables Formula....Pages 453-486
Back Matter....Pages 487-I7

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This is a new, revised edition of this widely known text. All of the basic topics in calculus of several variables are covered, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green's theorem, multiple integrals, surface integrals, Stokes' theorem, and the inverse mapping theorem and its consequences. The presentation is self-contained, assuming only a knowledge of basic calculus in one variable. Many completely worked-out problems have been included.
Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Vectors....Pages 3-48
Differentiation of Vectors....Pages 49-65
Functions of Several Variables....Pages 66-86
The Chain Rule and the Gradient....Pages 87-120
Front Matter....Pages 121-121
Maximum and Minimum....Pages 123-142
Higher Derivatives....Pages 143-179
Front Matter....Pages 181-181
Potential Functions....Pages 183-205
Curve Integrals....Pages 206-232
Double Integrals....Pages 233-268
Green’s Theorem....Pages 269-290
Front Matter....Pages 291-291
Triple Integrals....Pages 293-317
Surface Integrals....Pages 318-364
Front Matter....Pages 365-365
Matrices....Pages 367-384
Linear Mappings....Pages 385-411
Determinants....Pages 412-433
Applications to Functions of Several Variables....Pages 434-452
The Change of Variables Formula....Pages 453-486
Back Matter....Pages 487-I7
....