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Calculus of Several Variables

Calculus of Several Variables
Catalogue Information
Field name Details
Dewey Class 515.8
Title Calculus of Several Variables ([EBook]) / by Serge Lang.
Author Lang, Serge. , 1927-2005
Other name(s) SpringerLink (Online service)
Edition statement Third Edition.
Publication New York, NY : Springer , 1987.
Physical Details XII, 619 pages : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9781461210689
Summary Note 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.:
Contents note One Basic Material -- I Vectors -- II Differentiation of Vectors -- III Functions of Several Variables -- IV The Chain Rule and the Gradient -- Two Maxima, Minima, and Taylor’s Formula -- V Maximum and Minimum -- VI Higher Derivatives -- Three Curve Integrals and Double Integrals -- VII Potential Functions -- VIII Curve Integrals -- IX Double Integrals -- X Green’s Theorem -- Four Triple and Surface Integrals -- XI Triple Integrals -- XII Surface Integrals -- Five Mappings, Inverse Mappings, and Change of Variables Formula. -- XIII Matrices -- XIV Linear Mappings -- XV Determinants -- XVI Applications to Functions of Several Variables -- XVII The Change of Variables Formula -- Appendix Fourier Series -- §1. General Scalar Products -- §2. Computation of Fourier Series -- Answers to Exercises.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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