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Calculus of Several Variables
Tag Description
099$aOnline resource: Springer
100$aLang, Serge.$d1927-2005.
245$aCalculus of Several Variables$h[EBook]$cby Serge Lang.
250$aThird Edition.
260$aNew York, NY$bSpringer$c1987.
300$aXII, 619 pages$bonline resource.
338$aonline resource
440$aUndergraduate Texts in Mathematics,$x0172-6056
505$aOne 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.
520$aThe present course on calculus of several variables is meant as a text, either for one semester following A First Course in Calculus, or for a year if the calculus sequence is so structured. For a one-semester course, no matter what, one should cover the first four chapters, up to the law of conservation of energy, which provides a beautiful application of the chain rule in a physical context, and ties up the mathematics of this course with standard material from courses on physics. Then there are roughly two possibilities: One is to cover Chapters V and VI on maxima and minima, quadratic forms, critical points, and Taylor's formula. One can then finish with Chapter IX on double integration to round off the one-term course. The other is to go into curve integrals, double integration, and Green's theorem, that is Chapters VII, VIII, IX, and X, §1. This forms a coherent whole.
538$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710$aSpringerLink (Online service)
830$aUndergraduate Texts in Mathematics,
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