Calculus of several variables. / Serge Lang.
By: Lang, Serge.
Material type: BookSeries: Undergraduate texts in mathematics.Publisher: New York ; London : Springer Verlag, 1994Edition: 3rd ed.Description: xii, various pagings : ill. ; 24 cm. + hbk.ISBN: 0387964053 (m) (New York); 3540964053 (v) (Berlin).Subject(s): Calculus | Functions of several real variablesDDC classification: 515.84Item type | Current library | Call number | Copy number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|
General Lending | MTU Bishopstown Library Lending | 515.84 (Browse shelf(Opens below)) | 1 | Available | 00069965 |
Enhanced descriptions from Syndetics:
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.
Includes index.
Part one: Basic material -- Part 2: Maxima, minima and Taylor's formula -- Part three: Curve integrals and double integrals -- Part four: Triple and surface integrals -- Part five: Mappings, inverse mappings and change of variables formulas.
Table of contents provided by Syndetics
- I Basic Material
- 1 Vectors
- 2 Differentiation of Vectors
- 3 Functions of Several Variables
- 4 The Chain Rule and the Gradient
- II Maxima, Minima, and Taylor's Formula
- 5 Maximum and Minimum
- 6 Higher Derivatives
- III Curve Integrals and Double Integrals
- 7 Potential Functions
- 8 Curve Integrals
- 9 Double Integrals
- 10 Green's Theorem
- IV Triple and Surface Integrals
- 12 Triple Integrals
- V Mappings, Inverse Mappings, and Change of Variables Formula
- 13 Matrices
- 14 Linear Mappings
- 15 Determinants
- 16 Applications to Functions of Several Variables
- 17 The Change of Variables Formula
- Appendix: Fourier Series