Introduction to Analysis in Several Variables
Advanced Calculus
Seiten
2020
American Mathematical Society (Verlag)
978-1-4704-5669-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5669-6 (ISBN)
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After a review of topics from one-variable analysis and linear algebra, this text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds.
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables.
After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory.
The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss-Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables.
After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory.
The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss-Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
Michael E. Taylor, University of North Carolina, Chapel Hill, NC
Background.
Multivariable differential calculus.
Multivariable integral calculus and calculus on surfaces.
Differential forms and the Gauss-Green-Stokes formula.
Applications of the Gauss-Green-Stokes formula.
Differential geometry of surfaces.
Fourier analysis.
Complementary material.
Bibliography.
Index.
| Erscheinungsdatum | 21.09.2020 |
|---|---|
| Reihe/Serie | Pure and Applied Undergraduate Texts |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 812 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 1-4704-5669-9 / 1470456699 |
| ISBN-13 | 978-1-4704-5669-6 / 9781470456696 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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