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.
- 462 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
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Table of contents
- Cover
- Title page
- Copyright
- Contents
- Preface
- Some basic notation
- Chapter 1. Background
- Chapter 2. Multivariable differential calculus
- Chapter 3. Multivariable integral calculus and calculus on surfaces
- Chapter 4. Differential forms and the Gauss-Green-Stokes formula
- Chapter 5. Applications of the Gauss-Green-Stokes formula
- Chapter 6. Differential geometry of surfaces
- Chapter 7. Fourier analysis
- Appendix A. Complementary material
- Bibliography
- Index
- Back Cover
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Yes, you can access Introduction to Analysis in Several Variables by Michael E. Taylor in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.