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 ...
Read More
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.
Read Less
Add this copy of Introduction to Analysis in Several Variables: Advanced to cart. $70.52, very good condition, Sold by BooksRun rated 4.0 out of 5 stars, ships from Philadelphia, PA, UNITED STATES, published 2020 by American Mathematical Society.
Add this copy of Introduction to Analysis in Several Variables: Advanced to cart. $106.93, new condition, Sold by Booksplease rated 4.0 out of 5 stars, ships from Southport, MERSEYSIDE, UNITED KINGDOM, published 2020 by American Mathematical Society.
