A Course in Analysis Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations

Authors : Niels Jacob (Swansea University, UK) and Kristian P Evans (Swansea University, UK)

Publisher : World Scientific

ISBN : 978-981-3273-51-1 (Hardcover), 978-981-3274-52-5 (Softcover)

There are currently no reviews for this book title.
In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.

Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard–Lindelöf and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm–Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.

Our introduction to the calculus of variations includes a discussion of the Euler–Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton–Jacobi theory. Related first order partial differential equations are treated in more detail.

The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.
Details for these authors are currently not available.
There are currently no reviews for this book title.
Buy this book, https://www.worldscientific.com/worldscibooks/10.1142/11078, 13575, false


Click on the "Buy this book" button
You can email us at book-review@enago.com and we will get back to you with the next steps shortly.

All featured publishers and authors can avail of a free promotional interview on Enago Academy! Write to us now!

[contact-form-7 id="40123" title="Global popup two"]

    Researchers Poll

    Which is the best strategy to support research integrity according to you?