Jacob, Niels.
A course in analysis. V. IV, Fourier analysis, ordinary differential equations, calculus of variations [electronic resource] / Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans. - Singapore : World Scientific Publishing Co. Pte Ltd., ©2018. - 1 online resource (768 p.) : ill.
Includes bibliographical references and index.
"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."--
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
9789813273528
Mathematical analysis--Textbooks.
Mathematics--Study and teaching (Higher)
Calculus--Textbooks.
Electronic books.
QA300 / .J27 2018
515
A course in analysis. V. IV, Fourier analysis, ordinary differential equations, calculus of variations [electronic resource] / Fourier analysis, ordinary differential equations, calculus of variations Niels Jacob, Kristian P. Evans. - Singapore : World Scientific Publishing Co. Pte Ltd., ©2018. - 1 online resource (768 p.) : ill.
Includes bibliographical references and index.
"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."--
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
9789813273528
Mathematical analysis--Textbooks.
Mathematics--Study and teaching (Higher)
Calculus--Textbooks.
Electronic books.
QA300 / .J27 2018
515