From Ordinary to Partial Differential Equations
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Beschreibung
This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.
This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.
Presents mathematics from the age of Riemann and Poincaré to modern studies on regularity theory for elliptic equations Includes a careful selection of brilliant ideas and methods by Caccioppoli, De Giorgi and Nash Offers a systematic introduction to the Fourès-Bruhat method for solving the Cauchy problem for general relativity with non-analytic initial data Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras
Autor*in
Giampiero Esposito
Themen in »From Ordinary to Partial Differential Equations«
Partial differential equations Ordinary differential equations Riemann's zeta function Fuchsian functions Characteristic conoid Fundamental solution Green function Parametrix Kirchhoff formulae Pseudoholomorphic functions
Stimmen zu »From Ordinary to Partial Differential Equations«
“The selection of material is quite interesting and the book could be useful for graduate students and specialists conducting research in related areas.” (Svitlana P. Rogovchenko, zbMath 1419.00002, 2019)
“This is a comprehensive textbook, making it well suited for beginner to intermediate graduate-level courses in partial differential equations. … This book would benefit from the addition of exercise problems, but this fact does not detract from its many merits. In the end, this text is well organized and offers a clear conceptual framework to approach proofs. Summing Up: Recommended. Graduate students, researchers,and faculty.” (V. K. Chellamuthu, Choice, Vol. 55 (9), May, 2018)
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