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Essentials of Partial Differential Equations de Marin Marin

Essentials of Partial Differential Equations

Autor Marin Marin, Andreas Öchsner
en Limba Engleză Hardback – 25 mai 2018
This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.
Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects ofthe theory of partial differential equations. 

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Specificații

ISBN-13: 9783319906461
ISBN-10: 3319906461
Pagini: 392
Ilustrații: XI, 380 p.
Dimensiuni: 160 x 241 x 27 mm
Greutate: 0.7 kg
Ediția:1st ed. 2019
Editura: Springer
Locul publicării:Cham, Switzerland

Cuprins

PART I: Quasilinear equations.- Operators of second order.- The theory of potential.- Elliptic operators.- Operational calculus.- Parabolic equations.- Hyperbolic equations.- Part II: Elements of distributions.- Integral formulas.- Equations of the first order.- Equations of second order.- Harmonic functions.- Weak solutions.- Regularity of the solutions.- Parabolic equations.- Hyperbolic equations.
 

Notă biografică

Sorin Vlase is a full professor of Mechanics at Transilvania University of Brasov. He finished the Faculty of Mechanics at Transilvania University of Brasov (1976) and the Faculty of Mathematics at the University of Bucharest. In the year 1989, he defend his Ph.D. Thesis in the field of Mechanical Engineering. In the period 1976–1978, he was an engineer at the Factory of trucks in Brasov, and in the period 1978–1980, he was a design engineer at the Research Center for Automotive Engineering in Brasov. From 1980 to 1984, he was an assistant professor at the Department of Mechanical Engineering, from 1984 to1991 lecturer, from 1991 to 1996 associated professor, and in 1996 become full professor at Transilvania University of Brasov. From 2004 to 2020 he was the head of Department of Mechanical Engineering. In 2014, he became doctor Habil in the domain of automotive engineering. From 2012, he is a member of the Technical Sciences Academy of Romania. From 2024 he is a researcher at the Romanian Academy, Institute of Solid Mechanics. Marin Marin is a full professor of Applied Mathematics at Transilvania University of Brasov. He graduated the Faculty of Mathematics with "Diploma of Merit" at University "Al. Cuza" of Jassy, Romania in 1979 (and with a master’s degree). In the year 1994, he defend his Ph.D. Thesis in the field of Applied Mathematics at the Faculty of Mathematics, University of Bucharest. In 2013, he became the professor Habil in the domain of Applied Mathematics, at the Faculty of Mathematics, University of Bucharest. Professor Marin was awarded by the Romanian Academy in 2012, and in 2019, he received the title of Honoris Causa from the "Ovidius" University of Constanta. Since 2023, he has been a member of the Academy of Romanian Scientists. Andreas Öchsner is a full professor of Lightweight Design and Structural Simulation at Esslingen University of Applied Sciences, Germany. After completing his Dipl.-Ing. degree in Aeronautical Engineering at the University of Stuttgart (1997), he served as a research and teaching assistant at the University of Erlangen-Nuremberg from 1997 to 2003 while pursuing his Doctor of Engineering Sciences (Dr.-Ing.) degree. From 2003 to 2006, he was an assistant professor at the Department of Mechanical Engineering and the head of the Cellular Metals Group affiliated with the University of Aveiro, Portugal. He spent seven years (2007–2013) as a full professor at the Department of Applied Mechanics, Technical University of Malaysia, where he was also the head of the Advanced Materials and Structure Lab. From 2014 to 2017, he was a full professor at the School of Engineering, Griffith University, Australia. Maria Luminita Scutaru is a highly accomplished individual with master degrees in Computational Mechanics and doctoral degree in the field of Industrial Engineering and Mechanical Engineering at the Transilvania University of Brasov. From 2019 to present, she is the head of Mechanical Engineering Department. In the year 2015, she defended her Ph.D. Thesis in the field of Mechanical Engineering and became doctor habil in the Mechanical Engineering field. In 2016, she became a full professor at Transilvania University of Brasov. She has extensive experience as a full professor and currently serves as a Ph.D. supervisor in Mechanical Engineering with a focus on dynamics systems, multibody systems, and innovative materials. With an H Index of 18 on Web of Science, she has published over 100 papers in ISI Journals, showcasing her expertise and contribution to the field.

Textul de pe ultima copertă

This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.
Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.

Caracteristici

Offers a two-step approach to partial differential equations: first an introduction to the theory and then modern problems Presents all the important classical notions: differential operators, characteristic surfaces, Levi functions, and Green’s theory Includes the main initial boundary value problems associated with elliptic, parabolic, and hyperbolic equations