Partial Differential Equations by Victor Ivrii
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About this book :-
Partial Differential Equations written by
Victor Ivrii.
cover the 1-dimensional waves, Heat equation in 1D, Separation of variables and Fourier Series, Fourier transform, Separation of variables, Laplace equation, Separation of variables, Wave equation, Variational methods, Distributions and weak solutions, Nonlinear equations, Eigenvalues and eigenfunctions
(Victor Ivrii)
Book Detail :-
Title: Partial Differential Equations
Edition:
Author(s): Victor Ivrii
Publisher:
Series:
Year: 2017
Pages: 310
Type: PDF
Language: English
ISBN:
Country: Canada
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About Author :-
The author Victor Ivrii
is a Soviet, Canadian mathematician who specializes in analysis, microlocal analysis, spectral theory and partial differential equations. He is a professor at the University of Toronto Department of Mathematics. He was an invited speaker at International Congress of Mathematicians, Helsinki—1978 and Berkeley—1986. He graduated from Physical Mathematical School at Novosibirsk State University in 1965, received his University Diploma (equivalent to MSci) in 1970 and PhD in 1973 in Novosibirsk State University. He defended his Doktor nauk thesis in St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy of Sciences in 1982.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications I by Victor Ivrii
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• Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications III by Victor Ivrii
• Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications IV by Victor Ivrii
• Download PDF Microlocal Analysis, Sharp Spectral Asymptotics & Applications V by Victor Ivrii
• Download PDF Precise Spectral Asymptotics for Elliptic Operators by Victor Ivrii
• Download PDF Partial Differential Equations by Victor Ivrii
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Book Contents :-
Partial Differential Equations written by
Victor Ivrii
cover the following topics.
'
Introduction
PDE Motivations and Context, Initial and Boundary Value Problems, Classification of equations, Origin of some equations, Problems
1-dimensional waves
First order PDEs, Appendix, First order PDEs (continued), Homogeneous 1D Wave equation, 1D Wave equation reloaded: characteristic coordinates, Wave equation reloaded (continued), 1D Wave equation: IBVP, Energy integral, Hyperbolic first order systems with one spatial variable
Heat equation in 1D
1D Heat equation, Heat equation (Miscellaneous), Project: Walk Problem
Separation of variables and Fourier Series
Separation of variables (the first blood), Eigenvalue problem, Orthogonal systems, Ortogonal systems and Fourier series, Other Fourier series, Calculation of negative eigenvalues in Robin problem, Multidimensional Fourier series, Harmonic Oscillator
Fourier transform
Fourier transform, Fourier integral, Appendices, Properties of Fourier transform, Appendix, Applications of Fourier transform to PDEs
Separation of variables
Separation of variables for heat equation, Separation of variables: Misc equations, Laplace operator in different coordinates, Laplace operator in the disk: separation of variables, Laplace operator in the disk. II, Linear second order ODEs, Problems
Laplace equation
General properties of Laplace equation, Potential theory and around, Green function
Separation of variables
Separation of variable in spherical coordinates, Separation of variable in polar and cylindrical coordinates, Separation of variable in elliptic and parabolic coordinates
Wave equation
Wave equation in dimensions 3 and 2, Wave equation: energy method
Variational methods
Functionals, extremums and variations, Functionals, extremums and variations, Variational methods in physics
Distributions and weak solutions
Distributions, Distributions: more, Applications of distributions, Weak solutions
Nonlinear equations
Burgers equation
Eigenvalues and eigenfunctions
Variational theory, Asymptotic distribution of eigenvalues, Properties of eigenfunctions, About spectrum, Continuous spectrum and scattering
Miscellaneous
Conservation laws, Maxwell equations, Some quantum mechanical operators
Appendices
Field theory, Some notations
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