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Partial Differential Equations by Victor Ivrii

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Partial Differential Equations written by Victor Ivrii, Department of Mathematics, University of Toronto, Ontario, Canada . This is an other book of mathematics 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

  • Download free pdf Partial Differential Equations by Victor Ivrii
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