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Essentials of partial differential equations : with applications

Author: Marin Marin; Andreas Öchsner
Publisher: Cham, Switzerland : Springer, [2018] ©2018
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1029889213
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marin Marin; Andreas Öchsner
ISBN: 9783319906478 331990647X
OCLC Number: 1035556443
Description: 1 online resource.
Contents: Intro; Preface; Contents; About the Authors; Part I Classical Solutions; 1 Quasilinear Equations; 1.1 Canonical Form in Two-Dimensional Case; 1.2 The Canonical Form for n>2; 2 Differential Operators of Second Order; 2.1 Green's Formula; 2.2 Levi Functions; 2.3 Potentials; 2.4 Boundary Value Problems; 3 The Theory of Potential; 3.1 The Newtonian Potential; 3.2 The Solid Angle; 3.3 The Double Layer Potential; 3.4 The Single Layer Potential; 3.5 Reduction of Boundary Value Problems to Fredholm Integral Equations; 4 Boundary Value Problems for Elliptic Operators 4.1 The Method of Green's Function4.2 The Dirichlet's Problem; 4.3 Properties of Harmonic Functions; 5 Operational Calculus; 5.1 The Laplace Transform; 5.2 The Fourier Transform for Functions from L1; 5.3 The Fourier Transform for Functions from L2; 6 Parabolic Equations; 6.1 Initial-Boundary Value Problems; 6.2 The Method of Green's Function; 6.3 The Cauchy Problem; 7 Hyperbolic Equations; 7.1 The Problem of the Infinite Oscillating Chord; 7.2 Problem with Initial and Boundary Conditions; 7.3 The Cauchy Problem; Part II Solutions in Distributions; 8 Elements of Distributions 8.1 Spaces of Distributions8.2 The Derivative of a Distribution; 8.3 The Primitive of a Distribution; 8.4 Tensor Product and Product of Convolution; 8.5 The Fourier Transform in Distributions; 9 Integral Formulas; 9.1 Differential Operators; 9.2 Classical Integral Formulas; 10 Partial Differential Equations of the First Order; 10.1 The Cauchy Problem; 10.2 Existence and Uniqueness of the Solution; 11 Linear Partial Differential Equations of Second Order; 11.1 The Cauchy Problem; 11.2 Classification of Partial Differential Equations of Second Order; 11.3 Linear Elliptic Operators 16.1 The Problem of the Infinite Vibrant Chord16.2 Weak Solutions of the Wave Equation; Bibliography
Responsibility: Marin Marin, Andreas Öchsner.

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