Linear Differential Equations
نویسنده
چکیده
1. Linearity and Continuity 1.1 Continuity 1.2 Linearity 1.3 Perturbation theory and linearity 1.4 Axiomatically linear equations 1.4.1 Fields, Maxwell equations 1.4.2 Densities on phase space in classical physics 1.4.3 Quantum mechanics and Schrödinger equation 2. Examples 2.1 Ordinary differential equations 2.2 The Laplace equation 2.3 The wave equation 2.4 The heat equation and Schrödinger equation 2.5 Equations of complex analysis 2.5.1 The Cauchy-Riemann equation 2.5.2 The Hans Lewy equation 2.5.3 The Misohata equation 3. Methods 3.1 Well posed problems 3.1.1 Initial value problem, Cauchy-Kowalewsky theorem 3.1.2 Other boundary conditions 3.2 Distributions 3.2.1 Distributions 3.2.2 Weak Solutions 3.2.3 Elementary solutions 3.3 Fourier analysis 3.3.1 Fourier transformation 3.3.2 Equations with constant coefficients 3.3.3 Asymptotic analysis, microanalysis.
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