Beyond partial differential equations: A course on linear and quasi-linear abstract hyperbolic evolution equations
by Horst R. Beyer
Publisher: arXiv 2011
Number of pages: 275
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout the course applications to problems from current relativistic (hyperbolic) physics are provided, which display the potential of semigroup methods in the solution of current research problems in physics.
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by Boris Dubrovin - SISSA
These are lecture notes on various topics in analytic theory of differential equations: Singular points of solutions to analytic differential equations; Monodromy of linear differential operators with rational coefficients.
by Paul Dawkins - Lamar University
Contents: Basic Concepts; First Order Differential Equations; Second Order DE; Laplace Transforms; Systems of Differential Equations; Series Solutions; Higher Order DE; Boundary Value Problems and Fourier Series; Partial Differential Equations.
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The differential equation must necessarily at first be viewed in connection with a 'primitive', from which it might have been obtained by the direct process, and the solution consists in the discovery of such a primitive, when it exists...