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| TATM64 | Partial Differential Equations, 4 p (sw) /Partiella differentialekvationer/ Advancement level: C | |
| Aim: The course will deal with the commonest linear partial differential equations which arise when one studies problems concerning, for example, heat conduction, fluid flow, elasticity and wave propagation. Important questions are: existence of solutions, their uniqueness, what properties they have in general as well as how one obtains exact or approximate expressions for them. Finding solutions using the method of separation of variables and by expanding in Fourier series, Fourier integrals or other orthogonal systems is an essential part of the course. Prerequisites: TATM 31 Algebra M; TATM 72 Analysis A, TATM 73 Analysis B, TATM 62 Calculus M, Second Course.Course organization: The course consists of lectures and problem classes.Course content: Fourier series and Fourier integrals. Conservation laws in physics. Linear partial differential equations with boundary conditions, for example Laplace's and Poisson's equations, the heat equation and the wave equation. The method of separation of variables. Sturm-Liouville equations and expansion in orthogonal systems, particularly Bessel functions and Legendre polynomials. Green's function, fundamental solutions. Characteristics. Difference methods for numerical solutions. Applications to problems involving heat conduction, diffusion as well as oscillating strings, membranes and beams.Course literature: Haberman, R: Elementary Applied Differential Equations. Prentice-Hall 1987. Andersson, L-E: Exempelsamling i Partiella Differentialekvationer för M. Mathematical Institute. Andersson, L-E: Formelsamling i Partiella Differentialekvationer för M. Mathematical Institute. | ||
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