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| TATM59 | Ordinary differential equations, 4 p (sw) /Ordinära differentialekvationer/ Advancement level: C | |
| Aim: The course will deal with those properties of ordinary differenial equations which are central to applied mathematics. Examples of important applications are the study of vibrations and other dynamical problems in elasticity theory, including the analysis of stability. Prerequisites: TATM 12, Algebra M; TATM 72, Calculus A; TATM73 Calculus B; TATM 62, Calculus M, second course.Course organization: Teaching is done in seminars.Course content: Existence and uniqueness for linear and non-linear differential equations. Construction of solutions by Euler's method, some numerical methods of solving ordinary differential equations. Linear systems with constant coefficients. Exponentials of matrices. Homogeneous and inhomogeneous systems. Some aspects of Sturm-Liouville theory and special functions. Automomous systems. Phase portrait. Linearisation of autonomous systems. Liapounov's method for stability analysis. Periodic solutions.Course literature: Andersson K, Böiers, L-C: Ordinära Differentialekvationer. Studentlitteratur, Lund. | ||
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