| TATA27 | Partial Differential Equations, 6 ECTS credits. /Partiella differentialekvationer/ |
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Prel. scheduled
hours: 48 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(G1, G2, A): A
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| Aim: The course deals mainly with linear partial differential equations of the second order. It gives some familiarity with the different types of equations occuring in physics, particularly in mechanics with heat conduction included. Furthermore, it discusses questions of existence and uniqueness and deals with the mathematical foundation of the finite-element method (F.E.M.). It is also essential to gain an understanding of the properties of different solutions in general, as well as some knowledge of the practical dealing with different types of boundary-value problems and initial-value problems. Some knowledge of distributions. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) TATM18 Linear Algebra, TATM72 Calculus, TATM73 Calculus, several variables, TATM41 Vector Analysis, TATA20 Fourier Analysis, or equivalent Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding. |
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| Organisation: Teaching is done with combined lectures/exercises. |
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| Course contents: Origin of PDE:s. The PDE landscape. Derivation of the heat equation, Laplace's equation and the wave equation, starting from physical balance laws. Classification of equations. Characteristics. Properties of harmonic functions. Connections with complex analysis. General properties of elliptic equations. Properties of solutions of time-dependent problems. Wave propagation. Integral transforms. Green's function. Distributions. The fundamental solution. Maximum principles. Introduction to finite-element methods. Weak solutions, weak formulation. Simple error analysis. Software for F.E.M. is demonstrated. |
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| Course literature: Strauss, W.A: Partial Differential Equations. An introduction. John Wiley & Sons 1992. |
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| Examination: | ||||
| Written examination |
4 p |
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6 ECTS |
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Course language is Swedish/under certain circumstances the course might be offered in English. Department offering the course: MAI. Director of Studies: Göran Forsling Examiner: Vladimir Kozlov Link to the course homepage at the department Course Syllabus in Swedish |
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