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# Details for Course FMA250F Partial Differential Equations with Distribution Theory

General
• FMA250F
• Temporary
Course Name
• Partial Differential Equations with Distribution Theory
Course Extent
• 7.5
Type of Instruction
• Course given jointly for second and third cycle
• 7151 (Centre of Mathematical Sciences / Mathematics)
•  -11-15
• FN1/Anders Gustafsson

## Current Established Course Syllabus

General
Aim
• The probably largest class of mathematical models among technichal systems is based on partial differential equations (PDE). An indispensable tool in the modern theory for these equations is distribution theory.

The aim of the course is on the one hand to give a more stable theoretical foundation for concepts and methods for PDEs that have been introduced in earlier courses, and a greater ability to independently use these, and on the other hand to develop the theory further. Moreover, the course aims to give the analytical background to some frequently used numerical solution methods.
Contents
• Distribution theory: derivatives, convergence, fundamental solutions, Green's functions, the Fourier transform, the Laplace and the wave operators.

Partial differential equations: spectral methods, eigenfunction expansions, weak solutions. Approximation methods. Integral equations, finite element methods. Geometrical methods. Characteristics. The study of some model equations.
Knowledge and Understanding
• For a passing grade the doctoral student must
• be able to explain the foundations of the theory at an oral examination.

be able to explain the concept of a weak solution to a PDE, and its connection to distribution theory.
Competences and Skills
• For a passing grade the doctoral student must
• with access to literature independenly be able to integrate methods and views from different parts of the course in order to solve problems and answer questions within the framework of the course.

in writing and orally, with proper terminology and clear logic be able to explain the solution to a mathematical problem within the course.
Judgement and Approach
• For a passing grade the doctoral student must
Types of Instruction
• Lectures
• Laboratory exercises
• Exercises
Examination Formats
• Written exam
• Oral exam
• Written assignments
• Written and/or oral test, to be decided by the examiner. Written assignments.
• Failed, pass
Assumed Prior Knowledge
Selection Criteria
Literature
• Renardy, M. & Rogers, Robert C.: An Introduction to Partial Differential Equations. Springer, 2004. ISBN 9780387004440.
• Material distributed by the department.
Further Information
Course code
• FMA250F
•  -11-15
• FN1/Anders Gustafsson

## All Established Course Syllabi

1 course syllabus.

Valid from First hand in Second hand in Established
Autumn 2013 2013‑10‑17 11:21:12 2013‑10‑29 15:58:40 2013‑11‑15

## Current or Upcoming Published Course Occasion

No matching course occasion was found.

## All Published Course Occasions

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0 course occasions.