Introduction to Partial Differential Equations

5 credits

Syllabus, Master's level, 1MA053

A revised version of the syllabus is available.

Code: 1MA053
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

BSc, 60 credits Mathematics with Several Variable Calculus, Linear Algebra II and Transform Methods

Learning outcomes

In order to pass the course (grade 3) the student should

know the most common partial differential equations that appear in problems concerning e.g. heat conduction, flow, elasticity and wave propagation;

understand basic questions concerning the existence and uniqueness of solutions, and continuous dependence of initial and boundary data;

be able to solve simple first order equations using the method of characteristics;

know the classification of second order equations;

be able to solve simple initial and boundary value problems using e.g. d'Alembert's solution formula, separation of variables, Fourier series expansion or expansion in other orthogonal systems;

be able to compute and analyse wave propagation and heat conduction and describe in mathematical terms;

be able to formulate maximum principles for various equations and derive consequences.

Content

First order equations. Classification of second order equations: elliptic, parabolic and hyperbolic, Physical models. Various solution techniques. Green functions. Maximum principles.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.