MM557: Partial Differential Equations and complex analysis

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300041102
Assessment: Second examiner: Internal
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Bachelor

STADS ID (UVA): N300041101
ECTS value: 5

Date of Approval: 01-11-2022


Duration: 1 semester

Version: Approved - active

Entry requirements

The course cannot be chosen by students who: passed MM511 or MM549.

Academic preconditions

Students taking the course are expected to:
  • Have knowledge of the concepts of calculus and linear algebra
  • Be familiar with the most common mathematical equations used in classical mechanics, electromagnetism and quantum mechanics.

Course introduction

Partial Differential Equations (PDEs) and complex analysis are instrumental tools in physics. This course aim to equip the students with the basic knowledge of PDEs and complex analysis focusing on applications stemming from modern physics.
The course builds on the knowledge acquired in the courses MM536, MM505, FY530, and applications are taken from the courses FY503, FY506, FY504, FY521, FY522.

The course provides a mathematical basis to study advanced topics in the master's program in physics, such as FY803, FY802 and FY817.
In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give skills to analyze practical and theoretical physics problems formulated in terms of PDEs
  • Give knowledge and understanding of theory of PDEs and their applications to physics problems
  • Give knowledge and understanding of complex analysis and its applications to physics problems

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  • recognize and solve the PDEs by methods presented in the course  
  • use the tools of complex analysis in problems from physics

Content

The following main topics are contained in the course:
  • introduction to PDEs 
  • Methods of solution for PDEs: separation of variables, Fourier transform, Green’s functions
  • Introduction to complex calculus: complex functions, differentiation and  holomorphic functions, power series
  • Complex integration and residue theory

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

Mandatory assignment

EKA

N300041102

Assessment

Second examiner: Internal

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

5

Indicative number of lessons

34 hours per semester

Teaching Method

At the faculty of science  the teaching is organized according to the three-phase model, ie. intro, the training and study phase.Teaching activities result in an estimated indicative distribution of the work effort of an average student in the following way:

  • Intro phase (lectures) - Number of hours: 20
  • Training phase: Number of hours: 14 

Teaching forms: traditional blackboard presentations, class discussions and the use of computer programs to present examples will be used.
Activities during the studyphase:

  • preparation of exercises in study groups
  • discussion of the key concepts presented in the lectures

Teacher responsible

Name E-mail Department
Michele Della Morte dellamor@cp3.sdu.dk Computational Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.