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
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
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
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
Timetable
Administrative Unit
Team at Educational Law & Registration
Offered in
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.