MATH270 Complex Analysis and Transformation Methods

Credits (ECTS):10

Course responsible:Susanne Solem, Arkadi Ponossov

Campus / Online:Taught campus Ås

Teaching language:Engelsk

Course frequency:Annually

Nominal workload:Theory: 125 hours. Exercises and preparations for the exam: 125 hours.

Teaching and exam period:This course starts in the Spring parallel. This course has teaching and evaluation in the Spring parallel.

About this course

The course deals with elementary theory in complex analysis and transformation methods. In the complex analysis part, students will be introduced to complex numbers and functions and methods of integration, including Cauchy's integral theorem and formula. Furthermore, the students will learn about the Fourier series and transforms, which have applications in for example signal and image processing, and the Laplace transform and its relation to stability of systems. The course also includes an introduction to numerical applications of the Fourier transform.

Learning outcome

After completion of the course, the student will have learnt elementary theory for analytical functions and transformation methods. The student will be able to apply this theory to relevant applied problems (in, for example, geomatics, physics, and technology). After completing the course, the students will master

Complex numbers
Complex functions
integration methods in complex analysis, including Cauchy's integral theorem and Cauchy's integral formula
Fourier series
Fourier transformations
Discrete Fourier transforms (DFT)
The Laplace transform and its relation to stability

Learning activities
The most important information on each topic of the course will be discussed in lectures. Problems on the same topics are given weekly, with the aims to practice calculation technique, understand methods and ideas, as well as be able to apply the subject to technical-physical problems. Problem-solving sessions with a teaching assistant present.
Teaching support
The students can either contact the lecturer in the office, by telephone, or by e-mail.
Prerequisites
MATH111 or MATH121
MATH112 and MATH113 or MATH122 and MATH123
Assessment method
A 3.5 hours written exam.

One written exam Grading: Letter grades Permitted aids: B2 Calculator handed out, other aids as specified
Examiner scheme
The external and internal examiners jointly prepare the exam questions and the correction manual. The external examiner reviews the internal examiner's examination results by correcting a random sample of candidate's exams as a calibration according to the department's guidelines for examination markings.
Mandatory activity
None
Notes
Lectures will be given in English.
Contact the course responsible if you plan to take this course in connection with your bachelor thesis.
Teaching hours
Lectures for 4 hours per week, and problem sessions for 2 hours per week.
Admission requirements
Special requirements in Science