# MATH250 Partial Differential Equations and Models

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#### Showing course contents for the educational year 2022 - 2023 .

Course responsible: Arkadi Ponossov
Teachers: Arkadi Ponossov
ECTS credits: 10
Faculty: Faculty of Science and Technology
Teaching language: EN
(NO=norsk, EN=Engelsk)
Teaching exam periods:
This course starts in the autumn parallel. This course has teaching/evaluation in autumn parallel.
Course frequency: Annually, minimum 5 students
First time: Study year 2004-2005
Course contents:

Lectures cover the most important parts of each topic. After this, the students are given exercises on the same topics. The exercises are intended to help students practice calculation technique, understand methods and ideas as well as be able to apply the subject to technical-physical problems. Projects based on MATLAB will be an important part of the course.

MATH250 deals with the following topics:

• Modeling. Derivation of partial differential equations like the  Laplace equation, the diffusion equation and the wave equation from fundamental principles (balance laws) as conservation of mass, charge, particle number, momentum, energy
• Analytical methods. Analytical solution methods for linear partial differential equations: Separation of variables, Hilbert - space theory, Sturm - Liouville theory, Fourier series.
• Numercal methods and simulation. Numerical solution of partial differential equations by means of difference methods. Usage of the program package PYTHON or MATLAB.
Learning outcome:

Students are to learn the basic theory of partial differential equations. They are to become capable of using this theory for solving problems in biology, geomatics, physics and technology.

After completing the course, the students should master the following topics: conservation laws, classification of partial differential equations, the wave equation, diffusion equations, the Laplace equation, separation of variable techniques, Sturm-Liouville theory, Fourier series and Fourier transform techniques, difference methods.

Students are to be able to use:

• relevant methods and techniques with emphasis on practical applications
• the computer programme PYTHON or MATLAB for solving and visualising problems that are part of the course
• They should also be able to make and analyse simple mathematical models.
Learning activities:
The teaching will be given as lectures and exercises with an assistant teacher present.
Teaching support:
The students can either contact the teacher in his office by telephone or by e-mail
Syllabus:
Reading list will be handed out in lectures.
Prerequisites:
MATH111, MATH112, MATH113, MATH280
Recommended prerequisites:
MATH270
Mandatory activity:
No compulsory assignments.
Assessment:
Final written examination, 3.5 hours.
Nominal workload:
Theory: 125 hours. Exercises: 125 hours.
Entrance requirements:
Special requirements in Science
Type of course:
Lectures: 4 hours per week. Calculation exercises: 2 hours per week. Python/MATLAB exercises: 2 hours per week.
Examiner:
The external and internal examiner 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.
Allowed examination aids: A1 No calculator, no other aids
Examination details: Written exam: Letter grades