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# Differential Equations

This is the study programme for 2020/2021.

Introduction to ordinary and partial differential equations.

### Learning outcome

The course consists of two parts: ordinary and partial differential equations. Students will learn methods for solving first order ordinary differential equations such as separation of variables and exact differential equations. Students will also analyze the second order linear differential equations, especially those with constant coefficients, together with higher order ordinary differential equations and systems of first order equations. Students will also learn to solve them by developing into power series and using the Frobenius method. They also will learn simple boundary value problems. Concerning partial differential equations, the students will be able to solve the wave equations, heat conduction equations, Laplace equation, by means of the separation method and Fourier series, and also solve boundary value problems. In addition, will the students get an introduction to Green's functions and Fourier transform.

### Contents

Green's functions and Fourier transformFirst order differential equations: linear, separable, exact. Second order and higher order linear
differential equations, systems of first order linear differential equations with constant
coefficients. Solving of second order linear differential equations by developing into power
series. Boundary problems. Orthogonal functions and Fourier series.
Solving of partial differential equations by separation of variables.

None.

### Recommended previous knowledge

MAT100 Mathematical Methods 1, MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis

### Exam

Weight Duration Marks Aid
Written exam1/14 hoursA - FSpecified printed and hand-written means are allowed. Definite, basic calculator allowed.

### Course teacher(s)

Course coordinator
Alexander Rashkovskii
Course teacher
Alexander Rashkovskii

### Method of work

Six hours lecturing and problem solving each week.

### Overlapping courses

Course Reduction (SP)
Differential Equations (BMF110_1) 10
Mathematics 4 - differential equations (TE0303_A) 5
Mathematics 4 - differential equations (TE0303_1) 5
Mathematics 4 - Differential Equations (ÅMA300_1) 5

### Open to

Biological Chemistry - Biotechnology - Bachelor's Degree Programme
Civil Engineering - Bachelor's Degree Programme
Computer Science- Bachelor's degree programme in computer science
Control Engineering and Circuit Design, Vocational Path
Control Engineering and Circuit Design - Bachelor's Degree Programme
Chemistry and Environmental Engineering - Bachelor's Degree Programme
Mechanical Engineering - Bachelor's Degree Programme, specialization in Mechanical Engineering and Materials Science
Mathematics and Physics - Bachelor's Degree Programme
Geosciences Engineering - Bachelor's Degree Programme
Petroleum Technology - Bachelor's Degree Programme
Biological Chemistry - Master of Science Degree Programme
Environmental Engineering - Master of Science Degree Programme
Industrial economics - Master's Degree Programme - 5 year
Industrial Automation and Signal Processing - Master's Degree Programme - 5 year
Mechanical and Structural Engineering and Materials Science- Master's Degree Programme - 5 years
Mathematics and Physics - Master of Science Degree Programme
Mathematics and Physics, 5-year integrated Master's Programme
Petroleum Geosciences Engineering - Master of Science Degree Programme
Petroleum Engineering - Master of Science Degree Programme
Petroleum Engineering - Master`s Degree programme in Petroleum Engineering, 5 years
Mathematics - One-year programme

### Course assessment

Form and/or discussion

### Literature

Literatur will be published as soon as it has been prepared by the course coordinator/teacher

This is the study programme for 2020/2021.

Sist oppdatert: 22.09.2020