# Differential Equations (MAT320)

Introduction to ordinary and partial differential equations.

Course description for study year 2022-2023

Facts

MAT320

1

10

Spring

1

Spring

English

Time table

## Content

First 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 value problems. Orthogonal functions and Fourier series.

Solving of partial differential equations by separation of variables.

Green's functions and Fourier transform.

## 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.

None

## Recommended prerequisites

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

## Course coordinator:

Alexander Rashkovskii

## Course teacher:

Paul Francis de Medeiros

## Course teacher:

Alexander Rashkovskii

## Method of work

Six hours lecturing and problem solving each week.

## Open for

Biological Chemistry - Biotechnology - Bachelor's Degree Programme Civil Engineering, Bachelor in Engineering Computer Science - Bachelor in Engineering Control Engineering and Circuit Design, Vocational Path - Bachelor in Engineering Control Engineering and Circuit Design - Bachelor in Engineering Chemistry and Environmental Engineering - Bachelor in Engineering Mechanical Engineering, Bachelor in Engineering Mathematics and Physics - Bachelor's Degree Programme Geosciences Engineering - Bachelor in Engineering Biological Chemistry - Master of Science Degree Programme Environmental Engineering - Master of Science Degree Programme Industrial Economics - Master of Science Degree Programme, Five Year Structural and Mechanical Engineering - Master of Science Degree Programme. Five Years Mathematics and Physics - Master of Science Degree Programme Mathematics and Physics - Five Year Integrated Master's Degree Programme Petroleum Geosciences Engineering - Master of Science Degree Programme Petroleum Engineering - Master of Science Degree Programme Petroleum Engineering - Master of Science Degree Programme, Five Years Exchange programme at Faculty of Science and Technology Mathematics - One-Year Programme

## Course assessment

Form and/or discussion

## Literature

Search for literature in Leganto