# Differential Equations (MAT320)

Introduction to ordinary and partial differential equations.

Course description for study year 2024-2025. Please note that changes may occur.

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 second order linear differential equations using power series. Boundary value problems. Orthogonal functions and Fourier series. Solving 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 analyse second order linear differential equations, including those with constant coefficients, together with higher order ordinary differential equations and systems of first order equations. Students will also learn how to solve them using 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 equation, the heat conduction equation and Laplace's equation using separability and Fourier series, and they will also be able to solve boundary value problems. In addition, the students will get an introduction to Green's functions and the 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 coordinator:

Paul Francis de Medeiros

## Course teacher:

Alexander Rashkovskii

## Method of work

5-6 hours of 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 Electrical Engineering, Vocational Path - Bachelor in Engineering Electrical Engineering - Bachelor in Engineering Environmental Engineering - Bachelor in Engineering Mechanical 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 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

There must be an early dialogue between the course supervisor, the student union representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital subject evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

## Literature

Search for literature in Leganto