# Differential Equations MAT320

Introduction to ordinary and partial differential equations.

Course description for study year 2022-2023

Facts
Course code

MAT320

Version

1

Credits (ECTS)

10

Semester tution start

Spring

Number of semesters

1

Exam semester

Spring

Language of instruction

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.
Required prerequisite knowledge
None
Recommended prerequisites
MAT100 Mathematical Methods 1, MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis
Exam
Course teacher(s)
Course coordinator: Alexander Rashkovskii
Course teacher: Alexander Rashkovskii