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.
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.
Required prerequisite knowledge
MAT100 Mathematical Methods 1, MAT200 Mathematical Methods 2, MAT210 Real and Complex Calculus, MAT300 Vector Analysis
Form of assessment
Specified printed and hand-written means are allowed. Definite, basic calculator allowed
There must be an early dialogue between the course coordinator, the student 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 course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.