Differential equations and integral transformsLaajuus (3 ECTS)

Objective

The student knows the basics of differential equations and how to use them to describe dynamical systems. Laplace transform and their applications.

Content

First and second order differential equations and separable differential equations. Laplace transform, transfer function and frequency response. Fourier analysis.

Qualifications

Previous courses in mathematics

Assessment criteria, satisfactory (1)

The student knows the basic concepts relating to differential equations and understands how differential equations can be used to describe simple phenomena. The student is able to solve simple differential equation. The student can perform basic Laplace-transformations and knows how to use Laplace-transformation to solve differential equations. The student understands the basic concepts of Fourier-analysis.

Assessment criteria, good (3)

In addition to the requirements above the student is able to solve more complicated differential equations and knows how to use differential equations to model various phenomena. The student also knows the basic principles to find numerical solutions for differential equations. The student is able to use Laplace-transformation to analyze solutions. The student knows how to use Fourier analysis in applications.

Assessment criteria, excellent (5)

In addition to the requirements above, the student has a deep understanding of the topics covered in the course and is able to apply them creatively and sensibly in different applications.