Differentiaali- ja differenssiyhtälöt (MATLA0008), 3 op

Basic information

Course name:	Differentiaali- ja differenssiyhtälöt Differential and Difference Equations
Course Winha code:	MATLA0008
Kurre acronym:	Diff.
Credits:	3
Type and level of course:	Basic studies
Year of study, semester or study period:	2.year
Implementation:	Spring semester, 3.period, 4.period
Semester:	0607
Language of tuition:	Suomi
Teacher:	Pirkka Peltola
Final assessment:	Grading scale (0-5)

Descriptions

Prerequisites

Basic Course in Mathematics A, Basic Course in Mathematics B and Laplace Transforms.

Course contents (core content level)

The concepts of the differential equation and of its solution. Techniques to solve simple differential equations; the main emphasis is on linear differential equations with constant coefficients. Initial value problems. Mathematical programs and numerical solutions of differential equations. Linearization of a single differential equation and a pair of differential equations. Discretization of a differential equation. Matrix exponential function. The system of differential equations in state-space representation and the form of the solution.

Course contents (additional)

The methods to solve numerically differential equations.
Outline of the principles to solve the system of linear differential equations by using matrix exponential function. Use of z transforms in the analysis of difference equations.

Core content level learning outcomes (knowledge and understanding)

The student is aware of different types of differential equations and different methods, characteristic to each type, to solve these equations. The student understands the connection of basic numerical methods and the information he or she sees in the direction field of a differential equation. The student knows that linearization and discretization change the values of the solution of a differential equation.

Core content level learning outcomes (skills)

The student is able to classify differential equations. The student can solve linear differential equations with constant coefficients. Given the direction field of the differential equation, the student is able to sketch solutions. The student can use mathematical programs when solving differential equations. The student is able to linearize a differential equation and estimate the effect of linearization to the solution. The student is able to choose a suitable step for discretization and convert a differential equation into the corresponding difference equation. The student is able to solve the difference equation and estimate the difference between the solutions of the original differential equation and the corresponding difference equation.

Teaching and learning strategies

Lectures and assignments.
Self study.
Laboratory assignments.
Exam.

Teaching methods and student workload

Exam
Lectures and assignments
Laboratory assignments

Assessment weighting and grading

Assessment of computer exercises. Final exam.

Related competences of the degree programme

International and intercultural skills
Theoretical basis and mathematical and science skills
Information acquisition skills and adaptation of new knowledge