Differential and Difference Equations

fakultatywne

mieszany: w sali i zdalnie

To familiarize the student with the theories of differential and difference equations, with special emphasis on the similarities and differences, and to deepen the ability to apply both theories in practice, with an emphasis on the accuracy of the choice of method to solve the problem and testing its stability.

Educational profile: general academic

Form of studies: full-time

Compulsory subject

Field: mathematical sciences, discipline: mathematics

Year of study: 1, semester: 2

Prerequisites: linear algebra, ordinary differential equations, mathematical analysis

Lecture 30 hours, exercises 15 hours, laboratory 15 hours.

Teaching methods: lectures, accounting exercises, consultations, work on literature, solving homework assignments, discussions in problem groups.

ECTS credits: 5

Balance of student workload:

participation in lectures 15x2h = 30h

participation in exercises 15x2h = 30h

preparation for classes 7x2h = 14h

finishing the tasks started during the exercises and preparing notes at home after the classes 10x3h = 30h participation in consultations 3x1h = 3h

preparation for the exam and participation in it 12h + 3h = 15h

preparation for colloquiums 2x4h = 8h

Quantitative indicators

student workload related to classes requiring the direct participation of an academic teacher: 63 hours.

[1] Edwards, C.H., Penney, D.E, Calvis, D., DIFFERENTIAL EQUATIONS Computing and Modeling, Fifth Edition, Pearson Education, New Jersey 2014.

[2] Elaydi N.S., An introduction to difference equations, Springer-Verlag New York, 1991.

[3] Zill, D.G., A First Course in Differential Equations with Modeling Appli- cations, Tenth Edition, Brooks/ Cole, Cengage Learning, Boston 2013.

He knows the basic concepts of the general theory of differential and difference (ordinary) equations. He can solve systems of linear differential and differential equations using appropriate analytical methods. He knows the basic theorem about the existence and uniqueness and knows how to investigate the existence of a solution to the initial problem.

He can examine the stability of a solution to a differential and differential equation and systems of equations. Can independently search for information on a given topic in the literature, understands names and mathematical terms in foreign languages. The student is prepared to apply the acquired knowledge to solve certain problems.

Lectures, tutorials, consultations, work on literature, solving homework, discussions in problem groups.

Means of verification: written / oral exam; a series of cards; test / colloquium; home accounting / problem work; presentation of solutions to tasks in the classroom; continuous observation of the student's activity;

The exam is written.

1. A student who passes the exercises is allowed to take the exam.

2. You can receive a total of 10 points for active participation in the exercises - the instructor will propose the exercises. 3. You can receive a total of 90 points for the written part of the exam.

It consists of 3 parts containing theoretical questions.

So a student can get a total of 100 points from all parts.

Depending on the number of points obtained, the final grade is in accordance with the presented grading scale:

91 -100 = very good;

81 - 90 = good plus;

71 - 80 = good;

61 - 70 = sufficient plus;

51 - 60 = satisfactory;

0 - 50 = insufficient.

In the case of a small number of missing points or a better grade (up to 5% of the exam points), an oral examination is possible.