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Course detail
FSI-3MAcad. year: 2023/2024
The course provides an introduction to the theory of infinite series and the theory of ordinary and partial differential equations. These branches form the theoretical background in the study of many physical and engineering problems. The course deals with the following topics:Number series. Function series. Power series. Taylor series. Fourier series.Ordinary differential equations. First order differential equations. Higher order linear differential equations. Systems of first order linear differential equations.Partial differential equations. Classification. Modelling with differential equations. Basic numerical methods for solving differential equations with a suitable software (e.g. Matlab).
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Linear algebra, differential and integral calculus of functions of a single variable and more variables.
Rules for evaluation and completion of the course
Course-unit credit is awarded on the following conditions: Active participation in seminars fulfilment of all conditions of the running control of knowledge (this concerns also the seminars in computer lab). At least half of all possible points in each of the both tests.Examination: The examination tests the knowledge of definitions and theorems (especially the ability of their application to the given problems) and practical skills in solving of examples. The exam has written and oral part. The written exam consists in particular of the examples on the following topics:Number and function series, the expansion of a function into Taylor series, solving of first order ODEs, solving of higher order linear ODEs, solving of system of first order linear ODEs, Fourier series, solving of ODEs via the infinite series and the Laplace tranform method, boundary value problems, basics of PDEs theory. Some theoretical queries concerning basic concepts can be included in the written part as well.Topics of practical part: The expansion of a function into Taylor series, solving of first order ODEs, solving of higher order linear ODEs, solving of system of first order linear ODEs.The final grade reflects the result of the written part of the exam (maximum 80 points) and the result of the oral part (maximum 20 points).Grading scheme is as follows: excellent (90-100 points), very good(80-89 points), good (70-79 points), satisfactory (60-69 points), sufficient (50-59 points), failed (0-49 points).
Attendance at lectures is recommended, attendance at seminars is obligatory and checked. Lessons are planned according to the week schedules. Absence from seminars may be compensated for by the agreement with the teacher.
Aims
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Prerequisites and corequisites
Basic literature
Recommended literature
Elearning
Classification of course in study plans
specialization STI , 2 year of study, winter semester, compulsoryspecialization MTI , 2 year of study, winter semester, compulsory
Lecture
Teacher / Lecturer
Syllabus
Exercise
Computer-assisted exercise