Differential Equations Field of study: Mathematics
Programme code: W4-N2MT19.2023

Module name: Differential Equations
Module code: W4-MT-N2-23-RRoz
Programme code: W4-N2MT19.2023
Semester: winter semester 2024/2025
Language of instruction: Polish
Form of verification: exam
ECTS credits: 6
Purpose and description of the content of education:
1. Metoda kolejnych przybliżeń i twierdzenie Picarda o istnieniu i jednoznaczności rozwiązań zadania Cauchy’ego. 2. Istnienie rozwiązań równań różniczkowych o ciągłej prawej stronie; twierdzenie Peano. 3. Analityczne rozwiązania równań różniczkowych zwyczajnych; twierdzenie Cauchy’ego. 4. Wybrane narzędzia teorii równań różniczkowych cząstkowych. Transformacja Fouriera, lemat Laxa-Milgrama. 5. Elementy teorii przestrzeni Sobolewa. 6. Słabe rozwiązania równań eliptycznych. 7. Metody przybliżone/numeryczne rozwiązywania równań różniczkowych cząstkowych.
List of modules that must be completed before starting this module (if necessary): not applicable
Learning outcome of the module Codes of the learning outcomes of the programme to which the learning outcome of the module is related [level of competence: scale 1-5]
Zna i rozumie klasyczną wiedzę z zakresu równań różniczkowych zwyczajnych i cząstkowych. [RRoz_1]
 K_W01 [3/5]
Zna i rozumie twierdzenia; Picarda, Peano, Cauchy’ego, oraz podstawy teorii równań różniczkowych cząstkowych. [RRoz_2]
 K_W03 [4/5]
Potrafi przeprowadzać podstawowe dowody w zakresie równań różniczkowych, w których stosuje w razie potrzeby narzędzia z innych działów matematyki. [RRoz_3]
 K_U04 [3/5]
Potrafi przygotować prezentacje dotyczące zagadnień z zakresu równań różniczkowych i prezentować je osobom nie będącymi specjalistami w zakresie tych zagadnień. [RRoz_4]
 K_U09 [3/5]
Potrafi określić swoje zainteresowania i je rozwijać; w szczególności jest w stanie nawiązać kontakt ze specjalistami z równań różniczkowych, rozumie ich wykłady przeznaczone dla młodych matematyków. [RRoz_5]
 K_K06 [3/5]
Potrafi posługiwać się językiem angielskim, na poziomie pozwalającym na korzystanie z tekstów obcojęzycznych dotyczących studiowanych zagadnień. [RRoz_6]
 K_U08 [4/5]
Jest gotów do dalszego samokształcenia. [RRoz_7]
 K_K01 [4/5]
Jest gotów do formułowania obiektywnych opinii w zagadnieniach, w których matematyka jest językiem opisu. [RRoz_8]
 K_K06 [4/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [RRoz_fns_1] 15 Formal lecture/ course-related lecture [a01]  exam RRoz_1 RRoz_2 RRoz_3 RRoz_5 RRoz_7 RRoz_8
discussion classes [RRoz_fns_2] 30 Activating method – peer learning [b08] 
Laboratory exercise / experiment [e01]  		course work RRoz_1 RRoz_2 RRoz_3 RRoz_4 RRoz_5 RRoz_6 RRoz_7 RRoz_8
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Literature reading / analysis of source materials [a02] Preparation for classes
reading the literature indicated in the syllabus; reviewing, organizing, analyzing and selecting source materials to be used in class
Developing practical skills [a03] Preparation for classes
activities involving the repetition, refinement and consolidation of practical skills, including those developed during previous classes or new skills necessary for the implementation of subsequent elements of the curriculum (as preparation for class participation)
Consulting materials complementary to those indicated in the syllabus [a04] Preparation for classes
agreeing on materials complementary to those indicated in the syllabus, supporting the implementation of tasks resulting from or necessary for class participation
Getting acquainted with the syllabus content [b01] Consulting the curriculum and the organization of classes
reading through the syllabus and getting acquainted with its content
Verification / adjustment / discussion of syllabus provisions [b02] Consulting the curriculum and the organization of classes
consulting the content of the syllabus, possibly in the presence of the year tutor or members of the class group, and, if necessary, reassessing the provisions concerning special conditions for class participation, e.g., space and time requirements, technical and other requirements, including conditions for participation in classes outside the walls of the university, classes organized in blocks, organized online, etc.
Consulting the schedule [b03] Consulting the curriculum and the organization of classes
getting acquainted with the class schedule, possibly in the presence of the year tutor, in order to optimize participation in classes, including those supplementary to the core subjects listed in the pursued study programme
Determining the stages of task implementation contributing to the verification of learning outcomes [c01] Preparation for verification of learning outcomes
devising a task implementation strategy embracing the division of content, the range of activities, implementation time and/or the method(s) of obtaining the necessary materials and tools, etc.
Studying the literature used in and the materials produced in class [c02] Preparation for verification of learning outcomes
exploring the studied content, inquiring, considering, assimilating, interpreting it, or organizing knowledge obtained from the literature, documentation, instructions, scenarios, etc., used in class as well as from the notes or other materials/artifacts made in class
Analysis of the corrective feedback provided by the academic teacher on the results of the verification of learning outcomes [d01] Consulting the results of the verification of learning outcomes
reading through the academic teacher’s comments, assessments and opinions on the implementation of the task aimed at checking the level of the achieved learning outcomes
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)