Mathematics 2 Field of study: Biomedical Engineering
Programme code: W4-S1IB19.2024

Module name: Mathematics 2
Module code: 08-IB-S1-17-2-M2
Programme code: W4-S1IB19.2024
Semester: summer semester 2024/2025
Language of instruction: Polish
Form of verification: exam
ECTS credits: 5
Purpose and description of the content of education:
Celem tego modułu jest zapoznanie studentów z podstawami rachunku różniczkowego i całkowego funkcji wielu zmiennych, z elementami równań różniczkowych zwyczajnych oraz z elementami teorii szeregów potęgowych (wraz z zastosowaniami w praktyce).
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]
Ma wiedzę o zastosowaniach równań różniczkowych w naukach przyrodniczych (ruch harmoniczny, wahadło, rozpad promieniotwórczy, rozwój populacji). [K_1]
 W01 [3/5]
Zna interpretację fizyczną równania zwyczajnego II rzędu o stałych współczynnikach. [K_2]
 W01 [3/5]
Zna kluczowe twierdzenia z poznanych działów matematyki. [K_3]
 W01 [3/5]
Potrafi obliczać pochodne cząstkowe funkcji wielu zmiennych oraz zna ich interpretacje fizyczną. Potrafi stosować pojęcie różniczki zupełnej do oszacowania niepewności pomiarowej. Potrafi obliczyć ekstrema funkcji wielu zmiennych. [K_4]
 U01 [2/5]
Potrafi stosować całkę podwójną i potrójną do obliczania pól, objętości i mas. Potrafi obliczyć pracę z wykorzystaniem pojęcia całki krzywoliniowej oraz twierdzenia Greena. [K_5]
 U01 [2/5]
Potrafi podać interpretację fizyczną całki powierzchniowej I i II rodzaju. Potrafi stosować twierdzenie Gaussa Ostrogradskiego do obliczenia całek powierzchniowych. [K_6]
 U09 [2/5]
Potrafi rozwiązać równania różniczkowe zwyczajne: o rozdzielonych zmiennych, liniowe I rzędu, liniowe II rzędu o stałych współczynnikach. [K_7]
 U09 [2/5]
Potrafi zbadać zbieżność szeregów potęgowych. Potrafi rozwinąć w szereg potęgowy pewne funkcje elementarne (sinus, cosinus, exp). [K_8]
 U09 [2/5]
Potrafi stosować metody matematyczne do opisu zagadnień technicznych. [K_9]
 U09 [2/5]
Form of teaching Number of hours Methods of conducting classes Assessment of the learning outcomes Learning outcomes
lecture [k_fs_1] 30 Formal lecture/ course-related lecture [a01]  exam K_1 K_2 K_3 K_4 K_5 K_6 K_7 K_8 K_9
practical classes [k_fs_2] 30 Explanation/clarification [a05] 
Working with another teaching tool [d03]  		course work K_1 K_2 K_3 K_4 K_5 K_6 K_7 K_8 K_9
The student's work, apart from participation in classes, includes in particular:
Name Category Description
Search for materials and review activities necessary for class participation [a01] Preparation for classes
reviewing literature, documentation, tools and materials as well as the specifics of the syllabus and the range of activities indicated in it as required for full participation in classes
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)
Production/preparation of tools, materials or documentation necessary for class participation [a05] Preparation for classes
developing, preparing and assessing the usefulness of tools and materials (e.g. aids, scenarios, research tools, equipment, etc.) to be employed in class or as an aid when preparing for classes
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
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
Development of a corrective action plan as well as supplementary/corrective tasks [d02] Consulting the results of the verification of learning outcomes
reviewing and selecting tasks and activities enabling the elimination of errors indicated by the academic teacher, their verification or correction resulting in completing the task with at least the minimum passing grade
Attachments
Module description (PDF)
Information concerning module syllabuses might be changed during studies.
Syllabuses (USOSweb)
Semester Module Language of instruction
(no information given)