312.220 (20S) Partial Differential Equations 1

Sommersemester 2020

Registration deadline has expired.

First course session
05.03.2020 14:00 - 16:00 N.2.01 On Campus
... no further dates known

Overview

Lecturer
Course title german Partial Differential Equations 1
Type Lecture
Hours per Week 2.0
ECTS credits 4.0
Registrations 11
Organisational unit
Language of instruction English
possible language(s) of the assessment German , English
Course begins on 05.03.2020
eLearning Go to Moodle course

Time and place

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Course Information

Intended learning outcomes

Partielle Differentialgleichungen spielen eine wesentliche und tatsächlich dominante Rolle bei der Modellierung von Phänomenen in Anwendungen, die von den Ingenieurwissenschaften über Physik, Biologie und Medizin bis hin zu Sozial- und Wirtschaftswissenschaften reichen. In deisem Sinne werden sie oft als die lingua franca der Angewandten Mathematik bezeichnet.

Nach erfolgreicher Absolvierung dieser LV kennen Studierende Methoden und die dazugehörigen theoretischen Resultate über partielle Differentialgleichungen. Sie verstehen diese, können die Sätze beweisen und die Methoden anwenden.

Teaching methodology including the use of eLearning tools

Vortrag

Course content

Grundbegriffe

Vier wichtige partielle Differentialgleichungen

Explizite Lösungsmethoden

Theorie linearer elliptischer, parabolischer und hyperbolischer Differentialgleichungen

Literature

Lawrence C. Evans: Partial Differential Equations, American Mathematical Society, 1998

Vorlesungsskriptum im moodle

Intended learning outcomes

Partial differential equations play a crucial and actually dominant role for modeling phenomena in applications, ranging from engineering  via pyhisics, biology and medicine to social and economic sciences. In this sense, they are often characterized as the lingua franca of applied mathematics.

After successful completion of this course, students will know methods and corresponding theoretical results on partial differential equations. They will understand and will be able to prove these theorems and will be able to apply these methods.

Teaching methodology including the use of eLearning tools

lecture

Course content

fundamentals

four important PDEs

explicit solution methods

analysis of linear elliptic, parabolic, and hyperbolic PDEs

Literature

Lawrence C. Evans: Partial Differential Equations

lecture notes in moodle

Examination information

Im Fall von online durchgeführten Prüfungen sind die Standards zu beachten, die die technischen Geräte der Studierenden erfüllen müssen, um an diesen Prüfungen teilnehmen zu können.

Modified examination information (exceptional COVID-19 provisions)

During the exceptional situation due to the COVID-19 pandemic, exams are held online (via BigBlueButton) at https://classroom.aau.at/b/bka-3nh-a2g according to the guidelines https://www.aau.at/corona/pruefungen 

Examination methodology

Mündliche Prüfung (typischerweise 30-45 Minuten)

Examination topic(s)

Inhalt der Vorlesung

Assessment criteria / Standards of assessment for examinations

Bei der Beurteilung der mündlichen Prüfung wird auf

  • die Kenntnis der Methoden, Definitionen und Resultate
  • die gute Erklärung der entsprechenden Beweise und Herleitungen

Wert gelegt.

Examination methodology

Oral exam (approx. 30-45 minutes).

Examination topic(s)

contents of the lecture

Assessment criteria / Standards of assessment for examinations

The assessment of the oral exam relies on

  • knowledge of the methods, definitions and results;
  • good explanation of the correspoding proofs and derivations.

Grading scheme

Grade / Grade grading scheme

Position in the curriculum

  • Thematic Doctoral Programme Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (SKZ: ---, Version: 16W.1)
    • Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems (Compulsory subject)
      • Modeling-Analysis - Optimization of discrete, continuous and stochastic systems ( 0.0h XX / 0.0 ECTS)
        • 312.220 Partial Differential Equations 1 (2.0h VO / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Analysis (Compulsory elective)
      • 4.7 Partial Differential Equations 1 ( 2.0h VO / 4.0 ECTS)
        • 312.220 Partial Differential Equations 1 (2.0h VO / 4.0 ECTS)
  • Masterstudium Mathematics (SKZ: 401, Version: 18W.1)
    • Subject: Applied Mathematics (Compulsory elective)
      • Lehrveranstaltungen aus den Vertiefungsfächern ( 0.0h XX / 12.0 ECTS)
        • 312.220 Partial Differential Equations 1 (2.0h VO / 4.0 ECTS)
  • Master's degree programme Technical Mathematics (SKZ: 401, Version: 13W.1)
    • Subject: Analysis (Compulsory subject)
      • Partielle Differentialgleichungen 1 ( 2.0h VU / 3.0 ECTS)
        • 312.220 Partial Differential Equations 1 (2.0h VO / 4.0 ECTS)
  • Doctoral programme Doctoral programme in Technical Sciences (SKZ: 786, Version: 12W.4)
    • Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums (Compulsory subject)
      • Studienleistungen gem. § 3 Abs. 2a des Curriculums ( 16.0h XX / 32.0 ECTS)
        • 312.220 Partial Differential Equations 1 (2.0h VO / 4.0 ECTS)

Equivalent courses for counting the examination attempts

Sommersemester 2022
  • 312.220 VO Partial Differential Equations 1 (2.0h / 4.0ECTS)
Sommersemester 2019
  • 312.220 VO Partial Differential Equations 1 (2.0h / 4.0ECTS)