312.220 (20S) Partial Differential Equations 1
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
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
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 schemePosition 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)
-
Modeling-Analysis - Optimization of discrete, continuous and stochastic systems (
0.0h XX / 0.0 ECTS)
-
Subject: Modeling-Analysis-Optimization of discrete, continuous and stochastic systems
(Compulsory subject)
- 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)
-
4.7 Partial Differential Equations 1 (
2.0h VO / 4.0 ECTS)
-
Subject: Applied Analysis
(Compulsory elective)
- 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)
-
Lehrveranstaltungen aus den Vertiefungsfächern (
0.0h XX / 12.0 ECTS)
-
Subject: Applied Mathematics
(Compulsory elective)
- 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)
-
Partielle Differentialgleichungen 1 (
2.0h VU / 3.0 ECTS)
-
Subject: Analysis
(Compulsory subject)
- 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)
-
Studienleistungen gem. § 3 Abs. 2a des Curriculums (
16.0h XX / 32.0 ECTS)
-
Subject: Studienleistungen gem. § 3 Abs. 2a des Curriculums
(Compulsory subject)