Applied Mathematics II
| Title | ΕΦΑΡΜΟΣΜΕΝΑ ΜΑΘΗΜΑΤΙΚΑ ΙΙ / Applied Mathematics II |
| Code | ΜΑΥ204 |
| Faculty | Sciences |
| School | Physics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Coordinator | Georgios Vougiatzis |
| Common | No |
| Status | Active |
| Course ID | 40002883 |
| Academic Year | 2023 – 2024 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 4 |
| Class ID | 600236238
|
Course Type 2016-2020
- Background
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600236238
- At the Website of the School: http://www.physics.auth.gr/courses/137
- Other: http://users.auth.gr/voyatzis/DIFEQU
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus
Learning Outcomes
The Students will be able to
1. solve first order differential equations using an appropriate method.
2. model simple physical models and study their evolution by using differential equations
3. solve special equations of higher order Differential equations which are related with particular physical models.
4. solve Linear equations/systems.
5. to understand the notion of solution of a partial differential equation and solve 1st order linear equations and some particular linear equations of higher order.
6. τo acquire the ability of developing mathematical tecqniques for modelling, processing and solving problems in physics or other sciencies.
General Competences
- Apply knowledge in practice
- Generate new research ideas
Course Content (Syllabus)
1 Introduction and solution existence theorems
2 Ordinary Differential equations (ODEs) of 1st order (separable,homogeneous, linear, exact, special cases
3 Problems with differential equations of 1st order
4 Special forms of higher order ODEs
5 Linear ODEs, theory of solutions. Linear ODEs with constant coefficients
6 Linear Oscillators - problems
7 Linear systems (2x2) of ODEs with constant coefficients
8 Problems with Linear systems (2x2). Systems with higher dimensions
9 Introductionary concepts of nonlinear systems of ODEs
10 Introduction to partial differential equations (PDEs)
11 Solutions of PDEs of 1st order
12 Linear PDEs of higher order with constant coefficients
Keywords
Differential Equations
Educational Material Types
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 117 | ✓ | |||
| Tutorial | 39 | ||||
| Exams | 3 | ||||
| Problem solving | 21 | ||||
| Total | 180 |
Student Assessment
Student Assessment methods
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ, Βουγιατζής Γεώργιος Β., Μπόζης Γεώργιος Δ.,Παπαδόπουλος Δημήτριος Β. ΕΚΔΟΣΕΙΣ ΚΛΕΙΔΑΡΙΘΜΟΣ 2012
ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, ΘΩΜΑΣ ΚΥΒΕΝΤΙΔΗΣ, ΕΚΔΟΣΕΙΣ ΚΥΒΕΝΤΙΔΗ 2007
ΣΥΝΗΘΕΙΣ ΔΙΑΦΟΡΙΚΕΣ ΕΞΙΣΩΣΕΙΣ, ΤΡΑΧΑΝΑΣ ΣΤΕΦΑΝΟΣ, ΠΑΝΕΠΙΣΤΗΜΙΑΚΕΣ ΕΚΔΟΣΕΙΣ ΚΡΗΤΗΣ, 2008
Additional bibliography for study
R. Bronson "Διαφορικές Εξισώσεις", σειρά Schaum's, Κλειδάριθμος 2007.
M. Tenenbaum and H. Pollard, ORDINARY DIFFERENTIAL EQUATIONS, Dover
Last Update
06-11-2020
