Methods of Applied Mathematics ΙI (EM2): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === | ||
Γραμμή 15: | Γραμμή 17: | ||
|- | |- | ||
! Course Code | ! Course Code | ||
| | | EM2 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 2 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | Methods of Applied Mathematics ΙI | ||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
Γραμμή 27: | Γραμμή 29: | ||
|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
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! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
| | | | ||
Greek | |||
|- | |- | ||
! Is the Course Offered to Erasmus Students | ! Is the Course Offered to Erasmus Students | ||
| Yes | | Yes (in English) | ||
|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
Γραμμή 49: | Γραμμή 51: | ||
! Learning outcomes | ! Learning outcomes | ||
| | | | ||
The course is a first introduction to the basic methods of applied mathematics and particularly in perturbation theory. There are many situations in mathematics where one finds expressions that cannot be calculated with absolute precision, or where exact answers are too complicated to provide useful information. In many of these cases, it is possible to find a relatively simple expression which, in practice, is just as good as the complete, exact solution. The asymptotic analysis deals with methods for finding such approximations and has a wide range of applications, both in the fields of pure mathematics such as combinatorics, probability, number theory and applied mathematics and computer science. The goal of this course is to introduce some of the basic techniques and to apply these methods to a variety of problems. Upon completion of this course students will be able to: | |||
* Recognize the practical value of small or large parameters for calculating mathematical expressions. | |||
* Understand the concept of (divergent) asymptotic series, and distinguish between regular and singular perturbations. | |||
* Find dominant behaviors in algebraic and differential equations with small and large parameters. | |||
* Calculate dominant behavior of integrals with a small parameter. | |||
* Find a (in particular cases) the full asymptotic behavior of integrals. | |||
* Identify the boundary layers in solutions of differential equations, and apply appropriate expansions to calculate the dominant solutions. | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
* Adapting to new situations | |||
* Decision-making | |||
* Working independently | |||
* Team work | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Introduction and notation of perturbation theory, Regular and singular perturbations, Asymptotic expansions of integrals, Asymptotic solutions of linear and nonlinear differential equations, Laplace and Fourier transforms (if time permits). | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
| | | | ||
In class | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | | ||
Use of computer (Mechanics) lab | |||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
Γραμμή 81: | Γραμμή 92: | ||
| 39 | | 39 | ||
|- | |- | ||
| | | Self study | ||
| | | 78 | ||
|- | |- | ||
| | | Homework - Projects | ||
| | | 70.50 | ||
|- | |- | ||
| Course total | | Course total | ||
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! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
* Weekly assignments | |||
* Final project | |||
|} | |} | ||
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General
School | School of Science |
---|---|
Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | EM2 |
Semester | 2 |
Course Title | Methods of Applied Mathematics ΙI |
Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
Course Type | Special Background |
Prerequisite Courses | - |
Language of Instruction and Examinations |
Greek |
Is the Course Offered to Erasmus Students | Yes (in English) |
Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
Learning outcomes |
The course is a first introduction to the basic methods of applied mathematics and particularly in perturbation theory. There are many situations in mathematics where one finds expressions that cannot be calculated with absolute precision, or where exact answers are too complicated to provide useful information. In many of these cases, it is possible to find a relatively simple expression which, in practice, is just as good as the complete, exact solution. The asymptotic analysis deals with methods for finding such approximations and has a wide range of applications, both in the fields of pure mathematics such as combinatorics, probability, number theory and applied mathematics and computer science. The goal of this course is to introduce some of the basic techniques and to apply these methods to a variety of problems. Upon completion of this course students will be able to:
|
---|---|
General Competences |
|
Syllabus
Introduction and notation of perturbation theory, Regular and singular perturbations, Asymptotic expansions of integrals, Asymptotic solutions of linear and nonlinear differential equations, Laplace and Fourier transforms (if time permits).
Teaching and Learning Methods - Evaluation
Delivery |
In class | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology |
Use of computer (Mechanics) lab | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
|
Attached Bibliography
- Εφαρμοσμένα Μαθηματικά, Logan D.J. Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 1η έκδοση, 2010.
- Perturbation Methods, A.H. Nayfeh, 1η έκδοση, Willey-VCH, 2000.