Methods of Applied Mathematics ΙI (EM2): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
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=== General ===
=== General ===
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|-
|-
! Course Code
! Course Code
| ΧΧΧ
| EM2
|-
|-
! Semester
! Semester
| 000
| 2
|-
|-
! Course Title
! Course Title
| ΧΧΧ
| Methods of Applied Mathematics ΙI
|-
|-
! Independent Teaching Activities
! Independent Teaching Activities
Γραμμή 27: Γραμμή 29:
|-
|-
! Course Type
! Course Type
| General Background
| Special Background
|-
|-
! Prerequisite Courses
! Prerequisite Courses
Γραμμή 34: Γραμμή 36:
! Language of Instruction and Examinations
! Language of Instruction and Examinations
|
|
ΧΧΧ
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
|
|
ΧΧΧ
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
|
|
ΧΧΧ
* Adapting to new situations
* Decision-making
* Working independently
* Team work
|}
|}


=== Syllabus ===
=== Syllabus ===


ΧΧΧ
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 ===
Γραμμή 66: Γραμμή 77:
! Delivery
! Delivery
|
|
ΧΧΧ
In class
|-
|-
! Use of Information and Communications Technology
! Use of Information and Communications Technology
|
|
ΧΧΧ
Use of computer (Mechanics) lab
|-
|-
! Teaching Methods
! Teaching Methods
Γραμμή 81: Γραμμή 92:
| 39
| 39
|-
|-
| ΧΧΧ
| Self study
| 000
| 78
|-
|-
| ΧΧΧ
| Homework - Projects
| 000
| 70.50
|-
|-
| Course total  
| Course total  
Γραμμή 93: Γραμμή 104:
! Student Performance Evaluation
! Student Performance Evaluation
|
|
ΧΧΧ
* Weekly assignments
* Final project
|}
|}


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Τελευταία αναθεώρηση της 05:15, 16 Ιουνίου 2023

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:

  • 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
  • Adapting to new situations
  • Decision-making
  • Working independently
  • Team work

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
Activity Semester Workload
Lectures 39
Self study 78
Homework - Projects 70.50
Course total 187.5
Student Performance Evaluation
  • Weekly assignments
  • Final project

Attached Bibliography

  • Εφαρμοσμένα Μαθηματικά, Logan D.J. Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 1η έκδοση, 2010.
  • Perturbation Methods, A.H. Nayfeh, 1η έκδοση, Willey-VCH, 2000.