Methods of Applied Mathematics ΙI (EM2): Διαφορά μεταξύ των αναθεωρήσεων
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! Learning outcomes | ! Learning outcomes | ||
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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. | |||
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! General Competences | ! General Competences | ||
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* Adapting to new situations | |||
* Decision-making | |||
* Working independently | |||
* Team work | |||
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Αναθεώρηση της 15:43, 10 Νοεμβρίου 2022
Graduate Courses Outlines - Department of Mathematics
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:
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| General Competences |
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Syllabus
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