Undergraduate Courses Outlines - Department of Mathematics
General
School
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School of Science
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Academic Unit
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Department of Mathematics
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Level of Studies
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Undergraduate
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Course Code
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MAE848
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Semester
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8
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Course Title
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Scientific Computing
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Independent Teaching Activities
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Lectures (Weekly Teaching Hours: 3, Credits: 6)
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Course Type
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Special Background
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Prerequisite Courses
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-
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Language of Instruction and Examinations
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Greek
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Is the Course Offered to Erasmus Students
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Yes (in English)
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Course Website (URL)
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See eCourse, the Learning Management System maintained by the University of Ioannina.
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Learning Outcomes
Learning outcomes
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In most scientific disciplines, the integration of computers has defined new directions to perform research and has offered unprecedented potential to solve complicated problems. Combined with theory and experimentation, computational analysis is nowadays considered an integral part of science and research.
The main objective of the course is to familiarize the student with computational techniques that find application in the solution of ordinary and partial differential equations. In the context of this laboratory course, the student will gain access to the programming languages Matlab/Octave and Python, which are widely used to perform scientific calculations. Computational methods to be developed and implemented in PCs will significantly increase the skills and prospects of integrating graduates into the modern scientific and work environment. Starting from the mathematical modeling of problems of Mechanics and Applied Mathematics in general, and by synthesizing information from numerical analysis and numerical solution of ordinary and partial differential equations, students will acquire crucial knowledge in solving mathematical problems by computational means.
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Specifically, the objectives of the course are:
- Familiarity with the Matlab/Octave and Python programming languages to implement numerical methods, solve mathematical problems and graphically design the numerical results
- Apply numerical derivation using the Finite Difference method
- Analysis of the numerical schemes resulting from the Finite Difference method
- Solving ordinary differential equations using one-step and multi-step methods
- Solving parabolic and elliptic Partial Differential Equations with the Finite Difference Method
- Theoretical analysis of the Finite Element method
- Solving parabolic and elliptic Partial Differential Equations with the Finite Element method.
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General Competences
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The course aims to enable the student to:
- Search, analyze and synthesize data and information, using the available technologies
- Work autonomously
- Work in a team
- Promote free, creative and inductive thinking.
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Syllabus
- Initial Value Problems
- Boundary Value Problems
- Finite Difference method
- Equations of Difference
- Shooting methods and Method of undetermined coefficients
- One-step Methods (Euler, Taylor, Runge-Kutta)
- Multi-step Methods (Adams-Bashforth, Adams-Moulton, Predictor-Corrector)
- Finite Element Method (Galerkin).
Teaching and Learning Methods - Evaluation
Delivery
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In the laboratory
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Use of Information and Communications Technology
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Use of scientific computing software packages
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Teaching Methods
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Activity
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Semester Workload
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Lectures
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39
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Study of bibliography
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39
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Laboratory exercises
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39
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Home exercises (project)
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33
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Course total
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150
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Student Performance Evaluation
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- Weekly assignments
- Final project
- Written examination at the end of the semester
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Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
Πρότυπο:MAE848-Biblio