Computational mathematics
| Title | ΥΠΟΛΟΓΙΣΤΙΚΑ ΜΑΘΗΜΑΤΙΚΑ / Computational mathematics |
| Code | 0431 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 40000483 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 172
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2023 – 2024 |
| Class Period | Spring |
| Faculty Instructors |
|
| Instructors from Other Categories | |
| Weekly Hours | 3 |
| Class ID | 600230627
|
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
- Distance learning
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600230627
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=11392
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
Required Courses
- 0402 Numerical Analysis
- 0201 Calculus I
General Prerequisites
Calculus, Linear Algebra, Computer programming, Numerical Analysis
Learning Outcomes
After having successfully completed the course, the students will be able to:
• approximate functions with piecewise polynomials
• solve linear systems numerically
• apply numerical methods for calculating eigenvalues and eigenvectors of matrices
• solve numerically odes and systems of odes
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Adapt to new situations
- Work autonomously
- Work in teams
- Work in an international context
- Work in an interdisciplinary team
- Design and manage projects
- Advance free, creative and causative thinking
Course Content (Syllabus)
Interpolation and approximation with piecewise polynomials and splines , Numerical linear algebra: Gauss elimination for linear systems pivoting, LU- factorization and an introduction to the stability of systems and algorithms, norms of vectors and matrices, condition number, Iterative methods, Introduction to the numerical solution of eigenvalue-eigenvector problem, Numerical solution of ODEs (existence and uniqueness of initial value problem). Euler method, Taylor method, Runge-Kutta methods and multistep methods. Application in the Computer Lab using the Matlab/Octave programming environment.
Keywords
Piecewise polynomials, Splines, Hermite, Numerical solution of linear systems, Numerical calculation of eigenvalues and eigenvectors, Numerical solution of odes, Numerical solution of systems of odes
Educational Material Types
- Slide presentations
- Video lectures
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Laboratory Teaching
- Use of ICT in Communication with Students
- Use of ICT in Student Assessment
Description
The complete course material is uploaded in elearning in form of slides.
Apart from the three-hour by week theory-lectures, the students are also asked to attend a computer lab-course, for two hours per week. During the Lab-course, small projects are assigned and implemented in Matlab/Octave programming language.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 39 | 1.3 | ✓ | ✓ | |
| Laboratory Work | 40 | 1.3 | ✓ | ||
| Reading Assigment | 83 | 2.8 | ✓ | ✓ | |
| Exams | 3 | 0.1 | ✓ | ✓ | |
| Total | 165 | 5.5 |
Student Assessment
Description
The final grade is the weighted average of the Written Examination (80%) and the participation at the Computer lab with accomplishing various Computer assignments and a final Coursework (20%).
Student Assessment methods
- Written Exam with Short Answer Questions (Formative, Summative)
- Written Exam with Extended Answer Questions (Formative, Summative)
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
- Labortatory Assignment (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Υπολογιστικά Μαθηματικά, Μ. Χ. Γουσίδου-Κουτίτα, 2013, Εκδόσεις Τζιόλα.
Εισαγωγή στην Αριθμητική Ανάλυση, Γ.Δ. Ακρίβης & Β.Α. Δουγαλής, 2017, Πανεπιστημιακές Εκδόσεις Κρήτης.
Αριθμητική Ανάλυση: Εισαγωγή, Μ.Ν. Βραχάτης, 2012, Εκδόσεις Κλειδάριθμος.
Additional bibliography for study
Αριθμητική Ανάλυση με εφαρμογές σε MATHEMATICA και MATLAB,Γ. Παπαγεωργίου & Χ. Τσίτουρας, 2015, Εκδ. Τσότρας.
Αριθμητική ανάλυση- Συνήθεις διαφορικές εξισώσεις, Μ.Ν. Βραχάτης, 2012, Εκδόσεις Κλειδάριθμος.
Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις, Γ.Δ. Ακρίβης, Β.Α. Δουγαλής, 2018 Πανεπιστημιακές Εκδόσεις Κρήτης.
Last Update
27-05-2024
