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: 247
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Elective Courses belonging to the selected specialization | Spring | - | 5.5 |
| Academic Year | 2021 – 2022 |
| Class Period | Spring |
| Instructors from Other Categories | |
| Weekly Hours | 3 |
| Class ID | 600187095
|
| Section | Instructors |
|---|---|
| 1. ΕΡΓΑΣΤΗΡΙΟ | Aikaterini Chatzifoteinou |
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600187095
- 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
- 0102 Introduction to Algebra
- 0402 Numerical Analysis
- 0201 Calculus I
- 0202 Calculus II
- 0430 Introduction to Computer Programming
- 0108 Linear Algebra
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.
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
- 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
During the lectures, small projects that have to be implemented in a programming language are assigned to the students
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
Written Examination and computer assignments with oral evaluation
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.
Last Update
29-09-2020
