Numerical Analysis
| Title | ΑΡΙΘΜΗΤΙΚΗ ΑΝΑΛΥΣΗ / Numerical Analysis |
| Code | 0402 |
| Faculty | Sciences |
| School | Mathematics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter/Spring |
| Common | No |
| Status | Active |
| Course ID | 40000481 |
Programme of Study: UPS of School of Mathematics (2014-today)
Registered students: 430
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| Core | Compulsory Course | 5 | 3 | 5.5 |
| Academic Year | 2020 – 2021 |
| Class Period | Winter |
| Instructors from Other Categories | |
| Weekly Hours | 3 |
| Class ID | 600166628
|
| Section | Instructors |
|---|---|
| 1. ΤΜΗΜΑ Α | Aikaterini Chatzifoteinou |
| 2. ΤΜΗΜΑ Β | Aikaterini Chatzifoteinou |
| 3. ΕΡΓΑΣΤΗΡΙΟ | Aikaterini Chatzifoteinou |
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600166628
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=11198
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
Required Courses
- 0102 Introduction to Algebra
- 0201 Calculus I
- 0202 Calculus II
- 0430 Introduction to Computer Programming
General Prerequisites
Calculus, Linear Algebra, Computer Programming
Learning Outcomes
After having successfully completed the course, the students will be able to:
• calculate the error in representing numbers in computer memory and in computer arithmetic
• use numerical methods to calculate the values of polynomials and the solution of equations
• perform numerical differentiation and integration
• approximate functions and estimate the approximation error
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
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
Errors - Number systems and number representation - Floating point arithmetic – Evaluation of polynomials - Interpolation and approximation with difference methods - Interpolation by Lagrange, Newton and Hermite polynomials - Error analysis – Numerical differentiation - Numerical integration by rectangle, midpoint, trapezoid, corrected trapezoid, Simpson, Richardson and Romberg methods - Numerical solution of non-linear equations by methods of bisection, Regula-falsi, Newton-Raphson and secant. The fixed point iteration method. Convergence criteria.
Keywords
Errors, Machine representation, Polynomials, Interpolation, Numerical Differentiation, Numerical integration, Numerical solution of equations
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)
Αριθμητική Ανάλυση, Μ. Χ. Γουσίδου-Κουτίτα, επανέκδοση 2017, Εκδόσεις Κυριακίδη.
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.
Last Update
29-09-2020
