# 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: 451
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course535.5

 Academic Year 2021 – 2022 Class Period Winter Instructors from Other Categories Weekly Hours 3 Class ID 600186988
SectionInstructors
1. ΤΜΗΜΑ ΑAikaterini Chatzifoteinou
2. ΤΜΗΜΑ ΒAikaterini Chatzifoteinou
3. ΕΡΓΑΣΤΗΡΙΟAikaterini Chatzifoteinou
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
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
• 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
Lectures391.3
Laboratory Work401.3
Exams30.1
Total1655.5
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.