Department of Information & Communication Systems Engineering
 SCHOOL OF ENGINEERING Department of Information & Communication Systems Engineering
 Information & Communication Systems Security Information Systems Artificial Intelligence Computer & Communication Systems Geometry, Dynamical Systems & Cosmology
Numerical Analysis

 Title: Numerical Analysis Lesson Code: 321-99002 Semester: 7 ECTS: 5 Theory Hours: 3 Lab Hours: Faculty: Fotiadis Georgios

Content outline

Errors, Computer Arithmetic, Error method and algorithm, Linear Systems, Method of Gauss, Gauss-Jordan, factorization LU, Method Choleski, Iterative method of Jacobi, Gauss, Gauss-seidel, SOR, Nonlinear equations and systems, partition method, fixed point, Newton-Raphson, secant, Interpolation and Approximation of Lagrange, Newton, Hermite, functions, spline, Numerical Differentiation and Integration type Lagrange, Taylor, Richardson, rule rectangle, trapezoid, Simpson, type Newton-Cotes, Numerical solution of ordinary differential equations, partial differential equations.

Learning outcomes

The purpose of this course is to provide a complete knowledge of numerical methods for solving problems that appear in Science and Technology.

More precisely the aim of this course is the comprehension of the basic numerical methods for approximating solutions of various mathematical problems using a computer.

Emphasis is also given on the theoretical/mathematical background of these methods for their full comprehension.

After the successful completion of this course, the student should be able to:

• understand the floating point arithmetic and floating point numbers.
• understand, calculate and estimate the error that occurs from approximate solutions of problems.
• approximate solutions of systems of linear and non-linear equations, using basic arithmetic methods.
• approximate solutions of non-linear equations, using basic arithmetic methods.
• describe the behavior of functions in one variable using suitable interpolation polynomials.
• approximate the derivative and the integral functions in one variable, using arithmetic differentiation and integration methods.
• apply basic arithmetic methods for solving simple differential equations.

Prerequisites

Not required.

Basic Textbooks
1. Michael N. Vrahatis, Numerical Analysis
2. Class lectures

1.  Introduction to Numerical Analysis, Akrivis G. D., Dougalis B. A.
2. Numerical Analysis, Nikolaos Misirlis.
3. Numerical Analysis, Sofianos Georgios S., Tychopoulos Evangelos Th.

Learning Activities and Teaching Methods

The course evaluation derives from:

• 3 compulsory exercises during the semester: counting 30% in the final grade.
• final exam: counting 70% in the final grade.

Final Grade = (0.3*M.V. Exercises) + (0.7*Final Exam)

One must have: Final Grade >= 5

Ατομικές εργασίες, τελική γραπτή εξέταση.

Lectures 39 hours

Personal study 83 hours
Final exams 3 hours
Course total 125 hours (5 ECTS)

Language of Instruction
Greek, English (for Erasmus students)

Μode of delivery

Face-to-face.

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