Department of Information & Communication Systems Engineering
University of the Aegean
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 
 
Additional References
  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

 
Assessment/Grading Methods

Ατομικές εργασίες, τελική γραπτή εξέταση.

Activity Semester workload
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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