Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT661 - MATHEMATICS (DOCTORATE DEGREE)

Code: MAT661 Course Title: FINITE DIFFERENCE METHODS I Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Fall Semester
Level of Course 3rd Cycle Degree Programme
Type of Course Optional
Department MATHEMATICS (DOCTORATE DEGREE)
Pre-requisities and Co-requisites None
Mode of Delivery Face to Face
Teaching Period 14 Weeks
Name of Lecturer SEYDİ BATTAL GAZİ KARAKOÇ (sbgkarakoc@nevsehir.edu.tr)
Name of Lecturer(s) SEYDİ BATTAL GAZİ KARAKOÇ,
Language of Instruction Turkish
Work Placement(s) None
Objectives of the Course

Learning Outcomes PO MME
The students who succeeded in this course:
LO-1 Find the solutions of the partial differential equations with finite difference approaches and make theirs convergence,consistence and stability analysis. PO-1 Students can design an original issue and explore new, different and / or comprehend complex issues.
PO-2 Students will understand all aspects of mathematics and deepen the knowledge level that can innovate in this field.
PO-4 At least one foreign language at an advanced level counterparts in written, oral and visual communicate and participate in academic discussions.
 		Examination
Performance Project
PO: Programme Outcomes
MME:Method of measurement & Evaluation

Course Contents
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 Introduction to Finite Differences, Fundamental definitions and theorems, Classification of Partial Dif. Equations Oral expression,question and answer, solving problem
2 Boundary and Initial Conditions for One-dimensional Problems Vector and Matrix Norms Oral expression,question and answer, solving problem
3 A Limit for Spectral Radius 1. Gerschgorin's Theorem Oral expression,question and answer, solving problem
4 Gerschgorin Circle Theorem Difference Equations Oral expression,question and answer, solving problem
5 Eigenvalues ​​of a triple band matrix Finite difference approximations for 1st order derivatives Oral expression,question and answer, solving problem
6 Fourier Analysis Oral expression,question and answer, solving problem
7 Finite difference representation of the time-dependent heat conduction equation Explicit Method Oral expression,question and answer, solving problem
8 mid-term exam
9 Neumann Boundary Condition Heat Conduction Equation for Explicit Method Oral expression,question and answer, solving problem
10 Robin Boundary Condition Heat Conduction Equation for Explicit Method Oral expression,question and answer, solving problem
11 Implicit Method Neumann Boundary Condition Heat Conduction Equation for Implicit Method Oral expression,question and answer, solving problem
12 Robin Boundary Condition Heat Conduction Equation for Implicit Method Oral expression,question and answer, solving problem
13 Crank-Nicolson Finite Difference Method Neumann Boundary Condition Heat Conduction Equation for Crank-Nicolson Finite Difference Method Oral expression,question and answer, solving problem
14 Robin Boundary Condition Heat Conduction Equation for Crank-Nicolson Finite Difference Method Oral expression,question and answer, solving problem
15 Stability Analysis for Classical Finite Difference Methods Oral expression,question and answer, solving problem
16 final exam
Recommend Course Book / Supplementary Book/Reading
1 1. G. D. Smith “Numericel solution of partial differential equations” (Clarendon press-Oxford 1985).
2 2. D. M. Causon, C. G. Mingham “Introductory Finite Difference Methods for PDEs” (Ventus Publishing ApS, 2010)
3 3. P. G. Ciarlet, Jacques Louis Lions , Philippe G. Ciarlet , "Handbook of Numerical Analysis: Finite Difference Methods” (North-Holland March 1990).
Required Course instruments and materials
The books of lecture

Assessment Methods
Type of Assessment Week Hours Weight(%)
mid-term exam 8 2 40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam 16 2 60

Student Work Load
Type of Work Weekly Hours Number of Weeks Work Load
Weekly Course Hours (Theoretical+Practice) 3 14 42
Outside Class
       a) Reading 3 14 42
       b) Search in internet/Library 2 7 14
       c) Performance Project 2 8 16
       d) Prepare a workshop/Presentation/Report 0
       e) Term paper/Project 0
Oral Examination 0
Quiz 0
Laboratory exam 0
Own study for mid-term exam 3 8 24
mid-term exam 2 1 2
Own study for final exam 3 15 45
final exam 2 1 2
0
0
Total work load; 187