TR
11111

COURSE INTRODUCTION AND APPLICATION INFORMATION

dm.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall/Spring
Prerequisites
None
Course Language
Course Type
Elective
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be able to apply finite-difference methods to approximation of derivatives
  • will be able to model a problem consisting of a parabolic equation in 1-D and 2-D
  • will be able to solve the model problem using various numerical techniques
  • will be able to solve hyperbolic equations using numerical techniques
  • will be able to solve elliptic equations numerically
Course Description

 



Course Category

 Core Courses
Major Area Courses
Supportive Courses
X
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Introduction and Finite Difference Formulae: Descriptive treatment of parabolic, elliptic and hyperbolic equations, Finite-difference approximations to derivatives Numerical Solution of Partial Differential Eqautions, Finite Difference Methods, G.D. Smith, 3 rd Edition.
2 Parabolic equations in one space variable: a model problem, an explicit scheme for the model problem, difference notation and truncation error Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
3 Convergence of the explicit scheme, an implicit method, theta method Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
4 A three-time level scheme, more general boundary conditions and linear problems, nonlinear problems Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
5 2-D parabolic equation: An explicit method, and ADI method Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
6 Hyperbolic equations in one space dimension: Characteristics, The CFL condition, The Lax-Wendroff scheme Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
7 The box scheme, the leap-frog scheme Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
8 Midterm
9 Consistency, convergence and stability Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
10 Finite difference approximations, consistency, order of accuracy and convergence, calculating stability conditions Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
11 Elliptic equations: Examples Numerical Solution of Partial Differential Eqautions, Finite Difference Methods, G.D. Smith, 3 rd Edition.
12 The general diffusion equation, convection-diffusion problems Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
13 Finite difference method solutions Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
14 Boundary conditions on a curved boundary Numerical Solution of Partial Differential Eqautions, Finite Difference Methods, G.D. Smith, 3 rd Edition.
15 Review of semester
16 Review of semester
Course Notes/Textbooks Numerical Solution of Partial Differential Eqautions, Finite Difference Methods, G.D. Smith, 3 rd Edition. // Numerical Solutions of Partial Differential Equations: An Introduction, K.W. Morton and D.F. Mayers, Cambridge University Press, 2005.
Suggested Readings/Materials None

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
2
40
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
30
Total

Weighting of Semester Activities on the Final Grade
3
70
Weighting of End-of-Semester Activities on the Final Grade
1
30
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
1
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
2
15
Seminar / Workshop
Oral Exam
Midterms
1
20
Final Exams
1
25
    Total
138

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
 Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

 X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,
10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

 X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

 X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,
14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,
15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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