FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 440 | Course Introduction and Application Information

Course Name
Numerical Solutions of Partial Differential Equations
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 440
Fall/Spring
3
0
3
6

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives This course focus on numerical techniques for finding solutions to hyperbolic, parabolic, and elliptical partial differential equations by examining the problems of compressible, heat, and incompressible flow.
Learning Outcomes The students who succeeded in this course;
  • will be able to understand basic finite difference methods for partial differential equations.
  • will be able to solve numerically any given linear or nonlinear partial differential equation.
  • will be able to discuss the concepts of consistency, stability and convergence.
  • will be able to solve partial differential equations by using a computer program (C, C , Fortran, Matlab).
  • will be able to discuss the consistency, convergence and stability for schemes.
  • will be able to do error analysis.
Course Description This course focuses on the fundamentals of modern and classical numerical techniques for linear and nonlinear partial differential equations, with application to a wide variety of problems in science, engineering and other fields. The course covers the basic theory of scheme consistency, convergence and stability and various numerical methods.

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Finite difference approximations to derivatives "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 2.1
2 Parabolic equations, local truncation error "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 2.2, 2.3
3 Consistency, convergence "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 , Section 2.4,2.5
4 Stability, the Crank-Nicholson implicit method "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 2.6,2.7
5 Hyperbolic equations in one space dimension: The CFL condition, error analysis of the upwind scheme "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 4.2, 4.3
6 Fourier analysis of the upwind scheme "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 4.4
7 The Lax-wedroff scheme, the leap-frog scheme "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 4.5,4.7
8 Midterm
9 The finite difference mesh and approximations "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 5.2,5.3
10 Stability "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 5.5
11 Linear second order elliptic equations in two dimensions: The general diffusion equation "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 6.3
12 Boundary conditions on a curved boundary "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 6.4
13 Error analysis "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 6.5
14 Error analysis "Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259 Section 6.5
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

"Numerical Solution of Partial Differential Equations" by K.W. Morton, D.F. Mayers, Cambridge University Press, 1999. ISBN-13: 978-3540761259  

Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
10
30
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
11
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
3
42
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
10
3
30
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
27
27
Final Exam
1
33
33
    Total
180

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.

X
2

To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.

X
3

To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.

X
4

To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.

5

To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.

6

To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.

7

To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.

X
8

To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.

9

To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.

10

To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.

11

To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.

12

To be able to speak a second foreign language at a medium level of fluency efficiently.

13

To be able to relate the knowledge accumulated throughout the human history to their field of expertise.

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

 


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