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;
|
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. |
Related Sustainable Development Goals |
| Core Courses | |
Major Area Courses | X | |
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
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 |
Semester Activities | Number | Weigthing |
Participation | ||
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 10 | 30 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
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 |
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 | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 10 | 3 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 1 | 27 | |
Final Exams | 1 | 33 | |
Total | 180 |
# | 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