FACULTY OF ARTS AND SCIENCES

Department of Mathematics

MATH 309 | Course Introduction and Application Information

Course Name
Equations of Mathematical Physics
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 309
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 The aim of this course is to teach the modeling of physical phenomena with differential equations and to analyze the relationship between mathematics and physics.
Learning Outcomes The students who succeeded in this course;
  • will be able to use 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 do numerical analysis of hyperbolic equations.
  • will be able to solve elliptic equations numerically.
Course Description Smoothing of partial differential equations, modeling of displacement equation, wire oscillation and diffusion equations, Fourier transforms and applications, Fourier integral representations, Fourier transform method to wave and heat equation, Fourier cosine and sine transforms, solutions of problems in the semi-infinite range.

 



Course Category

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

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
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" by G.D. Smith, Oxford University Press, U.S.A., 3 Edition, 1986. ISBN-13: 978-0198596509 Chapter 2
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" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 2.1, 2.2, 2.3, 2.4, 2.5
3 Convergence of the explicit scheme, an implicit method, theta method "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Section 2.6, 2.7, 2.8, 2.9
4 A three-time level scheme, more general boundary conditions and linear problems, nonlinear problems "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 2.12, 2.13, 2.16
5 2-D parabolic equation: An explicit method, and ADI method "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Chapter 3
6 Hyperbolic equations in one space dimension: Characteristics, The CFL condition, The Lax-Wendroff scheme "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 4.1, 4.2, 4.3, 4.4. 4.5,4.6
7 The Box scheme, the Leap-Frog scheme "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 4.8, 4.9
8 Midterm
9 Consistency, convergence and stability "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 5.1, 5.2 , 5.3
10 Finite difference approximations, consistency, order of accuracy and convergence, calculating stability conditions "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Sections 5.4, 5.5, 5.6
11 Elliptic equations: Examples "Numerical Solution of Partial Differential Eqautions, Finite Difference Methods" by G.D. Smith, Oxford University Press, U.S.A., 3 Edition, 1986. ISBN-13: 978-0198596509 Chapter 5
12 The general diffusion equation, convection-diffusion problems "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Section 6.7,6.8, 6.9
13 Finite difference method solutions "Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933 Chapter 5
14 Boundary conditions on a curved boundary "Numerical Solution of Partial Differential Eqautions, Finite Difference Methods" by G.D. Smith, Oxford University Press, U.S.A., 3 Edition, 1986. ISBN-13: 978-0198596509 Chapter 5
15 Semester Review
16 Final Exam

 

Course Notes/Textbooks

"Numerical Solutions of Partial Differential Equations: An Introduction" by K.W. Morton and D.F. Mayers, Cambridge University Press, 2nd Edition, 2005. ISBN-13: 978-0521607933

"Numerical Solution of Partial Differential Eqautions, Finite Difference Methods" by G.D. Smith,  Oxford University Press, U.S.A., 3 Edition, 1986. ISBN-13: 978-0198596509

Suggested Readings/Materials

 

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 Exams
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
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
0
Presentation / Jury
0
Project
2
20
40
Seminar / Workshop
0
Oral Exam
0
Midterms
1
20
20
Final Exam
1
30
30
    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.

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.

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.

X
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.

X
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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