MATH 536 | Course Introduction and Application Information - Applied Mathematics and Statistics – With Thesis

Course Name

Numerical Methods for Partial Differential Equations Using Programming Languages

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 536	Fall/Spring	3	0	3	7.5

Prerequisites	None
Course Language	English
Course Type	Elective
Course Level	Second Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Problem Solving Lecture / Presentation
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Doç. Dr. Sevin GÜMGÜM
Assistant(s)	Arş.Gör. Merve KAHRAMAN ARİMAN

Course Objectives	The aim of this course is to introduce numerical techniques to solve hyperbolic, parabolic, and elliptic partial differential equations that arise in compressible flow, heat transfer, and incompressible flow problems.
Learning Outcomes	The students who succeeded in this course; Apply basic finite difference methods for partial differential equations. Solve numerically any given linear or nonlinear partial differential equation. Discuss the concepts of consistency, stability and convergence. Solve partial differential equations by using a computer program Discuss the consistency, convergence and stability for schemes. Determine the convergence order of numerical schemes through 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.
Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Finite difference approximations to derivatives; Numerical Derivatives with MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press. (Chapter 1, Sections 1.1-1.4), (Chapter 2, Section 2.1)
2	Parabolic equations, Evaluation of the local truncation error in MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Sections 2.2-2.3)
3	Consistency, convergence	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press. (Chapter 2, Sections 2.4-2.5), (Chapter 5, Section 5.1)
4	The Crank-Nicholson implicit method with MATLAB/Mathematica Applications	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 5, Sections 5.2-5.4)
5	Hyperbolic equations in one space dimension: The CFL condition, error analysis of the upwind scheme	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 5, Sections 5.5-5.7)
6	Fourier analysis of the upwind scheme	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 5, Section 5.8)
7	The Lax-wendroff scheme, the leap-frog scheme with Applications in MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 5, Sections 5.9-5.11)
8	The finite difference mesh and approximations	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Sections 2.6-2.8)
9	The finite difference mesh and approximations	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Sections 2.6-2.8)
10	Stability	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 4)
11	Linear second order elliptic equations in two dimensions: The general diffusion equation with Applications in MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Sections 2.6-2.8)
12	Boundary conditions on a curved boundary	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Section 2.9), (Chapter 6, Section 6.2)
13	Error analysis with Applications in MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Section 2.10), (Chapter 5, Section 5.13)
14	Error analysis with Applications in MATLAB/Mathematica	Mazumder S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods. Academic Press (Chapter 2, Section 2.10), (Chapter 5, Section 5.14), Chapter 8
15	Semester Review
16	Final Exam

Course Notes/Textbooks

Mazumder, S. (2016). Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods, Academic Press. ISBN-13: 978-0128498941

Suggested Readings/Materials

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

LeVeque, R.J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems. SIAM. ISBN-13: 978-0898716290

Li, J. and Chen, Y.-T. (2019). Computational Partial Differential Equations Using MATLAB, 2nd ed., Taylor & Francis/CRC Press. ISBN 978-0-367-21774-7

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments	1	10
Presentation / Jury	1	20
Project	1	20
Seminar / Workshop
Oral Exams
Midterm
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

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	5	70
Field Work			0
Quizzes / Studio Critiques			0
Portfolio			0
Homework / Assignments	1	10	10
Presentation / Jury	1	20	20
Project	1	33	33
Seminar / Workshop			0
Oral Exam			0
Midterms			0
Final Exam	1	44	44
		Total	225

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Program Competencies/Outcomes

* Contribution Level

1

2

3

4

5

1

To be able to demonstrate independent and critical thinking in Applied Mathematics and Statistics.

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X

-

2

To be able to define problems in Applied Mathematics/Statistics and verify whether they are mathematically/statistically consistent.

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X

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3

To be able to analyse and solve real life problems using applied methods and interdisciplinary approach of Mathematics/Statistics.

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X

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4

To be able to independently conduct, conclude, and report on specialized research in Applied Mathematics and Statistics.

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X

-

5

To be able to efficiently use national and international resources, for staying updated in the field, communicating with colleagues, and following the related literature.

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6

To be able to develop proficiency in using computer software widely utilized in the fields of Applied Mathematics and Statistics.

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X

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7

To be able to evaluate solution processes efficiently using mathematical reasoning and modeling in order to contribute to the solutions of social and scientific problems.

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8

To be able to synthesize theoretical frameworks with practical applications through mathematical and statistical methods.

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9

To be able to develop strategies, policies and plans for problems and research areas in Applied Mathematics/Statistics in order to interpret the results and translate them into practice.

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10

To be able to translate key topics, events, and phenomena in Applied Mathematics and Statistics into the context of other scientific disciplines.

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11

To be able to engage in lifelong learning by continuously updating and improving knowledge and skills in Applied Mathematics and Statistics.

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MATH 536 | Course Introduction and Application Information

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

EVALUATION SYSTEM

ECTS / WORKLOAD TABLE

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IZMIR UNIVERSITY OF ECONOMICS GÜZELBAHÇE CAMPUS

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VALUING PEOPLE

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