11111

COURSE INTRODUCTION AND APPLICATION INFORMATION


umi.fbe.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 define canonical forms.
  • will be able to solve Wellposed and Illposed problems.
  • will be able to define Adjoint operators.
  • will be able to understand D’Alembert Formula and Duhamel principle.
  • will be able to solve Goursat problem for equation with variable coefficient based on characteristics.
  • will be able to solve Cauchy problem for equations with variable coefficients by using Riemann method.
  • will be able to understand Maximum principle for equations with variable coefficients.
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 Variable transformations and characteristics. Classification of equations and canonical forms. Partial differential equations : an introduction by Walter A.Strauss.
2 Initialvalue problems and the concept of classical solution. Wellposed and Ill posed problems. Equations of mathematical physics by A.A. Samarskii.
3 Hadamard example. Adjoint operators. Applied Partial Differential Equations: An Introduction by Alan Jeffrey.
4 Cauchy problem on infinite interval. Dalambert’s Formula and Duhamel principle. Partial Differential Equations with Fourier Series and Boundary Value Problems”  by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall
5 Integral representation of Hyperbolic equation. The solution of Cauchy problem in the region given by characteristics. Partial Differential Equations of Mathematical Physics by Sobolev S.L., Dover, Newyork,1964.
6 Energy method and its physical interpretation. Seperation of variables method for hyperbolic problems on finite intervals. Applied Partial Differential Equations: An Introduction by Alan Jeffrey.
7 The Goursat problem for equation with variable coefficient based on characteristics over data. Successive approximations method. Applied Partial Differential Equations: An Introduction by Alan Jeffrey.
8 Cauchy problem for equation with variable coefficients: Riemann method. Equations of mathematical physics by A.A. Samarskii.
9 Maximum principle for equation with variable coefficients. Equations of mathematical physics by A.A. Samarskii.
10 Results of maximum principle. Cauchy problem in infinite interval. Partial differential equations : an introduction by Walter A.Strauss.
11 Parabolic problems in semi infinite region. Harmonic functions and their properties. Partial differential equations : an introduction by Walter A.Strauss.
12 Maximum principle. Partial differential equations : an introduction by Walter A.Strauss.
13 Green function and fundamental solution. Partial Differential Equations with Fourier Series and Boundary Value Problems”  by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall
14 Inner and outer boundary value problems for Poisson and laplace equations. Partial Differential Equations with Fourier Series and Boundary Value Problems”  by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall
15 Seperation of variables and Fourier method for Laplace operator. Partial Differential Equations with Fourier Series and Boundary Value Problems”  by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall
16 Review. Partial Differential Equations with Fourier Series and Boundary Value Problems”  by Nakhle H. Asmar. 2nd Edition, 2005, PearsonPrentice Hall
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials None

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
40
Final Exam
1
60
Total

Weighting of Semester Activities on the Final Grade
40
Weighting of End-of-Semester Activities on the Final Grade
60
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
6
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
37
Final Exams
1
50
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

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

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

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

 

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