Course Name Code Semester T+U Hours Credit ECTS
Nonlinear Partial Differantial Equations MAT 623 0 3 + 0 3 6
Precondition Courses <p>Recommended course of undergraduate education has received partial differential equations.</p>
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. ÖMER FARUK GÖZÜKIZIL
Course Lecturers
Course Assistants
Course Category
Course Objective

It is useful for graduate students in mathematics and engeneering.

Course Content

Adomian Decomposition Method , Solution of Nonlinear PDEs by Adomian Method, Solution of Nonlinear PDEs Systems by Adomian Method. Linear and Nonlinear Physical Models. The Goursat Problem. The Telegraph Equation .Schrodinger Equation. Fourth-order Parabolic Equation. The Pad´e Approximants. Solitons and Compactons.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 To learn the details of partial differential equations. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
2 To recognize the non-linear partial differential equations. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
3 To learn methods of solution of nonlinear partial differential equations. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
4 To learn the methods of numerical solution of nonlinear partial differential equations. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
5 To learn to linear and nonlinear physical models. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
6 To solve to the Goursat problem, telegraph equation and the Schrodinger equation. Lecture, Question-Answer, Discussion, Drilland Practice, Motivations to Show, Group Study, Self Study, Problem Solving, Testing, Homework, Performance Task,
Week Course Topics Preliminary Preparation
1 Adomian decomposition method.
2 Solution of nonlinear partial differential equations by using adomian method.
3 Solution of nonlinear partial differential equations by using adomian method.
4 Linear and Nonlinear Physical Models.
5 The Goursat Problem.
6 The Telegraph Equation.
7 Schrodinger Equation.
8 Fourth-order Parabolic Equation.
9 Midterm
10 The Pad´e Approximants.
11 The Pad´e Approximants.
12 Solitons
13 Solitons
14 Compactons
Resources
Course Notes
Course Resources

1.Nonlinear Partial Differential Equations for Scientist and Engineers,Debnath L., Boston , 1997.
2. Partial Differential Equations and Solitary Waves Theory, Abdul-Majid Wazwaz,Springer, 2009.

Order Program Outcomes Level of Contribution
1 2 3 4 5
0 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 60
1. Kısa Sınav 20
1. Ödev 20
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Quiz 1 10 10
Assignment 1 10 10
Final examination 1 15 15
Total Workload 151
Total Workload / 25 (Hours) 6.04
dersAKTSKredisi 6