Syllabus ( MATH 305 )

Basic information


Course title: 
Partial Differential Equations 
Course code: 
MATH 305 
Lecturer: 
Assoc. Prof. Dr. Feray HACIVELİOĞLU

ECTS credits: 
6 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
3, Fall 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Compulsory

Language of instruction: 
English

Mode of delivery: 
Face to face

Pre and corequisites: 
None 
Professional practice: 
No 
Purpose of the course: 
The methods of solutions, applications to engineering and other sciences, Heat and Wave equations, Boundaryvalue problems 



Learning outcomes


Upon successful completion of this course, students will be able to:

Transfer the mathematical applications to engineering and other applied sciences
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Ability to work in interdisciplinary research teams effectively.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Homework assignment

Perceive the solution methods of partial differential equations
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Written exam

Gain the capability of mathematical modeling
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Homework assignment


Contents


Week 1: 
Quasilinear and linear Partial Differential Equations (PDE) of first order 
Week 2: 
Series solutions of PDE, the Cauchy Kovalevskaya theorem 
Week 3: 
Characteristics, classification and caninical forms of linear PDE of second order 
Week 4: 
Conception of the wellposed and illposed boundaryvalue problems 
Week 5: 
Hyperbolic type PDE, Wave equation, energetic inequalities 
Week 6: 
Uniqueness of the solutions of Cauchy problem and mixed problem 
Week 7: 
MIDTERM EXAM I. The D’Alembert, Kirchhoff and Poisson formulas 
Week 8: 
General scheme of Fourier method, application to the mixed problem for onedimensipnal wave equation

Week 9: 
Elliptic type PDE, Helmholtz, Laplace and Poisson equations 
Week 10: 
Uniqueness of the solutions of the interior and exterior boundaryvalue problems for Laplace equation 
Week 11: 
Green’s functions, existence of the solutions of the boundaryvalue problems for Laplace equation 
Week 12: 
MIDTERM EXAM II. Parabolic type PDE, Heat and diffusion equations, Principle of maximum in the bounded domains 
Week 13: 
Existence and uniqueness of the solution for Cauchy problem for heat equation 
Week 14: 
Existence and uniqueness of the solution for mixed problem for heat equation 
Week 15*: 
* 
Week 16*: 
Final Exam 
Textbooks and materials: 

Recommended readings: 
Introduction to Partial Differential Equations with Applications (E.C. Zachmanoglu, D.W,Thoe), Lectures on Partial Differential Equations (I G Petrovsky)


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
7, 12 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 
1, 2, 3, 4, 5, 6, 9, 10, 13, 14 
10 
Quiz: 

0 
Final exam: 
16 
50 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
3 
14 

Practice, Recitation: 
0 
0 

Homework: 
3 
10 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
8 
2 

Midterm: 
4 
2 

Personal studies for final exam: 
8 
1 

Final exam: 
2 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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