Information Package / Course Catalogue
Partial Differential Equations
Course Code: MAT322
Course Type: Area Elective
Couse Group: First Cycle (Bachelor's Degree)
Education Language: Turkish
Work Placement: N/A
Theory: 2
Prt.: 2
Credit: 3
Lab: 0
ECTS: 5
Objectives of the Course

Providing a foundational knowledge about partial differential equations (PDEs), classification of PDEs, emergence of initial value, boundary value problems and initial boundary value problems. Developing students’ understandings of the solution methods of partial differential equations

Course Content

Introduction to Partial Differential Equations (PDEs), and classifications of PDEs, First order linear PDEs, high order linear PDEs, homogeneous and nonhomogeneous high order PDEs with constant coefficents, second order linear PDEs with variable coeffients.

Name of Lecturer(s)
Learning Outcomes
1.To gain the ability of defining, classifying and obtaining partial differential equations
2.To be able to find the general solutions of first order linear, quasi linear and nonlinear PDEs, and to solve the Cauchy problems for these equations by the method of characteristics or the general solutions
3.To be able to classify and solve second order linear PDEs using canonical forms
4.To be able to classify high order linear and quasi linear PDEs, and to reduce PDEs to canonical form
5.To be able to gain the skill of interpreting some interrelations among these concepts
Recommended or Required Reading
1.Partial Differential Equations, Duchateau P. and Zachmann D.W., Mcgraw-Hill, Schaum’s Outline series, 1986.
2.Erich Zauderer, Partial Differential Equations of Applied Mathematics,1989.
3.Türevli denklemler (Equations with Derivations), K.Koca, Gündüz Eğitim ve Yayıncılık 2001
Weekly Detailed Course Contents
Week 1 - Theoretical & Practice
Definition and classifications of PDEs, some examples of PDEs of pyhsical problems, initial and boundary value problems
Week 2 - Theoretical & Practice
Obtaining partial differential equations, tangent planes
Week 3 - Theoretical & Practice
First order linear PDEs, Langrange methods and the generalization of the Langrange method
Week 4 - Theoretical & Practice
Obtaining the surface integral over a given curve
Week 5 - Theoretical & Practice
First order nonlinear PDEs, Charpit Methods
Week 6 - Theoretical & Practice
Special types of first order nonlinear PDEs
Week 7 - Theoretical & Practice
Nonlinear PDEs which are convertable to standard forms
Week 8 - Theoretical & Practice
Second order linear PDEs with constant coefficients, Midterm Exam
Week 9 - Theoretical & Practice
Repetitive factorization of operators
Week 10 - Theoretical & Practice
Generalizations of PDEs with constant coefficients, irreducible equations
Week 11 - Theoretical & Practice
Euler equation, Nonhomogeneous linear PDEs, finding special solutions
Week 12 - Theoretical & Practice
Euler equation, Nonhomogeneous linear PDEs, finding special solutions
Week 13 - Theoretical & Practice
Classification of second order quasi linear PDEs, Reducing to canonical form
Week 14 - Theoretical & Practice
Some special cases of second order linear PDEs with variable coefficients
Week 15 - Final Exam
Final Exam
Assessment Methods and Criteria
Type of AssessmentCountPercent
Midterm Examination1%40
Final Examination1%60
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory140228
Lecture - Practice140228
Individual Work140228
Midterm Examination118119
Final Examination120121
TOTAL WORKLOAD (hours)124
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
PÇ-10
PÇ-11
PÇ-12
PÇ-13
PÇ-14
PÇ-15
PÇ-16
PÇ-17
PÇ-18
OÇ-1
3
4
2
3
4
4
2
3
4
2
2
2
OÇ-2
4
2
4
4
4
3
4
4
3
3
3
OÇ-3
2
4
2
5
4
4
2
4
4
4
3
3
OÇ-4
3
4
3
4
4
4
2
4
4
4
3
4
OÇ-5
Adnan Menderes University - Information Package / Course Catalogue
2026