DOCTOR LECTURER Ayşe KABATAŞ,ASSOC. PROF. DR. Yasemin SAĞIROĞLU,

Language of instruction

Turkish

Professional practise ( internship )

None

The aim of the course:

This course aims to provide students with general knowledge on formulating problems that arises in applied sciences as mathematical models, solving such models through analytical and qualitative as well as interpreting solutions within the concept of physical problem at hand.

Learning Outcomes

CTPO

TOA

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

LO - 1 :

formulate mathematical models for a variety of problems

1,2

1

LO - 2 :

solve the model using analytical, qualitative and partically some numerical methods,

1,2

1

LO - 3 :

interprate the solution within the concept of the phenomenon being modelled.

1,2

1

LO - 4 :

obtain solution for models studied within the scope of the course

1,2

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Differential equations and basic concepts. Differential equations as mathematical model (Ordinary differential equations, order and degree of differential equations. Derivation of differential equations.) General, particular and singular solutions of the differential equations. Separable, homogenous, exact differential equations and transforming to exact differential equation by using integrating factor. Linear differential equations, Bernoulli differential equation and applications of the first order differential equations(Population model, acceleration-velocity model, temperature problems). Change of variables. Reducible differential equations (single variable and non-linear differential equations). General solution of nth order linear differential equations (linearly independent solutions, superposition principle for the homogeneous equations, particular and general solutions). General solution of nth order constant coefficient homogenous differential equations. Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters). Initial Value Problems (IVP) and Boundary Value Problems (BVP) Physical applications, mechanical vibrations, electrical circuits. Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler differential equation). Reduction of order. Power series solutions of differential equations around ordinary points. Laplace and inverse Laplace transformations. Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations.

Course Syllabus

Week

Subject

Related Notes / Files

Week 1

Differential equations and basic concepts. Differential equations as mathematical model Ordinary differential equations, order and degree of differential equations.

Week 2

Derivation of differential equations. General, particular and singular solutions of the differential equations.

Week 3

Separable, homogenous differential equations,

Week 4

Exact differential equations and transforming to exact differential equation by using integrating factor.

Week 5

Linear differential equations, Bernoulli differential equation, change of variables method

Week 6

Applications: Population model, acceleration-velocity model, temperature problems

Week 7

General solution of nth order linear differential equations (linearly independent solutions, super position principle for the homogeneous equations, particular and general solutions). General solution of nth order constant coefficient homogenous differential equations.

Week 8

Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters)

Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler, differential equation). Reduction of order method.

Week 12

Power series solutions of differential equations around ordinary points.

Week 13

Laplace and inverse Laplace transformations.

Week 14

Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations.

Week 15

Review

Week 16

Final exam

Textbook / Material

1

Edwards, C.H., Penney, D.E. (Çeviri Ed. Akın, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara.

2

Edwards, C.H., Penney, D.E. (Çeviri Ed. Akın, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara.

Recommended Reading

1

Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.

2

Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.

3

Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.

4

Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.

5

Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.

6

Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.

7

Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.

8

Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.

9

Spiegel, M.R. 1965; Theory and Problems of Laplace Transforms, McGraw-Hill Book company, New York.

10

Spiegel, M.R. 1965; Theory and Problems of Laplace Transforms, McGraw-Hill Book company, New York.