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802334A A Second Course in Differential Equations, 5 ECTS cr 
Code 802334A  Validity 01.06.2015 -
Name A Second Course in Differential Equations  Abbreviation A Second Course 
Scope5 ECTS cr   
Type Intermediate Studies Discipline3250 Mathematics 
TypeCourse   
  Grading1 - 5, pass, fail 
 
   
Unit Field of Mathematics 

Description
ECTS Credits 

5 ECTS credits

 
Language of instruction 

Finnish

 
Timing 

2nd year or later, 3rd period

 
Learning outcomes 

On successful completion of this course, the student will be able to:

- apply method of Frobenius to solve second order linear differential equations

- derive and prove the basic properties of Bessel functions, Legendre polynomials and Hermite polynomials

- apply integral transformations to solve some integral equations and ordinary differential equations with constant coefficients

- recognize heat and wave equations and choose the proper method to solve them.

 
Contents 

The course is devoted to second order ordinary differential equations that are important in applications and classical partial differential equations such as heat and wave equations. Method of Frobenius is introduced to solve second order ordinary differential equations. Some special functions (Gamma function and Bessel functions etc.) and also orthogonal polynomials (Legendre and Hermite polynomials) are considered. Basic facts about Fourier series and Fourier transform are given. Laplace transform is discussed at more advanced level than in earlier studies. Separation of variables is introduced as a method to solve certain boundary value problems for heat and wave equations.

 
Mode of delivery 

Face-to-face teaching

 
Learning activities and teaching methods 

Lectures 28 h, exercises 14 h

 
Target group 

Students majoring in mathematics or applied mathematics, physics or engineering students.

 
Prerequisites and co-requisites 

Differential equations, Complex analysis

 
Recommended optional programme components 

-

 
Recommended or required reading 

Lecture notes. Additional reading: Colton D, Partial differential equations, Dover, 1988 Lebedev N N, Special Functions and their applications, Dover, 1972 Nagle R K, Fundamentals of differential equations and boundary value problems, Addison-Wesley, 1996 Zill D G and Cullen M R, Differential equations with boundary-value problems, Brooks/Cole, 2001.

 
Assessment methods and criteria 

Final exam

 
Grading 

Fail, 1-5

 
Person responsible 

Valery Serov

 
Working life cooperation 

No

 


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