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 
Scope  5 ECTS cr 


Type  Intermediate Studies 
Discipline  3250 Mathematics 
Type  Course 




Grading  1  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 
Facetoface 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 corequisites 
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, AddisonWesley, 1996 Zill D G and Cullen M R, Differential equations with boundaryvalue problems, Brooks/Cole, 2001. 
Assessment methods and criteria 
Final exam 
Grading 
Fail, 15 
Person responsible 
Valery Serov 
Working life cooperation 
No 

Current and future instruction
No instruction in WebOodi 
Future examinations
No examinations in WebOodi 