Data on the course

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 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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