Courses list

Wersja polska

Course code: IBN20251o14
Semester: 2014/2015 winter
Name: Mathematics
Major: Civil Engineering
Study Type: second cycle
Course type: compulsory
Study Semester: 1
ECTS points: 3
Hours (Lectures / Tutorials / Other): 9 / 9 / 0
Lecturer: dr Zbigniew Jurzyk
Language of instruction: Polish


Learning outcomes: Knowledge: Student • has knowledge about ordinary differential equations of 1st and 2nd order • understands and distinguishes initial and boundary conditions • has basic knowledge on systems of ordinary differential equations • knows about partial differential equations and their classification (hyperbolic, parabolic, elliptic equations) • knows applications of differential equations in technical sciences • knows concept of trigonometric series • knows the Euler-Fourier formulae and expansion of selected functions into the Fourier series • knows elements of variational calculus, including the Euler theorem • knows definition of tensor, its properties and fields of its applications Skills: • can solve typical ordinary differential equations of 1st and 2nd order • can solve initial and boundary value problems for specified ODE • can describe spmple engineering problems using ordinary differential equations and its systems • can solve partial differential equations of hyperbolic, parabolic and elliptic type • can state typical initial- and initial-boundary value problems for PDE • can expand some function into Fourier series • can apply the Euler principle in variational calculus • can use tensor calculus methods

Competences: • Student is aware of applying differential equations methods to problems in technical and natural sciences

Prerequisites: differential and integral calculus of single variable ant their applications, function of two real variables; partial derivatives

Course content: • Ordinary differential equations of 1st and 2nd order: definitions, properties and solution methods. • Solving systems of ordinary differential equations. • Applications of ODE in technical sciences. • Stating typical initial and initial-boundary value problems. • Trigonometric series. • Fourier transformation and Fourier series. • Elements of variational calculus. • Elements of tensor calculus.

Recommended literature: 1. M. Gewert, Z. Skoczylas, Równania różniczkowe zwyczajne, Oficyna Wydawnicza GiS, Wrocław 2008 2. W. Krysicki, L. Włodarski. Analiza matematyczna w zadaniach cz.2, PWN Warszawa 2006 3. M.M.Smirnow. Zadania z równań różniczkowych cząstkowych, PWN Warszawa 1974 4. L.S. Pontriagin. Równania różniczkowe zwyczajne, PWN Warszawa 1964 5. Goering, Elementarne metody rozwiązywania równań różniczkowych, PWN Warszawa 1967

Assessment methods: 3 tests + one essay.

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