Course details
Mathematical Analysis 2 (international students)
MI2 Acad. year 2003/2004 Summer semester 7 credits
Ordinary differential equations, basic terms, exact methods, systems of linear differential equations, systems with constant coefficients, some numerical methods, examples of differential equation use. Partial differential equations, classifications ot the second-order equations, some principles of solution. Differential calculus in the complex domain, derivative, Caucy-Riemann conditions, holomorphic function. Integral calculus in the complex domain, Cauchy theorem, Caychy formula, Laurent series, singular points, residue theorem. Laplace transform, convolution, Heaviside theorems, applications. Fourier transform, relation to the Laplace transform, practical usage. Z transform, discrete systems, difference equations.
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Subject specific learning outcomes and competences
Studenst will be acquainted with some exact and numerical methods for differential equation solving and with the grounding of technique for formalized soluting by Laplace, Fourier and Z transforms.
Learning objectives
The student is acquainted with some fundamental methods for solving the ordinary and partial differential equations in the first part and with Laplace, Fourier and Z transforms in the other part.
Progress assessment
Tests.