Course detail
Mathematics II
FCH-BAT_MAT2Acad. year: 2009/2010
Metric spaces, fix point theorem, the simple iteration method. Implicitely given functions and the geometrical meaning. Ordinary differential equations (ODE). First-order ODE's and linear higher-order order ODE's with constant coefficients. The numerical method of nets. Double and triple integrals, transformation theorem ans some important transformations, e.g. polar and spherical ones. Elementary information on curves. Elements of the field theory (Hamilton operator and its meaning, elementary kinds of fields). Curve and surface integrals, geometrical and physical applications. Integral theorems - Stokes, Gauss-Ostrogradski and Green, applications in physics. Complex numbers and elementary concepts of the complex analysis.
Infinite series, numerical and functional. Elementary kinds of convergency and criterion for convergence. Power and Taylor series, the concept of an analytical function.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Offered to foreign students
Learning outcomes of the course unit
Prerequisites
Elements of the differential calculus of functions of more variables given explicitely. First order ordinary differential equation, the existence and uniqueness theorem of its solution with respect to the initial condition. The solution of the most simple kinds of such equations, particularly those with separated variables and the linear ones.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
The examination consists of test ond oral parts. The participation on lectures is not compulsory.
Course curriculum
2. Higher-order linear differential equations with constant coefficients.
3. Double and triple integrals, applications.
4. Scalar and vector fields, Hamilton operator.
5. Curve and surface integrals in scalar and vector fields, applications.
6. Stokes and Gauss-Ostrogradski theorem, applications.
7. Infinite series - numeric and functional (power and Taylor series).
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
- Programme NPCP_CHM_INT Master's
branch NPCO_CHM , 1 year of study, winter semester, elective
- Programme BPCP_CHCHT_INT Bachelor's
branch BPCO_CHTOZP , 1 year of study, winter semester, elective
branch BPCO_CHM , 1 year of study, winter semester, not stated - Programme CKCP_CZV lifelong learning
branch CKCO_CZV , 1 year of study, winter semester, not stated