Course detail
Mathematics II
FCH-BCT_MAT2Acad. year: 2015/2016
1. Linear algebra: systems of linear equations, vector space Rn, products, forms.
2. Calculus in several variables.
3. Ordinary differential equations of the 1st order.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Learning outcomes of the course unit
Students manage the classification and solution of the simpliest kinds of first-order differential equations and the n-th order linear differential equations with constant coefficients. They will master its solution by the method of the variation of constants and by the method of improper coefficients. Passing the course, students are able follow and apply the methods of differential calculus of n variables. In more details, they learn to find, describe and express domains, graphs, contour lines of functions. They master the concepts of a limit, partial and direction derivative and total differential with their properties.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
The exam is written.
Course curriculum
2 The vector space Rn (especially n = 2, n = 3). Innne, outer and cross products - features and applications. Linear and quadratic forms, classification of quadratic forms, Sylvester criterion.
3 Functions of several variables. Basic concepts, domain, graph (contour and level surfaces), limit and continuity.
4 Partial derivatives, directional derivatives, total and partial differentials, the equation of the tangent plane and normal to the graph function.
5 Partial derivatives and differentials of higher orders. Taylor polynomial.
6 Local extremes.
7 Constrained and global extremes.
8 Double and triple integrals - definition and calculation on elementary areas by Fubini's theorem.
9 Substitution theorem, polar, cylindrical and spherical coordinates.
10 Application of double and triple integrals.
11 Ordinary differential equations - basic notions (general and particular solutions, the initial problem, boundary value problem). ODE1 - Introduction (existence and uniqueness of solutions of the initial problem).
12 ODE1 - analytical solution methods (separation of variables, linear equations, variation of constants, substitution method - homogeneous functions, Bernoulli equation).
13 ODE1 - numerical methods (one-step methods, multistep methods, type predictor-corrector).
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Polcerová M., Polcer J.: Sbírka příkladů z matematiky II. FCH VUT v Brně, Brno. (CS)
Rektorys K.: Přehled užité matematiky I, II. Prometheus Praha. (CS)
Škrášek J., Tichý Z: Základy aplikované matematiky III. SNTL Praha. (CS)
Škrášek J., Tichý Z.: Matematika 1,2. SNTL Praha. (CS)
Veselý P.: Matematika pro bakaláře. VŠCHT Praha. (CS)
Recommended reading
Eliáš J., Horváth J., Kajan J., Šulka R.: Zbierka úloh z vyššej matematiky. ALFA Bratislava. (CS)
Ivan, J.: Matematika 2. Alfa Bratislava. (CS)
Kosmák, L., Potůček, R., Metrické prostory, Academia 2004, ISBN 80-200-1202-8 (CS)
Mortimer, R.: Mathematics for Physical Chemistry. Academic Press, Memphis. (CS)
Smith, R., Minton, R.B.: Calculus - Early Trancscendental Functions. MacGraw Hill, New York. (CS)
Classification of course in study plans
- Programme BPCP_CHTP Bachelor's
branch BPCO_CHP , 1 year of study, summer semester, compulsory
branch BPCO_BT , 1 year of study, summer semester, compulsory - Programme BKCP_CHTP Bachelor's
branch BKCO_PCH , 1 year of study, summer semester, compulsory
branch BKCO_BT , 1 year of study, summer semester, compulsory - Programme BPCP_CHCHT Bachelor's
branch BPCO_SCH , 1 year of study, summer semester, compulsory
branch BPCO_CHMN , 1 year of study, summer semester, compulsory
branch BPCO_CHM , 1 year of study, summer semester, compulsory
branch BPCO_CHTOZP , 1 year of study, summer semester, compulsory - Programme BKCP_CHCHT Bachelor's
branch BKCO_CHTOZP , 1 year of study, summer semester, compulsory
branch BKCO_SCH , 1 year of study, summer semester, compulsory
branch BKCO_CHM , 1 year of study, summer semester, compulsory - Programme CKCP_CZV lifelong learning
branch CKCO_CZV , 1 year of study, summer semester, compulsory
- Programme BPCP_CHCHT_AKR Bachelor's
branch BPCO_SCH , 1 year of study, summer semester, compulsory
Type of course unit
Exercise
Teacher / Lecturer