Course detail

Mathematics II

FCH-BCT_MAT2Acad. year: 2011/2012

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

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jiří Tomáš, Dr.

Department

Institute of Physical and Applied Chemistry (ÚFSCH)

Learning outcomes of the course unit

The knowledge of the solution of simple tasks, particularly those of the physical character. Managing of the both of the mathematical courses should enable reading and comprehension the mathematical symbolics used in the literature extending the knowlege in the studied branch.

Prerequisites

Differential and integral calculus of functions of one variable, elements of the linear algebra and analytical geometry.
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

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

For an active participation in practices, a credit is given. It is a necessary condition for making the examination.
The examination consists of test ond oral parts. The participation on lectures is not compulsory.

Course curriculum

1. Implicitely given functions.
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

Not applicable.

Aims

The aim of the course is forming the theoretical background necessary for studies of physics, particularly elementary kinds of differential equations, elements of the theory of fields, Hamilton operator and integral theorems.

Specification of controlled education, way of implementation and compensation for absences

Necessary conditions for obtaining a credit are the regular participation on practies and reaching at least 50% of marks from control works. In addition to calculus skills, the control works also check the ability of their applications to simple problems. Moreover, there is a semestral work consisting of 20 computative examples. Finally, students are claimed to perform a short presentation on a given topic with accent to physical and chemical applications. If a student fails at a control work, he has a possibility of its correction. If there are serious reasons, some claim can be replaced by an alternative one.
If the conditions are not fulfilled, a teacher can give alternative conditions for obtaining a course-unit credit.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Škrášek J., Tichý Z: Základy aplikované matematiky III. SNTL Praha. (CS)
Škrášek J., Tichý Z.: Matematika 1,2. SNTL Praha. (CS)
Polcerová, M.: Matematika II v chemii a v praxi, skripta. FCH VUT v Brně, Brno. (CS)
Veselý P.: Matematika pro bakaláře. VŠCHT Praha. (CS)
Rektorys K.: Přehled užité matematiky I, II. Prometheus Praha. (CS)
Polcerová M., Polcer J.: Sbírka příkladů z matematiky II. FCH VUT v Brně, Brno. (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)
Bubeník F.: Mathematics for Engineers. ČVUT Praha. (CS)
Smith, R., Minton, R.B.: Calculus - Early Trancscendental Functions. MacGraw Hill, New York. (CS)
Mortimer, R.: Mathematics for Physical Chemistry. Academic Press, Memphis. (CS)

Classification of course in study plans

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_SCH , 2. year of study, winter semester, compulsory-optional

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_SCH , 2. year of study, winter semester, compulsory-optional

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_CHTOZP , 2. year of study, winter semester, compulsory-optional

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_CHTOZP , 2. year of study, winter semester, compulsory-optional
    branch BPCO_CHM , 2. year of study, winter semester, compulsory-optional

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_CHM , 2. year of study, winter semester, compulsory-optional

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_CHMN , 2. year of study, winter semester, compulsory-optional

  • Programme BPCP_CHTP Bachelor's

    branch BPCO_BT , 2. year of study, winter semester, compulsory-optional

  • Programme BKCP_CHTP Bachelor's

    branch BKCO_BT , 2. year of study, winter semester, compulsory-optional
    branch BKCO_PCH , 2. year of study, winter semester, compulsory-optional

  • Programme BPCP_CHTP Bachelor's

    branch BPCO_CHP , 2. year of study, winter semester, compulsory-optional

  • Programme CKCP_CZV lifelong learning

    branch CKCO_CZV , 1. year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Jiří Tomáš, Dr.

Guided consultation in combined form of studies

65 hours, optionally

Teacher / Lecturer

doc. RNDr. Jiří Tomáš, Dr.

Exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Jiří Tomáš, Dr.