doc. RNDr. Miroslav Kureš, Ph.D.

Institute of Physical and Applied Chemistry (ÚFSCH)

The knowledge and skills will appear on the following fields
1. Students will manage successfully a work with matrices.
2. Students will be endowed with the knowledge of elementary functions and their properties. Students are expected to manage the concept of a limit and derivative and comprehend their meaning.They master their computation applying basic rules including the L´Hospital rule. Students will also be able to investgate the course of a function of one variable.
3. Students will be endowed with the knowledge of the indefinite and definite integral including the improper integral. They learn the basic methods of integral computations and be aquaitanced with the basic applications.
4. Students will be acquainted with the elementary commands of MATLAB and will be able to apply them for computations.
5. Students obtain the ability of solving simple tasks of the physical character and tasks occuring in the advanced courses.

Elementary knowledge of mathematics on the level of the secondary school. Linear and quadratic equations, inequalities, elements of the geometry of lines and planes.

Not applicable.

Not applicable.

Škrášek J., Tichý Z.: Základy aplikované matematiky 1 SNTL Praha 1989, ISBN 80-03-00150-1 (CS)
http://www.vutbr.cz/elearning (CS)
Karásek J., Mezník I.: Matematika pro strojní fakulty. SNTL Praha (CS)
Švarc S., Krupková V., Studená V.: Matematická analýza I. Skriptum VUT Brno (CS)
Bayer J., Polcerová M.: Analytická geometrie v příkladech. Skriptum FCH VUT v Brně (CS)
Veselý P., Matematika pro bakaláře. VŠCHT Praha (CS)
Bican L.: Lineární algebra. Academia Praha (CS)
Karásek J.: Matematika II. Skriptum FSI VUT v Brně (CS)
Eliáš J., Horváth J., Kajan J., Šulka R.: Zbierka úloh z vyššej matematiky. ALFA Bratislava (CS)
Rektorys K.: Přehled užité matematiky, díl I, II. Prometheus Praha. (CS)
Bubeník, F.: Mathematics for Engineers. ČVUT Praha (CS)
Howard A., Irl B., Stephen D.: Calculus. John Wiley and Sons (CS)
Jordan, D.W., Smith, P.,: Mathematical Techniques. Oxford (CS)
http://www.vutbr.cz/elearning (CS)

The course uses teaching methods in form of Lecture - 2 teaching hours per week, seminars - 2 teaching hours per week, computer support - 1 teaching hour per week. The e-learning system (LMS Moodle) is available to teachers and students.

Students must first obtain the credit from seminars. Compulsory attendance at seminars. In the exercises are included 2 tests (each at most 10 points) and a test from the computer support (5 points). In total the exercises can receive a maximum of 25 points. A student has to obtain at least 5 points from each test and at least 2 points from the computer support. (Students are allowed to undergo corrective control work. Evaluation of corrective labor inspection is final.)

The exam is written.

Czech

Not applicable.

1. Number sets, vectors, matrices. Matrix operations.
Sem. The recapitulation of selected themes of secondary schools. Introduction to matrices.
2. Linear independence, rank of matrices, determinants.
Sem. Matrix operations. Elementary row operations, rank.
3. Systems of linear equations. Frobenius theorem, Gaussian elimination, Cramer's rule.
Sem. Determinants to order 3. Systems of linear equations.
4. Geometry in E2 and E3: inner, outer and vector products. Lines and planes.
Sem. Systems of linear equations. Application of the products.
5. Geometry in E2 and E3: the role of angles and distances. Conics.
Sem. Parametric and general equations of lines and planes. Classification of conic sections and quadrics without mixed member (filling into a square).
6. Functions of one real variable. Basic features, graph. Inverse function.
Sem. TEST 1: 1) Matrix multiplication 2) Determinant 3) The system of linear equations 4) The geometry of lines and planes 5) Classification of conic sections and quadrics
7. Elementary functions: polynomials, rational functions, power functions, exponential and logarithmic functions, trigonometric functions.
Sem. Domains of elementary functions.
8. Derivative, geometric and physical meaning, calculation, chemical applications.
Sem.. Calculations of derivatives.
9. Calculations limits using of derivative (L'Hospital's rule). Taylor polynomial.
Sem. Taylor polynomial (briefly). Calculations of limits.
10. The determination of functions properties (with emphasis on the extremes).
Sem. Functions properties.
11. The method of least squares.
Cv. The method of least squares.
12. Interpolation polynomials and splines.
Cv. TEST 2: 1) Domain of functions 2) Derivative 3) [six-point example] Graphing functions
13. Summarizing lecture, discussion.
Cv. Interpolation polynomials and splines. Evaluation of seminars, granting credits.

The aim of the course is making acquitance with the basic concepts of mathematics necessary for managing the following courses of physics, chemistry and engineering disciplines. Another claim is obtaining the basic principles of mathematical thinking and skills and applying them in the above mentioned courses.

The compulsory attendance at seminars. In the exercises are included 2 tests (each at most 10 points) and a test from the computer support (5 points). In total the exercises can receive a maximum of 25 points. A student has to obtain at least 5 points from each test and 2 points from the thest from the computer support.

• Programme BPCP_CHCHT Bachelor's

  branch BPCO_SCH , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BKCP_CHCHT Bachelor's

  branch BKCO_SCH , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BPCP_CHCHT Bachelor's

  branch BPCO_CHTOZP , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BKCP_CHCHT Bachelor's

  branch BKCO_CHTOZP , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BPCP_CHCHT Bachelor's

  branch BPCO_CHMN , 1. year of study, winter semester, 8 credits, compulsory
  branch BPCO_CHM , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BKCP_CHCHT Bachelor's

  branch BKCO_CHM , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BPCP_CHTP Bachelor's

  branch BPCO_BT , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BKCP_CHTP Bachelor's

  branch BKCO_BT , 1. year of study, winter semester, 8 credits, compulsory
  branch BKCO_PCH , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme BPCP_CHTP Bachelor's

  branch BPCO_CHP , 1. year of study, winter semester, 8 credits, compulsory
  

• Programme CKCP_CZV lifelong learning

  branch CKCO_CZV , 1. year of study, winter semester, 8 credits, compulsory
  

13 hours, compulsory

RNDr. Marie Polcerová, Ph.D.
doc. RNDr. Miroslav Kureš, Ph.D.