Course detail

Mathematics I

FCH-BC_MAT1Acad. year: 2019/2020

Basics of calculus of functions of one real variable. Basics of linear algebra.

Language of instruction

Czech

Number of ECTS credits

7

Mode of study

Not applicable.

Learning outcomes of the course unit

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 obtain the ability of solving simple tasks of the physical character and tasks occuring in the advanced courses.

Prerequisites

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

Co-requisites

Not applicable.

Planned learning activities and teaching methods

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

Assesment methods and criteria linked to learning outcomes

Students must first obtain the credit from seminars. Compulsory attendance at seminars. In the exercises are included 2 tests (each at most 12 points).. In total the exercises can receive a maximum of 24 points. A student has to obtain at least 6 points from each test. (Students are allowed to undergo corrective control work. Evaluation of corrective labor inspection is final.)

The exam is written. Students do not use any electronic devies during the exam, however they can use written preparation in the range of two A4 sheets.

Course curriculum

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.

Work placements

Not applicable.

Aims

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.

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

The compulsory attendance at seminars. In the exercises are included 2 tests (each at most 12 points). In total the exercises can receive a maximum of 24 points. A student has to obtain at least 6 points from each test.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Matematika online, http://mathonline.fme.vutbr.cz/ (CS)
Thomas G. B.: Calculus, Addison Wesley (EN)
Thomas G.B., Finney R.L.: Calculus and Analytic Geometry, Addison Wesley (EN)

Recommended reading

Děmidovič B. P.: Sbírka úloh a cvičení z matematické analýzy (CS)
Rektorys K. a spol.: Přehled užité matematiky I,II ,SNTL (CS)

Elearning

Classification of course in study plans

  • Programme BPCP_CHTOZP Bachelor's 1 year of study, winter semester, compulsory
  • Programme BPCP_CHTM Bachelor's 1 year of study, winter semester, compulsory
  • Programme BPCP_CHCHTE Bachelor's 1 year of study, winter semester, compulsory

  • Programme BPCP_CHTPO Bachelor's

    specialization BT , 1 year of study, winter semester, compulsory
    specialization PCH , 1 year of study, winter semester, compulsory
    specialization CHPL , 1 year of study, winter semester, compulsory

  • Programme BPCP_CHCHT Bachelor's

    branch BPCO_CHTOZP , 1 year of study, winter semester, compulsory
    branch BPCO_CHM , 1 year of study, winter semester, compulsory
    branch BPCO_CHMN , 1 year of study, winter semester, compulsory
    branch BPCO_SCH , 1 year of study, winter semester, compulsory

  • Programme BKCP_CHCHT Bachelor's

    branch BKCO_CHM , 1 year of study, winter semester, compulsory
    branch BKCO_CHTOZP , 1 year of study, winter semester, compulsory
    branch BKCO_SCH , 1 year of study, winter semester, compulsory

  • Programme BPCP_CHTP Bachelor's

    branch BPCO_BT , 1 year of study, winter semester, compulsory
    branch BPCO_CHP , 1 year of study, winter semester, compulsory

  • Programme BKCP_CHTP Bachelor's

    branch BKCO_BT , 1 year of study, winter semester, compulsory
    branch BKCO_PCH , 1 year of study, winter semester, compulsory

  • Programme BKCP_CHTPO Bachelor's

    specialization CHPL , 1 year of study, winter semester, compulsory
    specialization PCH , 1 year of study, winter semester, compulsory
    specialization BT , 1 year of study, winter semester, compulsory

  • Programme BKCP_CHTOŽP Bachelor's 1 year of study, winter semester, compulsory
  • Programme BKCP_CHCHTE Bachelor's 1 year of study, winter semester, compulsory
  • Programme BKCP_CHTM Bachelor's 1 year of study, winter semester, compulsory
  • Programme AKREDITACE revize Bachelor's 1 year of study, winter semester, compulsory