Course detail

Mathematics I

FCH-BCT_MAT1Acad. year: 2017/2018

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

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 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.

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.

Recommended optional programme components

Not applicable.

Recommended or required reading

Not applicable.

Planned learning activities and teaching methods

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.

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 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.

Language of instruction

Czech

Work placements

Not applicable.

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.

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 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.

Classification of course in study plans

  • 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