Mathematics 1 for TT

Studijní plán: Cestovní ruch - platný pro studenty, kteří započali studium od ZS 2013/2014

PředmětMathematics 1 for TT (MAT1Ca-1)
GarantujeKatedra matematiky (KM)
Garantdoc. RNDr. Petr Gurka, CSc.
JazykAnglicky
Počet kreditů5
Ekvivalent
Prezenční studium
Přednáška2 h
Cvičení2 h
Studijní plán Typ Sem. Kred. Ukon.
Cestovní ruch - platný pro studenty, kteří započali studium od ZS 2013/2014 P 1 5 kr. ZA
Cestovní ruch - platný pro studenty, kteří započali studium od ZS 2016/2017 P 1 5 kr. ZA

Sylabus

  • Sets, propositional calculus, basic elementary functions and their graphs.
  • Real function of one real variable. Basic definitions: domain and range, operations with functions, composite function, inverse function.
  • Limit at a point, continuity of a function at a point. Basic properties of limits.
  • Derivative. Physical meaning of the first derivative (velocity), geometrical meaning (slope, tangent line, normal to a graph).
  • Mean value theorems (Rolle, Lagrange, Cauchy). The l'Hospital rule. Asymptots to a graph.

  • Monotony of a function, local extreme values. Concave and convex functions, inflection points of the graph.
  • Sketching the graph of a function, global extreme values.
  • Approximation of the function: differential, the Taylor polynomial.
  • Systems of algebraic linear equations, matrices, linear independence of rows in a matrix, rank of a matrix, Gaussian elimination method.
  • Matrix algebra: linear combination of matrices, matrix multiplication. Determinants: definition, evaluating determinants of degree 2 and 3.
  • Matrix inverse. Cofactor, expanding a determinant about a row or a column, row or column transformations of determinants. Calculating a matrix inverse by determinats or by the Jordan elimination.
  • Systems of linear quations with a general matrix. Solvability (Frobenius theorem), solving a system by the Gaussian elimination.
  • Vector spaces: arithmetic vector space, vector space of functions on an interval.

Doporučená literatura

  • HOY, Michael, LIVERNOIS, John, MCKENNA, Chris, REES, Ray and STENGOS, Thanasis. Mathematics for Economics, 3rd edition, MIT Press, 2011, 958 pp., ISBN978-0-262-01507-
  • THOMPSON, Silvanus P., GARDNER, Martin. Calculus Made Easy. St. Martin´s Press, 1998, 243 pp., ISBN 0312185480.
  • STRANG, Gilbert. Introduction to linear algebra, 4th edition. Wellesley Cambridge Press, 2009, 584 pp., ISBN 0980232716.
  • STRANG, Gilbert. Calculus, 2th edition. Wellesley Cambridge Press, 20, 716 pp., ISBN 0980232740.

Anotace

Course objective.
The course aims to equip students with basic knowledge of mathematical analysis and linear algebra. Students should acquire basic computational skills relevant to the functions of one variable and for solving systems of linear equations. Lectures are focused on the interpretation of the concepts of the differential calculus, basic arithmetical procedures and solving of typical exercises. Exercises are intended to practice the relevant issues.
Knowledge.
The student is able to sketch graphs of elementary functions using the differential calculus. He also knows the basic concepts of linear algebra (matrices, determinants, etc.) including its applications in the linear programming.
Skills.
Students can search for extremal values of functions of one variable and determine other specific properties related to the first or the second derivative of the given function.
General eligibility.
Graduates are able to work with functions of one real variable, which is the basic description of dependence of variables. Moreover, they become familiar with the basic linear algebra algorithms, which are important tools for linear programming used for optimization of linear problems.

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