• PL
  • EN
  • EN

Mathematics

Block name: Mathematics

ECTS: 11

Language of instruction: Polish/English

Teaching methods/load: Lecture (30h / semester); Exercises (90h / semester)

TOTAL: 120h / semester

Teacher responsible: Sylwia Krawczyńska

 

Prerequisites

The student should have the knowledge of mathematics from high school.

 

Description of learning outcomes

The student should be able to:

  • formulate in the mathematical language problems encountered in engineering practice and know the precise tools to solve them,
  • use mathematical methods for engineering applications,
  • make the mathematical description of issues and processes,
  • use abstract thinking to understand the problems,
  • use statistical methods for the description of physical quantities,
  • use the probabilistic inference.

 

Content:

  • Sequences – their properties and limits.
  • Real functions  - their properties and limits.
  • Trigonometric functions.
  • The derivative of the function.
  • Properties of differentiable functions.
  • Derivatives of higher orders.
  • Local extremes and absolute extremes.
  • Indefinite and definite integrals.
  • Complex numbers.
  • Algebraic equations.
  • Matrix, matrix operations.
  • Systems of linear equations.
  • Elements of analytic geometry.
  • The plane in space.
  • Conics.
  • The surfaces of the second degree.
  • Multivariable real functions. Continuity of functions.
  • Partial derivatives.
  • Differential complete. Directional derivatives.
  • Extremes of functions of two variables.
  • The method of least squares.
  • The vector field.
  • Differential Equations.
  • Multiple integrals (double integral, triple integral).
  • Curvilinear integrals: directed and undirected.
  • Number series - convergence.
  • Alternating Series.
  • The criterion for the integral convergence of series in the study of convergence of improper integrals.
  • Series of functions.
  • Power series. The radius and the interval of convergence of power series.
  • Differentiation and integration of power series.
  • Derivative of complex function.
  • Holomorphic functions.
  • Surface integral (oriented and non-oriented).
  • Probability - the random variable and its parameters.
  • The normal distribution and its applications.
  • Elements of mathematical statistics.
  • Interval estimation.
  • Statistical hypotheses and their verification.

Pliki do pobrania

W ramach naszej witryny stosujemy pliki cookies w celu świadczenia Państwu usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Państwa urządzeniu końcowym. Mogą Państwo dokonać w każdym czasie zmiany ustawień dotyczących cookies. Więcej szczegółów w naszej polityce prywatności.