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Mathematics I (N413022SIS)

Lecture Exercise Laboratory Examination Credits
3 4 0 Z+Zk 9
   

Annotation:

Course is designed to enable a student to appreciate mathematics and its application to numerous disciplines. It develops and strengthens the concepts and skills of elementary mathematics, particularly skills related to various disciplines of the curriculum. It covers various topics of mathematics that are both conceptual and practical.

Syllabus:

  1. Elements of Mathematical Logic. Introduction to calculus
  2. Continuity and limits of the functions of one and two variables.
  3. Derivatives, Mean value theorem, L’ Hospital’s rule. Partial derivatives.
  4. Monotone functions, extreme values of a function, asymptotes of the graph.
  5. Newton’s methods. Taylor’s formula with remainder. Differential.
  6. Curves in plane, tangent vector. Polar coordinates.
  7. Antiderivative. Definite integral. Geometric and physical applications.
  8. Techniques of integration.
  9. Improper integrals. Numerical integration. The mean value theorem for integrals.
  10. Ordinary differential equations of the first order. Separable equations. Euler’s method.
  11. Linear differential equations of the first order and their applications.
  12. The space R^n , geometry in R^3, vectors, dot and cross products.
  13. Matrices and Determinants. Inverse matrix.
  14. The systems of linear algebraic equations. Gauss-Jordan method. Cramer’s rule.

Literature:

  • Klíč, Hapalová: Úvod do studia matematiky na VŠCHT, skripta, VŠCHT Praha, 1997
  • Klíč a kol.: Matematika I ve strukturovaném studiu, skripta, VŠCHT Praha, 2004
  • Petáková: Matematika - příprava k maturitě a k přijímacím zkouškám na vysoké školy, Prométheus, 2005
  • Heřmánek a kol.: Sbírka příkladů k Matematice I ve strukturovaném studiu, skripta, VŠCHT Praha, 2005
  • Míčka a kol.: Sbírka příkladů z matematiky, skripta, VŠCHT Praha, 2002
  • Krajňáková, Míčka, Machačová: Zbierka úloh z matematiky, Alfa a SNTL, 1988
  • Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001