SubjectsSubjects(version: 863)
Course, academic year 2019/2020
  
Mathematics I - Z413002
Title: Matematika I
Guaranteed by: Department of Mathematics (413)
Actual: from 2007
Semester: summer
Points: summer s.:9
E-Credits: summer s.:9
Examination process: summer s.:
Hours per week, examination: summer s.:3/3 C+Ex [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type:  
Old code: M1
Note: enabled for web enrollment
Interchangeability : N413002
Z//Is interchangeable with: N413022
Annotation -
Last update: TAJ413 (04.01.2006)
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.
Literature - Czech
Last update: TAJ413 (04.01.2006)

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

Syllabus -
Last update: TAJ413 (04.01.2006)

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.

 
VŠCHT Praha