SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Mathematics I - S413022
Title: Mathematics I
Guaranteed by: Department of Mathematics (413)
Actual: from 2014
Semester: both
Points: 10
E-Credits: 10
Examination process:
Hours per week, examination: 3/4 C+Ex [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type:  
Additional information: http://The course is lectured in winter semester exclusively
Note: you can enroll for the course in winter and in summer semester
Guarantor: Pokorný Pavel RNDr. Ph.D.
Annotation
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)
Basic course in Calculus for students in bachelor program. It provides mathematical skills necessary for other subjects (physics, physical chemistry,...) in bachelor program. Success in Mathematics I is a prerequisite for Mathematics II.
Aim of the course
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

General skills:

1. basic mathematical terms

2. knowledge and understanding of basic algorithms

3. individual problem solving

4. basic mathematical background for formulation and solving of natural and engineering problems

5. numerical algorithms (algebraic equations, integration).

Literature
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

R: Porubský: Fundamental Mathematics for Engineers, Vol.I, VŠCHT, 2001, ISBN: 80-7080-418-1

Syllabus - Czech
Last update: KNOBLOCL (15.12.2011)

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.

14. The systems of linear algebraic equations. Gauss-Jordan method. Cramer’s rule.

Registration requirements
Last update: Pokorný Pavel RNDr. Ph.D. (01.08.2013)

No requirements

 
VŠCHT Praha