SubjectsSubjects(version: 877)
Course, academic year 2020/2021
  
Mathematics A - AB413001
Title: Mathematics A
Guaranteed by: Department of Mathematics (413)
Actual: from 2020
Semester: winter
Points: winter s.:8
E-Credits: winter s.:8
Examination process: winter s.:
Hours per week, examination: winter s.:3/4 C+Ex [hours/week]
Capacity: 30 / 28 (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Level:  
For type: Bachelor's
Additional information: https://um.vscht.cz/studium/predmetyen
Old code: M1
Note: enabled for web enrollment
Guarantor: Maxová Jana RNDr. Ph.D.
Axmann Šimon Mgr. Ph.D.
Class: Předměty pro matematiku
Interchangeability : B413001, S413022
Z//Is interchangeable with: B413001
XP//In complex pre-requisite: AB413003, B413003
This subject contains the following additional online materials
Annotation -
Last update: Maxová Jana RNDr. Ph.D. (21.09.2020)
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 A is a prerequisite for Mathematics B.
Aim of the course -
Last update: Maxová Jana RNDr. Ph.D. (21.09.2020)

General skills:

1. elementary mathematical notions

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: Kubová Petra Ing. (06.03.2019)

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

Learning resources -
Last update: Kubová Petra Ing. (06.03.2019)

http://www.vscht.cz/mat/El_pom/sbirka/sbirka1.html

http://www.vscht.cz/mat/El_pom/Mat_MATH_MAPLE.html

http://www.vscht.cz/mat/MI/Aplikacni_priklady.pdf

Teaching methods -
Last update: Kubová Petra Ing. (06.03.2019)

Lectures and seminars

Requirements to the exam -
Last update: Maxová Jana RNDr. Ph.D. (18.09.2020)

It is necessary to actively participate in seminars and to work out homework. Attendance at seminars is compulsory. Another condition for granting the credit is the completion of the entrance test.

Credit granted is a necessary condition for passing the exam. The exam is combined - written and oral.

Syllabus -
Last update: Kubová Petra Ing. (06.03.2019)

1. Functions of a single real variable. Domain and range. Graphs of elementary functions. Basic properties. Composition of functions.

2. Inverse functions. Exponential and logarithmic functions. Trigonometric and inverse trigonometric functions.

3. Continuity of a function. Properties of continuous functions. Limits of sequences and functions.

4. Derivatives. Geometrical and physical meaning of derivatives. Rules for computing derivatives. Differential of a function.

5. Physical and geometrical applications of derivatives. L’Hospital’s rule. Approximation of a function value using Taylor polynomial. Analysis and graphing of a function.

6. Numerical solution of an equation of a single uknown variable - Newton’s method.

7. Antiderivatives and their properties. Newton definite integral, its properties and geometrical meaning.

8. Methods for computing indefinite and definite integrals – integration by parts and substitution method.

9. Integration of rational functions. Improper integrals. Numerical integration – trapezoidal method.

10. Definition of definite integral in physics – Riemann integral. Selected geometrical and physical applications of the integral.

11. Differential equations. Terminology, general and particular solution. Separation of variables.

12. First order linear differential equations. Variation of constants. Numerical solution of a first order differential equations – Euler’s method.

13. First and second order linear differential equations with constant coefficients and a special right-hand. Estimation method.

14. Application of differential equations in Physics, Chemistry, and Biochemistry. Revision and discussion.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (09.05.2019)

No requirements.

Course completion requirements -
Last update: Maxová Jana RNDr. Ph.D. (18.09.2020)

It is necessary to actively participate in seminars and to work out homework. Attendance at seminars is compulsory. Another condition for granting the credit is the completion of the entrance test.

Credit granted is a necessary condition for passing the exam. The exam is combined - written and oral.

Teaching methods
Activity Credits Hours
Konzultace s vyučujícími 0,5 14
Účast na přednáškách 1,5 42
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 2 56
Příprava na zkoušku a její absolvování 2 56
Účast na seminářích 2 56
8 / 8 224 / 224
Coursework assessment
Form Significance
Examination test 50
Oral examination 50

 
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