230-0201/15 – Mathematics (BcM1)
| Gurantor department | Department of Mathematics | Credits | 6 |
| Subject guarantor | RNDr. Petr Volný, Ph.D. | Subject version guarantor | RNDr. Petr Volný, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2026/2027 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is an essential part of education on technical universities. It should be considered rather the method in the study of technical courses than a goal.
The aim of the course is therefore to teach students not only basic mathematical knowledge, procedures and methods, but also to deepen their logical thinking.
Students should learn how to analyse problems, distinguish between important and unimportant, propose a solution procedure, verify each step of a method, generalize achieved results, analyse correctness of achieved results with respect to given conditions, apply these methods to solve technical problems, understand that mathematical methods and thought processes are applicable beyond mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
Mathematics I is connected with secondary school education. It is divided in three parts, differential calculus of functions of one real variable, linear algebra and analytic geometry in the three dimensional Euclidean space E3. The aim of the first chapter is to handle the concept of a function and its properties, limits of functions, derivatives of functions and their applications. The second chapter emphasizes the systems of linear equations and the methods of solution. The third chapter introduces the basics of vector calculus and linear objects in three dimensional space.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Ongoing submission of tasks assigned during the exercises on the dates set by the teacher. Written tests, discussion on specialized topics covered in the lectures.
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz
Other requirements
Passing the course, requirements
Course-credit
-participation on tutorials is obligatory, 30% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Real functions of one real variable. Definition, graph. Bounded function, monotonic functions, even, odd and periodic functions. One-to-one functions, inverse and composite functions.
2. Limit of a function, improper limit of a function. Limit at an improper point. Continuous and discontinuous functions.
3. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules. Derivative of elementary functions.
4. l’Hospital rule.
5. Differential of a function. Derivatives of higher orders.
6. Relation between derivative and monotonicity, convexity and concavity of a function.
7. Extrema of a function. Asymptotes. Plot graph of a function.
8. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse matrix.
9. Determinants, properties of determinants.
10. Solution of systems of linear equations. Frobenius theorem. Gaussian elimination algorithm. Cramer’s rule.
11. Analytic geometry. Euclidean space. Scalar, vector and triple product of vectors, properties.
12. Equation of a plane, line in E3. Relative position problems.
13. Distance problems.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.