714-0566/04 – Bachelor Mathematics I (BM I)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 5 |
| Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | Mgr. Dagmar Dlouhá, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | English |
| Year of introduction | 2016/2017 | Year of cancellation | 2019/2020 |
| Intended for the faculties | HGF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical
courses than a goal. Thus the goal of mathematics is train logical
reasoning than mere list of mathematical notions, algorithms and
methods.Students should learn how toanalyze problems, distinguish between important and unimportant, suggest a method of solution, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit
- participation on tutorials at least on 8 of 18 hours
condition satisfying for 5 points, more participation for 0 - 15 points.
Summary course 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 obtainsat least 5 points.
Point quantification in the interval 100 - 91 90 - 81 80 - 71 70 - 61 60 - 51 50 - 0
ECTS grade A B C D E F
Point quantification in the interval 100 - 86 85 - 66 65 - 51 51 - 0
National grading scheme excellent very good satisfactory failed
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz
http://mdg.vsb.cz/wiki/public/ZM_MI_listy.pdf
Other requirements
No more requirements.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Functions of one real variable (definitions and basic properties). Elementary functions. Limit of the function, continuity of the functions, basic rules.
2. Differential calculus of functions of one real variable: The derivative of a function (basic rules for differentiation). Derivatives of selected functions. Differential of the function. Taylor polynom. Parametric differentiation. Highes-order derivative. Applications of the derivatives. Monotonic functions and extremes of function, convexity and concavity of a function.
3. Linear algebra: Vectors, linear independence. Matrices (basic properties), determinants (basic properties, calculation, evaluation). Matrix inversion. Systems of linear equations, Cramer’s rule. Gaussian elimination
4. Analytical geometry in E3: Product of vectors (basic properties).
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.