230-0404/02 – Mathematics I (MI)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | RNDr. Petr Volný, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| 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. After completing the course, students will be able to use the acquired knowledge and procedures from differential calculus of one variable, linear algebra, and analytical geometry not only in the study of university mathematics, but also in professional subjects.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b).
The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.
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)
2 Elementary functions
3 Limit of the function, continuity of the functions , basic rules
4 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation).
5 Derivatives of selected functions
6 Differential of the function, Taylor polynom, parametric differentiation, highes-order derivative, L'Hospital rule
7 Applications of the derivatives, convexity and concavity of a function
8 Extremes of function, asmptotes, function graph constructing
9 Linear algebra: Vectors, linear independence. Matrices (basic properties)
10 Determinants (basic properties, calculation, evaluation)
11 Rank of matrix, matrix inversion
12 Systems of linear equations, Frobenius theorem, Gaussian elimination
13 Products of vectors (basic properties), line and plane equation in E3, mutual positions of lines and planes
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.