714-0366/04 – Mathematics I (MI)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | RNDr. Jan Kotůlek, Ph.D. | Subject version guarantor | Mgr. Monika Jahodová, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FS | 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 to
- analyze 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
Other activities
Summary
The subject is divided into four chapters.
In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications.
In the third chapter we study linear algebra. We introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Course-credit
For the participation on tutorials a student is classified with 5-20 points. In the case of absence, a homework can be handed in.
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.
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/M
http://mdg.vsb.cz/wiki
Other requirements
No more requirements are put on the student.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
I. Linear Algebra and Analytic Geometry
Linear algebra. Vector spaces, bases, dimension. Matrices, rank of a matrix. Determinant. Matrix inversion. Systems of linear equations, Gaussian elimination. Analytic geometry in Euclidean space. Dot product and cross product. Line and plane in 3D-Euclidean space.
II. Functions of one real variable
Definitions and basic properties, elementary functions, inverse function. Parametric and implicit functions. Limit and continuity of the function.
III. Differential calculus functions of one real variable
The derivative of function (basic rules for differentiation), parametric differentiation, higher-order derivative, applications of the derivatives, monotonic functions and extremes of function, convexity and concavity of a function
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction