230-0307/01 – Mathematics I (MI)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | Ing. Lukáš Pospíšil, Ph.D. | Subject version guarantor | Ing. Lukáš Pospíšil, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2021/2022 | Year of cancellation | |
| Intended for the faculties | FBI | 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
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, a limit of functions, a derivative of functions and its application. The second chapter emphasizes the systems of linear equations and the methods of their solution. The third chapter introduces the basics of vector calculus and basic linear objects in three dimensional space.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Passing the course, requirements
Course-credit (full-time study):
5 points:
-participation on tutorials is obligatory, 20% of absence can be accepted,
-submition of semestral project in predefined form.
5 – 15 poinst:
-accomplish the written tests,
-each test can be repeated once,
-it is necessary to get at least 5 out of 15 points.
Student has to gain at least 10 points in total to obtain credit and procced to final exam.
Course-credit (distance study):
Based on participation in consultations student can get 5 - 20 points, in case of absence student can get 5 points for elaboration of additional project.
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 National grading scheme
100 – 86 excellent
85 – 66 very good
65 – 51 satisfactory
50 – 0 failed
E-learning
http://mdg.vsb.cz/portal/en/Mathematics1.pdf
Other requirements
No more requirements are put on the student.
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. Elementary functions (including inverse trigonometric functions).
3. Limit of a function, infinite limit of a function. Limit at an improper point. Continuous and discontinuous functions.
4. Differential calculus of functions of one real variable. Derivative of a function, its geometrical and physical meaning. Derivative rules.
5. Derivative of elementary functions.
6. Differential of a function. Derivative of higher orders. l’Hospital rule.
7. Relation between derivative and monotonicity, convexity and concavity of a function.
8. Extrema of a function. Asymptotes. Plot graph of a function.
9. Linear algebra. Matrices. Matrix operations. Rank of a matrix. Inverse.
10. Determinants, properties of a determinant.
11. Solution of systems of linear equations. Frobenius theorem. Cramer’s rule. Gaussian elimination algorithm.
12. Analytic geometry. Euclidean space. Scalar, cross and triple product of vectors, properties.
13. Equation of a plane, line in E3. Relative position problems.
14. Metric or distance problems.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.