# 310-2301/01 – Mathematics 1 (Math 1)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 5 Subject guarantor RNDr. Jan Kotůlek, Ph.D. Subject version guarantor RNDr. Jan Kotůlek, Ph.D. Study level undergraduate or graduate Study language English Year of introduction 2019/2020 Year of cancellation Intended for the faculties FBI, FEI, FMT, FS, FAST, HGF Intended for study types Bachelor
Instruction secured by
BEL10 Mgr. Jana Bělohlávková
KOT31 RNDr. Jan Kotůlek, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### Subject aims expressed by acquired skills and competences

After completing this course, students should have the following skills: * Use rules of differentiation to differentiate functions. * Sketch the graph of a function using asymptotes, critical points. * Apply differentiation to solve problems. * Solve a system of linear algebraic equations. * Work with basic objects in three dimensional Euclidean space.

### Teaching methods

Lectures
Individual consultations
Tutorials

### Summary

I. Calculus. Function of one variable (basic notions, inverse function, elementary functions); Limits and Continuity of a function; Differentiation of a function (differentiation rules, application, L'Hospital's rule). II. Linear algebra. Vector spaces; Matrices and determinants; Systems of linear algebraic equations (Gaussian elimination, Frobeniu theorem). III. Introduction to analytic geometry (lines and planes in E3, intersection, distance, angle).

### Compulsory literature:

Neustupa J.: Mathematics I. ČVUT, Praha 2004. Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0. Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

### Recommended literature:

Neustupa J.: Mathematics I. ČVUT, Praha 2004. Demlova M., Hamhalter J.: Calculus I. ČVUT, Praha 1998, ISBN 80-01-01110-0 Doležalová, J., Mathematics I. VŠB-TU Ostrava 2005, ISBN 80-248-0796-3.

### Way of continuous check of knowledge in the course of semester

Course-credit -participation on tutorials is obligatory, 20% 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. 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 (in Czech)

### Other requirements

There is no further requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1 Linear algebra. Operations with matrices. Determinants. Properties of determinants. 2 Rank of a matrix. Inverse matrix. 3 Solution of linear equations. Frobenius theorem. Cramer's rule. 4 Gaussian elimination algorithm. 5 Real functions of one real variable. Definitions, graph. Function bounded, monotonous, even, odd, periodic. One-to-one function, inverse and composite functions. 6 Elementary functions. 7 Limit of a function. Continuous and discontinuous functions. 8 Differential calculus of one variable. Derivative of a function, its geometrical and physical applications. Rules of differentiation. 9 Derivatives of elementary functions. 10 Differential functions. Derivative of a function defined parametrically. Derivatives of higher orders. L'Hospital's rule. 11 Use of derivatives to detect monotonicity, convexity and concavity features. 12 Extrema of functions. Asymptotes. Graph of a function. 13 Analytic geometry in E3. Scalar, cross and triple product of vectors and their properties. 14 Equation of a line. Equation of a plane. Relative positions problems. Metric or distance problems.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80  30 3
Mandatory attendence participation: 80% of seminars

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Conditions for subject completion and attendance at the exercises within ISP: Two intermediate tests during the semester, attendace can be compensated by submission of homework in the form determined by the teaching assistant.

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner
ECTS Bc.-Mgr. 2024/2025 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2024/2025 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS - MechEng - Bachelor Studies 2023/2024 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS Bc.-Mgr. 2023/2024 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2022/2023 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS Bc.-Mgr. 2022/2023 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FMT+9360 2021/2022 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2021/2022 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS Bc.-Mgr. 2021/2022 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
FMT+9360 2020/2021 Full-time English Optional 600 - Faculty of Materials Science and Technology - Dean's Office stu. block
ECTS FCE Bc-Mgr 2020/2021 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
ECTS - MechEng - Bachelor Studies 2020/2021 Full-time English Choice-compulsory 301 - Study and International Office stu. block
ECTS FCE Bc-Mgr 2019/2020 Full-time English Choice-compulsory 200 - Faculty of Civil Engineering - Dean's Office stu. block
Additional Subjects 2019/2020 Full-time English Choice-compulsory 301 - Study and International Office stu. block
FMST 2019/2020 Full-time English Compulsory 601 - Study Office stu. block

### Assessment of instruction

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