MAT_z Mathematics I

Institute of Technology and Business in České Budějovice
winter 2019
Extent and Intensity
2/4/0. 7 credit(s). Type of Completion: zk (examination).
Teacher(s)
Ing. Květa Papoušková (seminar tutor)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
RNDr. Jana Vysoká, Ph.D. (seminar tutor)
Guaranteed by
doc. RNDr. Zdeněk Dušek, Ph.D.
Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Supplier department: Department of Informatics and Natural Sciences – Faculty of Technology – Rector – Institute of Technology and Business in České Budějovice
Timetable of Seminar Groups
MAT_z/D8: Sun 29. 9. 8:00–9:30 E1, 9:40–11:10 E1, Sat 2. 11. 13:05–14:35 B3, 14:50–16:20 B1, Sat 9. 11. 8:00–9:30 E1, 9:40–11:10 E1, Sun 10. 11. 13:05–14:35 E1, 14:50–16:20 E1, Sat 30. 11. 13:05–14:35 B1, 14:50–16:20 B1, Sat 21. 12. 11:25–12:55 E1, 13:05–14:35 E1, D. Smetanová
MAT_z/T1: Sun 29. 9. 8:00–9:30 E1, 9:40–11:10 E1, Sat 2. 11. 13:05–14:35 B3, 14:50–16:20 B1, Sat 9. 11. 8:00–9:30 E1, 9:40–11:10 E1, Sun 10. 11. 13:05–14:35 E1, 14:50–16:20 E1, Sat 30. 11. 13:05–14:35 B1, 14:50–16:20 B1, Sat 21. 12. 11:25–12:55 E1, 13:05–14:35 E1, D. Smetanová
MAT_z/P01: Wed 9:40–11:10 B2, J. Vysoká
MAT_z/S01: Tue 11:25–12:55 A6, Thu 8:00–9:30 A6, J. Vysoká
MAT_z/S02: Tue 16:30–18:00 A6, Wed 8:00–9:30 A4, J. Vysoká
MAT_z/S03: Wed 11:25–12:55 A7, Fri 8:00–9:30 B4, K. Papoušková
MAT_z/S05: Thu 8:00–9:30 A5, Fri 11:25–12:55 B4, K. Papoušková
Prerequisites
The student masters the range of secondary school mathematics or the ZAM course.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives supported by learning outcomes
The aim of this course is to provide the students with the basic knowledge of algebra, differential and integral calculus of functions of one variable needed in the study of specialized subjects. Then the aim is also to provide and clarify the main methods and algorithms.
Learning outcomes
After the successful completing of the course, the student solves basic tasks of the course (counting with vectors, matrices and determinants, solving systems of linear equations, properties and graphs of elementary functions, calculation of limits and function derivation, investigating of function process, counting of primitive functions, idefinite integral, the direct method, per-partes, substitution method, calculation of definite integrals and content of a plane figure) individually.
Syllabus
  • 1. Vector, vector space, equality of vectors, counting with the vectors, linear combinations of vectors, linear dependence and independence of vectors, basis and dimension of vector space, scalar product of vectors. 2. Matrices, rank of matrices, matrix addition and multiplication, inverse matrix, Frobenius theorem, solving systems of linear equations using Gaussian method. 3. Determinants, Cramer's rule. 4. Functions of one real variable, domain and field of functional values, basic algebraic functions and non-algebraic. Properties of logarithms. 5. Inverse functions, even and odd functions, inverse trigonometric functions. 6. Limit of function 7. Derivative function, basic rules for derivate, derivative compound function, function graph tangent. Differential of the function and its application in technical practice. 8. L'Hospital's rule. The importance of first and second derivative for the function course (increasing, decreasing, convex, concave, local extrema and inflection points). The local extremes in technical exercises. 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral and infinite integral. 13. Aplications of definite integrals (e.g., calculation of a plane figure).
Literature
    required literature
  • DOŠLÁ, Zuzana a LIŠKA, Petr. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. 1. vydání. Praha: Grada Publishing, 2014. 304 stran. Expert. ISBN 978-80-247-5322-5.
  • CHLÁDEK, Petr. Matematika I : studijní opora pro kombinované studium. 1. vyd. České Budějovice: Vysoká škola technická a ekonomická v Českých Budějovicích, 2012, 44 pp. ISBN 978-80-7468-004-5. info
    recommended literature
  • Higher Mathematics for Engineers and Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
  • CHARVÁT, Jura, Václav KELAR and Zdeněk ŠIBRAVA. Matematika 2 : sbírka příkladů. 2. vyd. V Praze: České vysoké učení technické, 2012, 206 pp. ISBN 978-80-01-04989-1. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika I : pro porozumění i praxi : netradiční výklad tradičních témat vysokoškolské matematiky. 2., dopl. vyd. Brno: VUTIUM, 2009, 339 pp. ISBN 978-80-214-3631-2. Obsah info
  • KAŇKA, Miloš. Sbírka řešených příkladů z matematiky : pro studenty vysokých škol. Vyd. 1. Praha: Ekopress, 2009, 298 s. ISBN 978-80-86929-53-8. Obsah info
Forms of Teaching
Lecture
Seminar
Tutorial
Consultation
Teaching Methods
Frontal Teaching
Group Teaching - Cooperation
Group Teaching - Collaboration
Critical Thinking
Teaching Supported by Multimedia Technologies
Student Workload
ActivitiesNumber of Hours of Study Workload
Daily StudyCombined Study
Preparation for Seminars, Exercises, Tutorial70122
Preparation for the Final Test3434
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion5226
Total:182182
Assessment Methods and Assesment Rate
Exam – oral 70 %
activity during seminars 30 %
Exam conditions
Grading of the course: Activity during seminar: maximum 30% (0-30 points), Final Test: maximum 70% (0-70 points).

Successful graduates of the course have to get totally at least 70 points: A 100 – 90, B 89,99 – 84, C 83,99 – 77, D 76,99 – 73, E 72,99 – 70, FX 69,99 – 30, F 29,99 - 0.

Language of instruction
Czech
Follow-Up Courses
Teacher's information
Attendance in lessons is defined in a separate internal standard of ITB (Evidence of attendance of students at ITB). It is compulsory, except of the lectures, for full-time students to attend 70 % lesson of the subjet in a semester.
The course is also listed under the following terms winter 2016, winter 2017, summer 2018, winter 2018, summer 2019, winter 2020, summer 2021, winter 2021, summer 2022, winter 2022, winter 2023, summer 2024, winter 2024.
  • Enrolment Statistics (winter 2019, recent)
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