MAT_1 Mathematics I

Institute of Technology and Business in České Budějovice
summer 2018
Extent and Intensity
2/2/0. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Dana Smetanová, Ph.D. (seminar tutor)
Guaranteed by
Ing. Jaroslav Staněk, DiS.
Study Department – Vice-Rector for Study Affairs – 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_1/CCV1: Fri 6. 4. 8:00–12:10 D516, Fri 20. 4. 8:00–12:10 D516, Fri 4. 5. 8:00–12:10 D516, D. Smetanová
MAT_1/CCV2: Sat 17. 3. 8:00–12:55 D416, Sat 14. 4. 13:05–16:20 D415, D. Smetanová
Prerequisites
OBOR(CAP)
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.
The capacity limit for the course is 1998 student(s).
Current registration and enrolment status: enrolled: 0/1998, only registered: 0/1998
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. 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. 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). 9. The primitive function, indefinite integral, direct integration. 10. The method of integration by-partes. 11. Substitution method. 12. Definite integral. 13. Calculation of a plane figure.
Literature
    required literature
  • Kaňka, M., Coufal, J., Klůfa, J., Učebnice matematiky pro ekonomy, Praha, Ekopress, 2007, 198 stran, ISBN 978-80-86929-24-8
    recommended literature
  • Charvát, J., Kelar, V., Šibrava, Z., Matematika 1, Sbírka příkladů, Česká technika - nakladatelství ČVUT, 2005, 1. vydání, ISBN 80-01-03323-6
  • Mathematics I / Neustupa Jiří. -- 2. přeprac. vyd. -- Praha : Vydavatelství ČVUT, 2004. -- 141 s. : il.
  • Higher Mathematics For Engineers And Physicists, Ivan Sokolnikoff and Elizabeth Sokolnikoff, 537 pp, http://www.freebookcentre.net/Mathematics/Basic-Mathematics-Books.html
  • 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
  • KLŮFA, Jindřich and Jan COUFAL. Matematika 1. Vyd. 1. Praha: Ekopress, 2003, 222 s. ISBN 80-86119-76-9. info
  • DEMIDOVIČ, Boris Pavlovič. Sbírka úloh a cvičení z matematické analýzy. 1. vyd. Havlíčkův Brod: Fragment, 2003, 460 s. ISBN 80-7200-587-1. 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 Lectures26 
Preparation for Seminars, Exercises, Tutorial2678
Preparation for the Final Test2626
Attendance on Lectures26 
Attendance on Seminars/Exercises/Tutorial/Excursion2626
Total:130130
Assessment Methods and Assesment Rate
Exam – written 70 %
activity during seminar 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
Further comments (probably available only in Czech)
The course is taught each semester.
Teacher's information
https://is.vstecb.cz/auth/do/5610/skripta/678006/1681523/682566/Matematika_I.pdf
The course is also listed under the following terms Summer 2007, Winter 2007, Summer 2008, Winter 2008, Summer 2009, Winter 2009, Summer 2010, Winter 2010, summer 2011, winter 2011, summer 2012, winter 2012, summer 2013, winter 2013, summer 2014, winter 2014, summer 2015, winter 2015, Summer 2016, winter 2016, summer 2017, winter 2017, winter 2018, summer 2019, winter 2019, winter 2020.
  • Enrolment Statistics (summer 2018, recent)
  • Permalink: https://is.vstecb.cz/course/vste/summer2018/MAT_1