Course code:  MT1A 
Course title in language of instruction:  Mathematics I 
Course title in Czech:  Mathematics I 
Course title in English:  Mathematics I 
Mode of completion and number of credits:  Exam (5 credits) (1 ECTS credit = 28 hours of workload) 
Mode of delivery/Timetabled classes:  fulltime, 2/2 (hours of lectures per week / hours of seminars per week) 
Language of instruction:  English 
Level of course:  bachelor 
Semester:  WS 2017/2018 
Name of lecturer:  RNDr. Karel Mikulášek, Ph.D. (supervisor) 
Prerequisites:  not Aplied Mathematics I 

Aims of the course: 
Students should get an understanding of the basic concepta and methods of linear algebra and calculus. Solving suitable problems at workhops, they will prepare to tackle simple mathematical problems they may come across in practice. 

Course contents: 
1.  Linear algebra (allowance 8/8)   a.  Vector spaces  b.  Matrices  c.  Determinants  d.  Systems of linear equations  e.  Matrix algebra 
 2.  Calculus (allowance 14/14)   a.  Functions, properties of functions, parametric functions  b.  Limits of functions, continuous functions  c.  Derivatives of functions, methods of differentiating  d.  Applications of derivatives, sketching the graph of a function  e.  Sequences, power series 
 3.  Integral calculus (allowance 6/6)   a.  Rieman integral, antiderivative  b.  Integration rules  c.  Applications of integrals 



Learning outcomes and competences: 
Generic competences:     ability to apply knowledge    ability to solve problems    ability to work independently    basic computing skills    general knowledge 
 Specific competences:     Student is able to describe properties of function and analyze it. Furthermore, from graph derivate their properties.    Student knows how to use operations with matrices and determinants for solving of systems of linear and matrix equations.    Student knows to calculate limits and derivatives of one variable functions and interpret it on function graphs.    Student knows to use derivatives for finding of extreme function values, i.e. its minimums and maximums.    Student will acquire properties and operations with matrices and determinants. This knowledge is necessary for solving of linear programming problems. 


Type of course unit:  required 
Year of study:  Not applicable  the subject could be chosen at anytime during the course of the programme. 
Work placement:  There is no compulsory work placement in the course unit. 
Recommended study modules:   

Learning activities and study load (hours of study load): 
Type of teaching method  Daily attendance  Direct teaching  lecture  28 h  practice  28 h  seminar  0 h  Selfstudy  preparation for exam  36 h  preparation for regular assessment  12 h  preparation for regular testing  36 h  elaboration and execution of projects  0 h  Total  140 h 


Assessment methods: 
At midterm, in a written test, students are required to submit solutions to several practical problems for them to see the improvement needed. To complete the course a written test consisting of practical and theoretical parts is required. In the practical part, students have to solve 3 to 4 problems and, in the theoretical part, to give correct answers to 3 to 4 questions to see whether they have a good understanding of the background theory. The points obtained in both parts are then added. To pass the examination, a student has to achieve at least 50 percent of the total number of points. 

Recommended reading: 
Type  Author  Title  Published in  Publisher  Year  ISBN 

RQ  BENCE, S.  HOBSON, M.  RILEY, K.  Mathematical Methods For Physics and Engineering  Cambridge  Cambridge University Press  2006  9780521861533  RQ  LANG, S.  A Firtst Course in Calculus  New York  Springer Verlag  1993  0387962018  RQ  STROUD, K.  Engineering Mathematics  New York  Palgrave acmillan  2001  9781403942463 
