Course code:  AMA 
Course title in language of instruction:  Aplikovaná matematika I 
Course title in Czech:  Aplied Mathematics I 
Course title in English:  Aplied 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, 3/2 (hours of lectures per week / hours of seminars per week) 
Language of instruction:  Czech 
Level of course:  bachelor 
Semester:  WS 2019/2020 
Name of lecturer:  doc. Ing. Mgr. Jitka Janová, Ph.D. (supervisor) RNDr. Dana Říhová, Ph.D. (examiner, instructor, lecturer) 
Prerequisites:  Physical Principles of Engineering Technologies or now Physical Principles of Engineering Technologies 

Aims of the course: 
Achieving the level of mathematical knowledge, strenghening mathematical skills and development of logical thinking.
Mastery of mathematical tools necessary to formulate and solve real problems.
Obtaining mathematical knowledge needed for applications in professional cources and other separate knowledge gathering by studying professional literature. 

Course contents: 
1.  Introduction (allowance 1/1)   a.  Set theory  b.  Propositional calculus 
 2.  Differential calculus (allowance 12/9)   a.  Function, basis concepts and properties  b.  Sequences  c.  Limit and continuity of function  d.  Derivative of function  e.  Applications of derivatives and curve sketching 
 3.  Integral calculus (allowance 10/7)   a.  Indefinite integral  b.  Definite integral and its applications  c.  Improper integral 
 4.  Linear algebra (allowance 12/7)   a.  Vectors. Linear dependence and independence of vectors. Vector space  b.  Matrices and determinants  c.  Systems of linear equations 
 5.  Polynomial approximation (allowance 7/4)   a.  Solution of algebraic equations  b.  Taylors polynomial, Lagranges interpolation formula  c.  Least square method 



Learning outcomes and competences: 
Generic competences:     Ability to apply knowledge    Ability to make decisions    Ability to solve problems    Ability to work independently    Basic computing skills 
 Specific competences:     Student is able to describe properties of one variable function and analyze it. Furthermore, from graph derivate their properties.    Student is able with using limit and integration methods solve improper integral.    Student knows approximate function with least square method.    Student knows how to use operations with matrices and determinants for solving of systems of linear and matrix equations.    Student knows to use derivatives for finding of extreme function values, i.e. its minimums and maximums.    Student knows with use of definite integral calculate surface area and volume of rotate solids. 


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  42 h  practice  28 h  Selfstudy  preparation for exam  40 h  preparation for regular assessment  10 h  preparation for regular testing  20 h  Total  140 h 


Assessment methods: 
The exam is written and consists of two parts: computerbased test and a written exam. To pass the exam, it is necessary to get at least 50% in each part.


Recommended reading: 
Type  Author  Title  Published in  Publisher  Year  ISBN 

RQ  RÁDL, P.  ČERNÁ, B.  STARÁ, L.  Základy vyšší matematiky   Mendelova univerzita v Brně  2014  9788075091109  RQ  ČERNÁ, B.  RÁDL, P.  AMA 1 oboru ARI  eLearningová opora      RE  DOŠLÁ, Z.  LIŠKA, P.  Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách  Praha  Grada  2014  9788024753225  RE  RÁDL, P.  MOUČKA, J.  Matematika pro studenty ekonomie, 2., upravené a doplněné vydání  Praha  Grada  2015  9788024754062  RE  ČERNÁ, B.  Matematika  lineární algebra  Brno  Mendelova zemědělská a lesnická univerzita v Brně  2007  9788073750800  RE   Thomas' calculus  Boston  Pearson  2016  9781292089799  RE   Applied calculus  Boston, MA  Brooks/Cole, Cengage Learning  2013  9781133103936 
