Course syllabus AMA - Aplied Mathematics I (FBE - WS 2017/2018)

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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: full-time, 3/2 (hours of lectures per week / hours of seminars per week)
Language of instruction: Czech
Level of course: bachelor
Semester: WS 2017/2018
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
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 methodDaily attendance
Direct teaching
     lecture42 h
     practice28 h
     preparation for exam40 h
     preparation for regular assessment10 h
     preparation for regular testing20 h
Total140 h
Assessment methods:
The exam is written and consists of two parts: computer-based test and a written exam. To pass the exam, it is necessary to get at least 50% in each part.

Recommended reading:
TypeAuthorTitlePublished inPublisherYearISBN
RQRÁDL, P. -- ČERNÁ, B. -- STARÁ, L.Základy vyšší matematikyBrnoMendelova univerzita v Brně2014978-80-7509-110-9
RQČERNÁ, B. -- RÁDL, P.AMA 1 oboru ARI - eLearningová opora
REDOŠLÁ, Z. -- LIŠKA, P.Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách978-80-247-5322-5
RERÁDL, P. -- MOUČKA, J.Matematika pro studenty ekonomie, 2., upravené a doplněné vydáníPrahaGrada2015978-80-247-5406-2
REČERNÁ, B.Matematika - lineární algebraBrnoMendelova zemědělská a lesnická univerzita v Brně2007978-80-7375-080-0
REThomas' calculus978-1-292-08979-9
REApplied calculusBoston, MABrooks/Cole, Cengage Learning2013978-1-133-10393-6


Last modification made by Ing. Jiří Gruber on 05/15/2017.

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