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Course detail
Mathematics I
Course unit code:  FSI1M  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  1  
Semester:  winter  
Number of ECTS credits:  9  



























Type of course unit:
Lecture:  52 hours, optionally 

Teacher / Lecturer:  doc. RNDr. Jan Čermák, CSc. prof. RNDr. Miroslav Doupovec, CSc., dr. h. c. prof. RNDr. Jan Franců, CSc. prof. Aleksandre Lomtatidze, DrSc. doc. RNDr. Jiří Tomáš, Dr. 
Syllabus:  Week 1: Basics of mathematical logic and set operations, matrices and determinants (transposing, adding, and multiplying matrices, common matrix types). Week 2: Matrices and determinants (determinants and their properties, regular and singular matrices, inverse to a matrix, calculating the inverse to a matrix using determinants), systems of linear algebraic equations (Cramer's rule, Gauss elimination method). Week 3: More about systems of linear algebraic equations (Frobenius theorem, calculating the inverse to a matrix using the elimination method), vector calculus (operations with vectors, scalar (dot) product, vector (cross) product, scalar triple (box) product). Week 4: Analytic geometry in 3D (problems involving straight lines and planes, classification of conics and quadratic surfaces), the notion of a function (domain and range, bounded functions, even and odd functions, periodic functions, monotonous functions, composite functions, onetoone functions, inverse functions). Week 5: Basic elementary functions (exponential, logarithm, general power, trigonometric functions and cyclometric (inverse to trigonometric functions), polynomials (root of a polynomial, the fundamental theorem of algebra, multiplicity of a root, product breakdown of a polynomial), introducing the notion of a rational function. Week 6: Sequences and their limits, limit of a function, continuous functions. Week 7: Derivative of a function (basic problem of differential calculus, notion of derivative, calculating derivatives, geometric applications of derivatives), calculating the limit of a function using L' Hospital rule. Week 8: Monotonous functions, maxima and minima of functions, points of inflection, convex and concave functions, asymptotes, sketching the graph of a function. Week 9: Differential of a function, Taylor polynomial, parametric and polar definitions of curves and functions (parametric definition of a derivative, transforming parametric definitions into polar ones and vice versa). Week 10: Primitive function (antiderivative) (definition, properties and basic formulas), integrating by parts, method of substitution. Week 11: Integrating rational functions (no complex roots in the denominator), calculating a primitive function by the method of substitution in some of the elementary functions. Week 12: Riemann integral (basic problem of integral calculus, definition and properties of the Riemann integral), calculating the Riemann integral (Newton' s formula). Week 13: Applications of the definite integral (surface area of a plane figure, length of a curve, volume and lateral surface area of a rotational body), improper integral. 
seminars:  44 hours, compulsory 
Teacher / Lecturer:  Mgr. Jaroslav Cápal Mgr. Monika Dosoudilová, Ph.D. Ing. Milan Hnízdil, Ph.D. Mgr. Jana Hoderová, Ph.D. Ing. Tomáš Holec Ing. Jaromír Hošek Ing. Pavel Hrabec RNDr. Jiří Klaška, Dr. Ing. Lukáš Kokrda Ing. Barbora Kopečková prof. Aleksandre Lomtatidze, DrSc. Ing. Barbora Navrátilová Mgr. Jan Pavlík, Ph.D. RNDr. Radovan Potůček, Ph.D. Mgr. Viera Štoudková Růžičková, Ph.D. Ing. Jan Šútora doc. RNDr. Jiří Tomáš, Dr. Mgr. Jitka Zatočilová, Ph.D. 
Syllabus:  The first week will be devoted to revision of knowledge gained at secondary school. Following weeks: seminars related to the lectures given in the previous week. 
seminars in computer labs:  8 hours, compulsory 
Teacher / Lecturer:  prof. RNDr. Miroslav Doupovec, CSc., dr. h. c. 
Syllabus:  Seminars in a computer lab have the programme MAPLE as a computer support. Obligatory topics to go through: Elementary arithmetic, calculations and evaluation of expressions, solving equations, finding roots of polynomials, graph of a function of one real variable, symbolic computations. 