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Course detail
Mathematics II
Course unit code:  FSI2M  

Academic year:  2016/2017  
Type of course unit:  compulsory  
Level of course unit:  Bachelor's (1st cycle)  
Year of study:  1  
Semester:  summer  
Number of ECTS credits:  8  



























Type of course unit:
Lecture:  39 hours, optionally 

Teacher / Lecturer:  doc. RNDr. Jan Čermák, CSc. prof. RNDr. Miroslav Doupovec, CSc., dr. h. c. doc. Mgr. Pavel Řehák, Ph.D. doc. Ing. Jiří Šremr, Ph.D. 
Syllabus:  Week 1: Functions in more variables: basic definitions, limit of a function, continuous functions, partial derivative. Week 2: Higherorder partial derivatives, gradient of a function, derivative in a direction, firstorder and higherorder differentials, tangent plane to the graph of a function in two variables. Week 3: Taylor polynomial, local maxima and minima of functions in several variables. Week 4: Relative maxima and minima, absolute maxima and minima. Week 5: Functions defined implicitly. Week 6: Double and triple integral, Fubini's theorem: calculation on normal sets. Week 7: Substitution theorem, cylindrical a spherical coordinates. Week 8: Applications of double and triple integrals. Week 9: Curves and their orientations, firsttype line integral and its applications. Week 10: Secondtype line integral and its applications, Green's theorem. Week 11: Line integrals independent of the integration path, potential, the nabla and delta operators, divergence and curl of a vector field. Week 12: Surfaces (parametric equations, orienting of a surface), firsttype surface integral and its applications. Week 13: Secondtype surface integral and its applications, Gauss' theorem and Stokes' theorem. 
seminars:  44 hours, compulsory 
Teacher / Lecturer:  Mgr. Jaroslav Cápal doc. RNDr. Jan Čermák, CSc. prof. RNDr. Jan Franců, CSc. Mgr. Jana Hoderová, Ph.D. doc. Mgr. Jaroslav Hrdina, Ph.D. RNDr. Ludmila Chvalinová, CSc. RNDr. Jiří Klaška, Dr. prof. Aleksandre Lomtatidze, DrSc. Mgr. Aleš Návrat, Ph.D. Ing. Barbora Navrátilová doc. Mgr. Zdeněk Opluštil, Ph.D. Mgr. Jan Pavlík, Ph.D. RNDr. Radovan Potůček, Ph.D. Mgr. Jana Procházková, Ph.D. doc. Mgr. Pavel Řehák, Ph.D. Mgr. Viera Štoudková Růžičková, Ph.D. doc. RNDr. Jiří Tomáš, Dr. Mgr. Jitka Zatočilová, Ph.D. 
Syllabus:  The first week: calculating improper integrals, applications of the Riemann integral. 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: Plotting of the graph of a function of more variables (given by explicit, implicit or parametric equations), extrema of functions of more variables. 