Course title  Mathematical Analysis IV 

Course code  MU/01004 
Organizational form of instruction  Lecture 
Level of course  Bachelor 
Year of study  not specified 
Semester  Summer 
Number of ECTS credits  5 
Language of instruction  Czech 
Status of course  Compulsory 
Form of instruction  Facetoface 
Work placements  This is not an internship 
Recommended optional programme components  None 
Course availability  The course is available to visiting students 
Lecturer(s) 


Course content 
1. Riemann integral (divisions, null sets, oscillation, Lebesgue Theorem on Riemann integral, Fubini Theorem, partition of unity, change of variables in integral). 2. Differential forms (tensors, antisymmetric tensors, differential forms, exterior differential). 3. Stokes Theorem (chains, integral over a chain, Stokes Theorem for chains, manifolds, tangent space, orientation, Stokes Theorem for manifolds, theorems on rotor and on divergence). 4. Elements of comlex analysis (functions of one comlex variable, derivative and integral for such functions, Cauchy formula, residues). 5. Ordinary differential equations (Theorem on existence and uniqueness of the solution, methods of solutions, linear equations).

Learning activities and teaching methods 
unspecified 
Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Branch of study Category  Recommended year of study  Recommended semester 

Mathematical Institute in Opava  Mathematics (2014IVT)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Mathematics (1IVT)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Mathematics (2014F)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Mathematics (2F)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Applied Mathematics (2014F)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Applied Mathematics (2014IVT)  Mathematics courses  2  Summer 
Mathematical Institute in Opava  Mathematical Analysis (1IVT)  Mathematics courses  2  Summer 