Course detail
Mathematical Analysis II
FSI-SA2 Acad. year: 2019/2020 Summer semester
The course Mathematical Analysis II is directly linked to the introductory course Mathematical Analysis I. It concerns differential and integral calculus of functions in several real variables. Students will acquire the theoretical background that is necessary in solving some particular problems in mathematics as well as in technical disciplines.
Language of instruction
Czech
Number of ECTS credits
8
Supervisor
Department
Learning outcomes of the course unit
Application of several variable calculus methods in physical and technical problems.
Prerequisites
Mathematical Analysis I, Linear Algebra.
Planned learning activities and teaching methods
The course is lectured through lessons supported by exercises. The content of lessons is focused on a theoretical background of the subject. The exercises have a practical/computational character.
Assesment methods and criteria linked to learning outcomes
Course-unit credit: active attendance at the seminars, successful passing through two written tests (i.e. receiving at least one half of all possible points from each of them).
Exam: will have both a written part as well as an oral part, the condition for admission to the oral part is receiving at least one half of all possible points from the written part).
Aims
Students should get familiar with basics of differential and integral calculus in several real variables. With such knowledge, various tasks of physical and engineering problems can be solved.
Specification of controlled education, way of implementation and compensation for absences
Seminars: obligatory.
Lectures: recommended.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Type of course unit
Lecture
52 hours, optionally
Teacher / Lecturer
Syllabus
1. Metric spaces, convergence in a metric space;
2. Complete and compact metric spaces, mappings between metric spaces;
3. Function of several variables, limit and continuity;
4. Partial derivatives, directional derivative, gradient;
5. Total differential, Taylor polynomial;
6. Local and global extrema;
7. Implicit functions, smooth mappings from R^n to R^m;
8. Extrema subject to constraints, double integral;
9. Triple integral, alternative approach to multiple integrals;
10. Substitution in a double and a triple integral, applications;
11. Plane and space curves, line integrals, Green's theorem;
12. Path independence for the line integrals and related notions, space surfaces;
13. Surface integrals, Gauss-Ostrogradsky's theorem and Stokes' theorem.
Exercise
33 hours, compulsory
Teacher / Lecturer
Syllabus
Seminars are related to the lectures in the previous week.
Computer-assisted exercise
6 hours, compulsory
Syllabus
This seminar is supposed to be computer assisted.