MUC12 Mathematical Analysis 2

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
Mgr. Ondřej Suchánek (seminar tutor)
Bc. Tomáš Škaryd (assistant)
Guaranteed by
Mgr. Petr Liška, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Tue 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
MUC12/01: Mon 19. 2. to Sun 26. 5. Wed 12:00–13:50 M2,01021, O. Suchánek
MUC12/02: Mon 19. 2. to Sun 26. 5. Fri 8:00–9:50 M6,01011, O. Suchánek
MUC12/03: Mon 19. 2. to Sun 26. 5. Fri 12:00–13:50 M6,01011, P. Liška
Prerequisites
Knowledge of the differential calculus in one variable is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives
The main objective is to understand basic notions, results, and techniques of computations and applications in the theory of integrals of one-variable functions.
After passing the course, the student will be able:
to define and interpret the basic notions in the theory of both definite and indefinite integrals:
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques of integrating one variable functions;
to apply acquired pieces of knowledge for the solution of specific problems, mainly in geometry and physics. Another objective is to understand some basic facts and properties of number series and function series, power series especially.
Learning outcomes
After passing the course, the student will be able:
to define and interpret the basic notions in theory of both definite and undefinite integrals:
to formulate relevant mathematical theorems and statements and to explain methods of their proofs;
to use effective techniques of integratring one variable functions;
to apply acquired pieces of knowledge for the solution of specific problems, mainly in geometry and physics.
Syllabus
  • Sequences, differential of a function, Taylor's theorem. Primitive function. Basic integration methods. Integrals of rational, trigonometric and some irrational functions. Riemann definite integral and its geometric applications. Improper integrals.
  • Number series and power series.
  • Basic problems of financial mathematics.
Literature
  • DOŠLÝ, Ondřej and Petr ZEMÁNEK. Integrální počet v R (Integral Calculus in R). 1. vydání. Brno: Masarykova univerzita, 2011, 222 pp. ISBN 978-80-210-5635-0. info
  • Kuben, Jaromír - Hošková, Šárka - Račková, Pavlína. Integrální počet funkcí jedné proměnné; VŠB-TU Ostrava, elektronický text vytvořený v rámci projektu CZ.04.1.03/3.2.15.1/0016 ESF ČR. Dostupné z: http://homel.vsb.cz/~s1a64/cd/pdf/print/ip.pdf.
  • NOVÁK, Vítězslav. Integrální počet v R. 2. vyd. Brno: Masarykova univerzita, 1994, 148 s. ISBN 8021009918. info
  • DULA, Jiří and Jiří HÁJEK. Cvičení z matematické analýzy : Riemannův integrál. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1988, 84 s. info
  • Integrální počet. Edited by Vojtěch Jarník. Vyd. 5. nezměn. Praha: Academia, 1974, 243 s. URL info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. 3. vyd. Brno: Masarykova univerzita, 2013, iv, 113. ISBN 9788021064164. info
Teaching methods
Lectures and group exercises.
Assessment methods
Either homework or two written tests. Exam in both oral and written form.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.
  • Enrolment Statistics (Spring 2024, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2024/MUC12