MUC12 Mathematical Analysis 2

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 4 credit(s). Type of Completion: zk (examination).
Taught in person.
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Zuzana Došlá, DSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
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 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.
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.
  • Numeber series.
  • Basic problems of finantial matematics.
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. Reimannův integrál. 1. vyd. Praha: Státní pedagogické nakladatelství, 1988. 84 s. info
  • JARNÍK, Vojtěch. Integrální počet (I). 5. vyd. Praha: Academia, 1974. 243 s. info
  • DOŠLÁ, Zuzana and Vítězslav NOVÁK. Nekonečné řady. 3. vyd. Brno: Masarykova univerzita, 2013. iv, 113. ISBN 9788021064164. info
Teaching methods
Lectures and group-exercices. The project working.
Assessment methods
One written test and the group project . Exam in both oral and written form. Subjects of projects: 1 History of the integration 2 Numerical integration 3 Theorems of Pappus 4 Applications in biology and chemistry 5 Applications in physics 6 Applications in probability and economics
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2020, Spring 2021.
  • Enrolment Statistics (Spring 2022, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2022/MUC12