Course detail

Mathematical Analysis 2

FIT-IMA2Acad. year: 2027/2028

Series. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.

Language of instruction

Czech, English

Number of ECTS credits

4

Assignment to study programme types

Bachelor's

Mode of study

Not applicable.

Guarantor

doc. Mgr. Veronika Novotná, Ph.D.

Department

Department of Quantitative Engineering (ÚKI)

Entry knowledge

The IMA1 course.

Rules for evaluation and completion of the course

Requirements for awarding credit:

Passing control tests and achieving at least 50% of points or completing a comprehensive written paper and achieving at least 50% of points.
Awarding credit is a necessary condition for taking the exam.

Exam requirements:

The exam is written.

For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory) and the student does not proceed to the oral part.

If the student does not achieve at least 50% of the total number of achievable points in the written paper, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).

Completion of the course for students with individual study:
Passing the comprehensive control test and achieving at least 55% of points.
Awarding credit is a necessary condition for taking the exam.
The exam is written.
For all tasks in the written part, a calculation must be written, or the procedure described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory).
If the student does not achieve at least 50% of the total number of achievable points in the written work, the written part and the entire exam are graded "F".

Participation in seminars is checked.

Aims

The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems and the ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.

Study aids

Not applicable.

Prerequisites and corequisites

Basic literature

Čermák, J., Nechvátal, L., Matematika III, skripta FSI VUT Brno, 2024 (CS)
Jirásek, F., Čipera, S., Vacek, M., Sbírka řešených příkladů z matematiky I, SNTL Praha 1986 (CS)
Karásek, J., Matematika II, skripta FSI VUT Brno, 2002 (CS)
Rektorys, K., Přehled užité matematiky, Prometheus, Praha 2000. (CS)

Recommended reading

Dalík, J., Matematika, Numerické metody, skripta FAST VUT Brno 2007, Nakladatelství VUT Brno (CS)
Dineen, Sean (University College of Dublin, Irela), Functions of Two Variables 2 000, Taylor & Francis Inc,, ISBN/EAN 978-15-848-8190-2 / 978-15-848-8190-2 (EN)
Kufner, A., Obyčejné diferenciální rovnice, ZČU Plzeň, 1993 (CS)
Serge Lang, Calculus of Several Variables, 2012, Springer, ISBN-13: 978-14-612-7001-0 (EN)
Slovák, J., Panák, M., Bulant, M., Matematika drsně a svižně, MU Brno 2013, ISBN 978-80-210-6307-5 (CS)
Škrášek, J., Tichý Z., Základy aplikované matematiky II, Praha SNTL 1986. (CS)

Classification of course in study plans

  • Programme BIT Bachelor's 2 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
  • Programme BIT Bachelor's 2 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
  • Programme IT-CZV-1 Lifelong learning 1 year of study, winter semester, elective

Type of course unit

 

Lecture

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

  1. Number series.
  2. Power series.
  3. Fourier series.
  4. Differential calculus of functions of several variables I: limit, continuity, partial derivatives, Schwarz theorem.
  5. Differential calculus of functions of several variables II: differential, tangent plane, Taylor polynomial.
  6. Differential calculus of functions of more variables III: local extrema, Hess matrix, Sylvester criterion.
  7. Integral calculus of functions of several variables I (particularly in 2 and 3 dimensions): definitions and basic concepts.
  8. Integral calculus of functions of several variables II: multidimensional and multiple integrals, Fubini theorem.
  9. Integral calculus of functions of several variables III: evaluation and applications of double and triple integrals.
  10. Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable and linear equations.
  11. Numerical solution of differential equations of the first order.

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Syllabus

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Self-study

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.

Individual preparation for an ending of the course

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Veronika Novotná, Ph.D.