Detail předmětu

Mathematics 2

FAST-BAA023-AAk. rok: 2026/2027

Jazyk výuky

angličtina

Počet kreditů

5

Garant předmětu

doc. Ing. Vladislav Kozák, CSc.

Zajišťuje ústav

Ústav matematiky a deskriptivní geometrie (MAT)

Nabízen zahraničním studentům

Všech fakult

Pravidla hodnocení a ukončení předmětu

During the semester, students take 2 written tests, each lasting 45 minutes. The condition for awarding credit is to achieve a total of at least 40% points, the assessment from the exercises is not transferred to the exam assessment. The condition for passing the exam is a minimum of 50% of points from the written exam according to the ECTS scale of the BUT Study and Examination Regulations. In the event of ambiguity in the exam assessment, the examiner may also require an oral exam. 

Učební cíle

Professional knowledge
  • After becoming familiar with the basic concepts of differential calculus of functions of two variables, or more variables, the student is able to navigate in specialized subjects of physical focus. Understanding partial derivatives, total differential or gradient is necessary to acquire the basics of higher mathematics for technical universities.
Professional skills
  • The student will understand the basic concepts of integral calculus of functions of several variables and some applications using integrals such as applications for the length of a curve, work with a generally defined curve, moments, etc. Knowledge in the area of ​​analytical solution of differential equations is crucial.
Competence
  • Familiarity with the presented teaching structure will enable students to orient themselves in the geometric and physical meaning of the mentioned issue. The concept of gradient or directional derivatives will expand the technical imagination of students.

Základní literatura

Larson, R.- Hostetler, R.P., Edwards, B.H.: Calculus (with Analytic Geometry). Brooks Cole 2005. (EN)
tein, S. K, Calculus and analytic geometry. New York 1989. (EN)

Doporučená literatura

Bhunia, S. C., Pal, S.: Engineering Mathematics. Oxford University Press 2015. (EN)
Serge L., Calculus of Several Variables, Springer 2012. (EN)

Zařazení předmětu ve studijních plánech

  • Program BPA-SIS bakalářský 1 ročník, letní semestr, povinný

Typ (způsob) výuky

 

Přednáška

26 hod., nepovinná

Vyučující / Lektor

doc. Ing. Vladislav Kozák, CSc.

Osnova

The lectures are divided into three thematic blocks, each block is presented by mostly 4 lectures:

  1. Definite integral of one variable, applications.
  2. Real function of several variables. Basic concepts, composite function. Limit and continuity. Partial derivative.
  3. Partial derivatives of a composite function, partial derivatives of higher orders. Directional derivatives, gradient. Total differentials.
  4. Taylor polynomial. Space curve, tangent vector of a curve. Tangent plane and normal to a surface. Local extrema of a function of two variables.
  5. Bound extrema, use of Lagrange multipliers. Global extrema of a function of two variables. Implicit functions of one and two variables.
  6. Double integral, calculation, properties. Calculation according to Fubini's theorem and using transformations (polar coordinates).
  7. Transformation and application of double integral. Example of the triple integral,.
  8. Line integral in a scalar field. Vector field, divergence, rotation. Line integral in a vector field.
  9. Work, circulation, Green's theorem. Independence of the curve integral on the integration path. Potential.
  10. Ordinary differential equations (ODE), basic concepts. First-order equations, separated.
  11. First-order equations, linear (and exact). Homogeneous DE of nth order.
  12. Homogeneous linear DE with constant coefficients, Wronskian.
  13. Inhomogeneous DE with special right-hand side and constant variation method. Application of DE in technical practice, boundary problems.

Cvičení

26 hod., povinná

Vyučující / Lektor

doc. Ing. Vladislav Kozák, CSc.

Osnova

The structure of the exercises corresponds to the lecture blocks. The last week is dedicated to completing the material and repeating some more demanding topics, such as differential equations. During the course, the student takes 2 tests. The recommended test duration is 45 minutes, the second teaching hour is dedicated to continuing the teaching.

  1. Definite integral of one variable.
  2. Domain of definition, partial derivative of a function of several variables.
  3. Directional derivatives, gradient. Partial derivatives of a composite function of several variables. Total differential and its meaning.
  4. Taylor polynomial, Normal and tangent plane. Local extrema...
  5. Bound and global extrema. Implicit functions.
  6. Recalling complex numbers. Test 1.
  7. Calculation of double integral. Transformation of double integral and applications. Example of calculation of the triple integral.
  8. Calculation of the curve integral in a scalar field. Calculation of the curve integral in a vector field.
  9. Applications, work, circulation, Green's theorem and its applications. Independence of the curve integral on the integration path. Potential.
  10. First-order DE, separated, linear.
  11. Test 2. Homogeneous DE of nth order.
  12. Inhomogeneous DE with special right side.
  13. Method of variation of constants. Credit.

Individuální příprava na ukončení

52 hod., nepovinná

Vyučující / Lektor

doc. Ing. Vladislav Kozák, CSc.

Samostudium

26 hod., nepovinná

Vyučující / Lektor

doc. Ing. Vladislav Kozák, CSc.