Mathematics B3 - MS710P16
Title: Matematika B3
Czech title: Matematika B3
Guaranteed by: Institute of Applied Mathematics and Information Technologies (31-710)
Faculty: Faculty of Science
Actual: from 2022
Semester: winter
E-Credits: 5
Examination process: winter s.:combined
Hours per week, examination: winter s.:2/3, C+Ex [HT]
Capacity: 25
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Note: enabled for web enrollment
Guarantor: RNDr. Hana Hladíková, Ph.D.
Teacher(s): RNDr. Hana Hladíková, Ph.D.
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Annotation -
Lectures on mathematics for programmes of applied geology. Scalar and vector fields. Double and triple integrals, geometrical and physical applications. Infinite series; power series, Fourier series. Convergence of series.
Please note, the lectures are given in Czech language only.
Last update: Hladíková Hana, RNDr., Ph.D. (26.09.2022)
Literature -

Hradilek L., Stehlík E., 1990: Matematika pro geology I. SNTL, 426 str.

Hradilek L., Stehlík E., 1991: Matematika pro geology II. SNTL, 419 str.

Hradilek L., Stehlík E., 1986: Matematika pro geology II. SPN, 329 str., skriptum

Hradilek L., Stehlík E., 1987: Matematika pro geology III. SPN, 338 str., skriptum

K. Rektorys a spolupracovníci: Přehled užité matematiky I, II, Prometheus 1995

Last update: Hladíková Hana, RNDr., Ph.D. (03.10.2022)
Requirements to the exam -
Please note, the lectures are given in Czech language only.
Last update: Hladíková Hana, RNDr., Ph.D. (02.10.2022)
Syllabus -

Scalar and vector fields. The equation of a curve and of a surface. Differentiating vector functins. Gradient, divergence, curl. Laplacian.

Multiple integrals. Double and triple integrals. Polar, cylindrical and sherical coordinates. Geometrical and physical applications. Improper multiple integrals.

Infinite series. Sequences. Infinite series. Tests for convergence. Absolute convergence.

Last update: Hladíková Hana, RNDr., Ph.D. (18.09.2024)
Learning outcomes -

The student will be able to:

  • Functions of Several Variables
    • Define and interpret functions of several variables
    • Compute partial derivatives and the gradient
    • Apply directional derivatives and the total differential
    • Use the chain rule for composite functions
    • Find local extrema using second derivatives
    • Apply the implicit function theorem
  • Taylor Polynomial and Approximation
    • Construct Taylor polynomials for functions of one or more variables
    • Estimate approximation error using the remainder of the Taylor series
    • Use polynomials for local approximation of functions
  • Integral Calculus
    • Work with improper integrals and determine their convergence
    • Compute double and triple integrals in various coordinate systems
    • Apply Fubini’s theorem and change of variables
    • Evaluate line integrals of the first and second kind
    • Interpret integrals geometrically and physically
  • Vector Analysis
    • Work with vector fields, gradient, divergence, and curl
    • Apply Gauss’s theorem to compute flux
    • Apply Stokes’s theorem to compute circulation
    • Interpret vector calculus in the context of physical phenomena
  • Series
    • Analyze numerical series and determine their convergence
    • Work with power series and determine their radius of convergence
    • Construct Taylor series for functions and determine the interval of convergence
    • Expand functions into Fourier series and interpret their significance
  • Differential Equations
    • Recognize types of ordinary differential equations (ODEs)
    • Use methods such as separation of variables and variation of constants for first-order ODEs
    • Interpret solutions in the context of real-world applications

Last update: Hladíková Hana, RNDr., Ph.D. (07.08.2025)