Course: Mathematics I

» List of faculties » FSI » USE
Course title Mathematics I
Course code USE/PU001
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Chytrý Vlastimil, doc. PhDr. Ph.D.
  • Zdráhal Tomáš, doc. RNDr. CSc.
  • Černohlávek Vít, Ing. Ph.D.
Course content
1. Numerical sequence and its limit, sum of numerical series. Convergence and divergence of sequences and series. 2. Elementary functions and their graphs (polynomial, rational, power, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, inverse hyperbolic). 3. Limit and continuity of function. Heine theorem. Properties of continuous functions. 4. Derivative of a function, its geometric and physical interpretation. Basic rules for differentiation, derivatives and differentials of higher order. Function increment theorem and its application. 5. Local and global extremes. Inflection points of the function, graph asymptotes, graphs of functions. 6. Extreme value theory and applications. 7. Antiderivative (primitive) functions, calculation of basic types of indefinite integrals (integration by parts and substitution methods). 8. Riemann integral, calculation of a definite integral, mean value of integral. 9. Geometric and physical applications of a definite integral (curve length, volume and surface of rotating bodies, center of gravity, angular momentum and inertia). Differential Equations - introduction and elementary methods of their solution. 10. Functional sequences, power series, differentiation and integration of power series. 11. Matrices, determinants, matrices of linear mappings. Eigenvalues and eigenvectors, quadratic form. Systems of linear equations and their solutions.

Learning activities and teaching methods
unspecified, unspecified
  • unspecified - 50 hours per semester
Learning outcomes
Objectives: The course is organized in the form of lectures (explanation of basic principles and theory) and seminars (focused on practical mastery of the subject). The aim of the course is to acquaint students with the basic principles of differential and integral calculus of functions of one variable with emphasis on technical applications.
Students will acquire basic knowledge of infinitesimal calculus in the sense that they will be able to solve special problems and problems of the real world by means of differential and integral calculus of functions of one variable.
Prerequisites
Knowledge and skills from the Mathematics preparatory course.

Assessment methods and criteria
unspecified
Recommended literature
  • Budinský, B., Charvát, J. Matematika I, SNTL, Alfa Praha. 1987.
  • Mezník, J., Karásek, J., Miklíček, J. Matematika pro strojní fakulty I, SNTL Praha. 1992.
  • Rektorys K. Přehled užité matematiky. SNTL, Praha, 1981.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester