Course: Mathematics

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Course title Mathematics
Course code KMD/MAT
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Salač Petr, RNDr. CSc.
Course content
Lectures: A -- Linear algebra 1. Arithmetic n-dimensional vector space, linear dependence/ independence of vectors, basis and dimension of a vector space. Scalar product and orthogonality of vectors. 2. Matrix algebra (addition, scalar multiple, matrix multiplication), rank of a matrix. 3. Determinant, definition and calculation. Matrix inverse. 4. Systems of linear algebraic equations, solvability, Frobenius theorem. Gaussian elimination. Cramer's rule. B -- Introduction to differential calculus 5. Real function of one real variable (domain, rank, graph), basic properties of functions and defined operations, review of elementary functions. 6. Limit and continuity of a function, one-sided limits, limit of a function at +/- infinity. Properties of continuous functions. 7. Derivative, geometric interpretation, tangent line of a function graph, differentiation rules, higher order derivatives, L' Hospital's rule. 8. Function investigation. Critical points, intervals of monotonicity, local and global extremes. 9. Convexity and concavity of function, inflex points. Function asymptotes. Examples. C -- Introduction to integral calculus 10. Primitive function and indefinite integral. Integration methods (integration by parts, method of substitution), simple examples of applications of the methods. 11. Integration by partial fractions and examples. 12. Riemann integral. Applications of Riemann integral in geometry and physics. 13. Summary. 14. Reserve.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Class attendance - 56 hours per semester
Learning outcomes
A. Introduction to linear algebra -- vector spaces and matrix algebra, solving linear systems of algebraic equations. B. Introduction to diferential calculus of real functions of one real variable -- function properties, continuity, limit, derivative, and applications. C. Introduction to Integral calculus -- indefinite integral, Riemann integral, and application.
A -- Linear algebra - arithmetic vectors and properties, matrices and operation with them, systems of linear algebraic equations, their solvability and solution, determinants and calculations. B -- Introduction to differential calculus - functions of one real variable, application of derivatives to investigation of function properties. C -- Introduction to integral calculus - calculation of indefinite integrals using basic rules and methods, calculation of definite integrals.
Prerequisites
High school level knowledge of mathematics

Assessment methods and criteria
Combined examination

Activity in seminars, 3 tests
Recommended literature
  • Blažek, J.:. Algebra a teoretická aritmetika. Praha, SPN, 1983. ISBN 14-514-83.
  • Dlouhý, Z. a kol.:. Úvod do matematické analýzy. Praha SPN, 1965. ISBN 16-915-65.
  • Kračmar, S. - Neustupa, J.:. Sbírka příkladů z matematiky 1. [Skriptum ČVUT, FS]. Praha, 2000.
  • Nekvinda, M. - Vild J.:. Matematické oříšky I. Liberec TU, 2000.
  • Nekvinda, M.:. Matematika I. Liberec TU, 1999.
  • Neustupa, J.:. Matematika 1. [Skriptum ČVUT, FS]. Praha, 2000.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Arts and Architecture Study plan (Version): Architecture (1) Category: Architecture 1 Recommended year of study:1, Recommended semester: Winter