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Mathematics 1

Type of study Bachelor
Language of instruction English
Code 310-2117/03
Abbreviation M1
Course title Mathematics 1
Credits 6
Coordinating department Department of Mathematics and Descriptive Geometry
Course coordinator RNDr. Jan Kotůlek, Ph.D.

Subject syllabus

1. Systems of linear equations, Gaussian elimination
2. Matrix algebra (operations with matrices, Matrix equations)
3. Vector and Euclidean spaces (Dot product and cross product, coordinate system in 3D space. Line and plane in 3D space)
4. Mutual positions and metric properties of subspaces in 3D-Euclidean space
5. Functions of one real variable (definitions and basic properties).
6. Elementary functions. Domains, properties and applications.
7. Limit of the function, continuous functions. Definition of the derivative.
8. Differential calculus functions of one real variable. Derivative (basic rules for differentiation).
9. Parametric differentiation, higher-order derivatives.
10-12. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hopital rule. Asymptotes.

Literature

BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1 .
NEUSTUPA, Jiří. Mathematics. 2. Vyd. Praha: Vydavatelství ČVUT, 2004. ISBN 80-01-02946-8 .
BĚLOHLÁVKOVÁ, Jana, Jan KOTŮLEK, Worksheets for Mathematics I. 1. vyd. Ostrava: VŠB-TUO, 2020.

Advised literature

ANDREESCU, Titu. Essential linear algebra with applications: a problem-solving approach. New York: Birkhäuser, [2014]. ISBN 978-0-8176-4360-7 .
HARSHBARGER, Ronald J. a REYNOLDS, James J. Calculus with applications. 2nd ed. Lexington: D.C. Heath, 1993. xiv, 592 s. ISBN 0-669-33162-7 .
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456