Mathematics 1
| Type of study | Bachelor |
|---|---|
| Language of instruction | Czech |
| Code | 310-2117/01 |
| Abbreviation | M1 |
| Course title | Mathematics 1 |
| Credits | 6 |
| Coordinating department | Department of Mathematics and Descriptive Geometry |
| Course coordinator | Mgr. Jiří Krček, Ph.D. |
Subject syllabus
1. Functions of one real variable (definitions and basic properties).
2. Elementary functions. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. 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'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.
2. Elementary functions. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. 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'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.
E-learning
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.
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
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