Mathematics 1

Garant předmětu:

Tomáš Neustupa

Lecturer:

Tomáš Neustupa, Jan Valášek

Tutor:

Tomáš Neustupa, Jan Valášek

Supervisor:

Institute of Economic Studies

Synopsis:

•Sets, statements and logic

•Introduction to linear algebra - basic properties of vector spaces, operations with vectors, linear independency, dimensions, bases

•Matrices - Gaussian elimination, rank of matrices, determinants, system of linear equations, the Cramer rule

•Sequences - basic properties (monotonicity, boundedness), limits

•Functions - domain and range, basic properties (monotonicity, periodicity, even and odd functions etc), inverse function, elementary functions

•Limits - finite and infinite limits of functions, one-sided limits, properties and calculations, definition of e.

•Derivatives - definitions, properties and calculations, geometrical and physical meaning, second derivative

•Application of derivatives - the l'Hospital rule, extremes, convexity and concavity

•Analysis of arbitrary function - domain, asymptotes, local extremes, inflection points, graph

•Integration - Definition of the Riemann and Newton integral, their connection, integral of elementary functions, rules for computations, substitution and integration by parts, integration of rational functions, applications in probability

Requirements:

Syllabus of lectures:

Syllabus of tutorials:

Study Objective:

Study materials:

Note:

Time-table for winter semester 2022/2023:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomDEJ:301 Neustupa T. 16:00–17:30 (lecture parallel1) Dejvice Jazyková
Tue
Wed	roomDEJ:309 Valášek J. 16:00–17:30 (parallel nr.101) Dejvice Seminární místnost
Thu
Fri

Time-table for summer semester 2022/2023:

Time-table is not available yet

The course is a part of the following study plans:

• Economics and Management 2019/20 (compulsory course)