Mathematics 1
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 32BE-P-MAT1-01 | Z,ZK | 6 | 2P+2C | English |
- Relations:
- It is not possible to register for the course 32BE-P-MAT1-01 if the student is concurrently registered for or has already completed the course U63E1101 (mutually exclusive courses).
- During a review of study plans, the course U63E1101 can be substituted for the course 32BE-P-MAT1-01.
- Course guarantor:
- Tomáš Neustupa
- Lecturer:
- Tomáš Neustupa, Jan Valášek
- Tutor:
- Tomáš Neustupa, Jan Valášek
- Supervisor:
- Institute of Economic Studies
- Synopsis:
- Requirements:
- Syllabus of lectures:
-
1) Sets, statements and logic
Linear Algebra
2) Introduction to linear algebra - basic properties of
vector spaces, operations with vectors, linear independency,
dimensions, bases
3) Matrices - Gaussian elimination, rank of matrices,
determinants, system of linear equations, the Cramer rule
Calculus - sequences and functions
4) Sequences - basic properties (monotonicity,
boundedness), limits
5) Functions - domain and range, basic properties
(monotonicity, periodicity, even and odd functions etc), inverse
function, elementary functions
6) Limits - finite and infinite limits of functions,
one-sided limits, properties and calculations, definition of e.
7) Derivatives - definitions, properties and
calculations, geometrical and physical meaning, second derivative
8) Application of derivatives - the l'Hospital rule,
extremes, convexity and concavity
9) Analysis of arbitrary function - domain, asymptotes,
local extremes, inflection points, graph
Calculus - An introduction to integration
10) 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
- Syllabus of tutorials:
-
1) Sets, statements and logic
Linear Algebra
2) Introduction to linear algebra - basic properties of
vector spaces, operations with vectors, linear independency,
dimensions, bases
3) Matrices - Gaussian elimination, rank of matrices,
determinants, system of linear equations, the Cramer rule
Calculus - sequences and functions
4) Sequences - basic properties (monotonicity,
boundedness), limits
5) Functions - domain and range, basic properties
(monotonicity, periodicity, even and odd functions etc), inverse
function, elementary functions
6) Limits - finite and infinite limits of functions,
one-sided limits, properties and calculations, definition of e.
7) Derivatives - definitions, properties and
calculations, geometrical and physical meaning, second derivative
8) Application of derivatives - the l'Hospital rule,
extremes, convexity and concavity
9) Analysis of arbitrary function - domain, asymptotes,
local extremes, inflection points, graph
Calculus - An introduction to integration
10) 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
- Study Objective:
- Study materials:
-
Literature:
Neustupa J.: Mathematics I (textbook CTU).
Various Calculus books and lectures on internet.
Finney T.: Calculus
Leon S.J. : Linear Algebra with Applications
- Note:
- Time-table for winter semester 2024/2025:
-
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 Tue Wed Thu Fri - Time-table for summer semester 2024/2025:
- Time-table is not available yet
- The course is a part of the following study plans: