Mathematics 1

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:

Lecturer:

Tutor:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: