**Department
of Mathematical Analysis**

Sokolovská
83, 4th floor, room K479

tel. 221913366

e-mail

**On maternity leave since February 14, 2013.**

**Program of Winter Semester 2012/13:**

I. Introduction. Elements of mathematical logic and set theory.
Real numbers.

II. Sequences. Limits.

III. Functions of one
real variable. Limits, continuity, derivatives. Investigation of a
function. **Exam terms:**

Tuesday January 15

Wednesday January 23

Tuesday January 29

Tuesday February 5

Tuesday February 12

**Students are supposed to ****enroll
for exam terms in SIS.**

There will be one more
term (the last one) at the beginning of Summer Semester: **Friday
February 22, 3:30 p.m., in Opletalova, O109 - the
examiner will be Tomáš Bárta (teacher of the Czech parallel)**.
See SIS for details.

Test Jan 15

Test Jan 23

Test Jan 29

Test Feb 5

Only the students who have fulfilled
credit requirements (see below) can approach exam on Mathematics I.

The exam starts with a **written part**
- test 120 min. approx. (4 calculus problems: limit of a sequence,
limits and continuity of functions, derivative, investigation of a
function and its graph). To pass this part, at least half of maximum
points is necessary. If a student passes the written part with 1/2 to
2/3 of maximum points and fails in the oral part, he/she must pass
the written part at next term again. With 2/3 or more, no repetition
of the written part is needed.

The **oral
part** (theory as read during the lectures) is
either the same day or the day after the written part (according to
actual number of students who passed the written exam). It involves
definition of a key notion - its correct formulation is necessary for
passing the oral part - another definition and formulation of two
theorems, one of them with proof. At the written part, students can
use written/printed materials, no electronic devices are allowed. At
the oral part, no materials are allowed, students have about 30 min.
to prepare themselves. Detailed **oral exam
requirements** (list of key notions,
definitions, theorems and proofs) here.

Lecture notes (supplemented
during the course), final version Dec 25, 2012; Jan 13: proofs of
Theorems 3.1 and 3.2 added on demand.

Limits to practise:
Homework problems with answers, two
more. **Credit requirements:**
There were three written tests (up to 30 min) on basic 'high-school'
calculus on seminars: Oct 17, Nov 7, Nov 28. Topics of the third
test: (in)equations with parameter, analytic geometry (expression of
lines and planes, distance between a point and a line/plane, planar
curves in R^2: elipse, parabola, hyperbola), limit of a sequence
(basic difficulty). Sample test 3 with solutions here.
Sample test 2 here. Sample test 1 here.
For credit, students have to pass at least two tests. Further, a
correct solution of a homework problem involving current topics of
the course is required. Homework problems
were submitted November 29. Those who have no exercise on the list
assigned are asked to choose a free one and let me know by e-mail.
Students have to perform a correct solution before entering the exam.

First test evaluation

Third test evaluation. The test with results here

Test retake (Dec 14)
evaluation

Skills
and knowledge necessary for understanding higher mathematics

The
text involves a series of exercises which are recommended to be done
at the beginning of the course. Answers
**Links **to
archives of the course materials:

by
Miroslav Zelený

by
Ondřej Kalenda - exercises

**Literature:**

A.C. Chiang: Fundamental Methods of Mathematical Economics

B.
P. Demidovich: Problems in Mathematical Analysis (also in Czech and
Russian)

W. Rudin: Principles of Mathematical Analysis

V.
Hájková, M. Johanis, O. John, O. F. K. Kalenda, M. Zelený,
Matematika, Matfyzpress, 2006 and 2012 (in Czech; pdf
here - pp. 1-118 for Mathematics 1)

Brief lecture notes
published here

Any introductory
book on mathematical analysis

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