## Mathematical Analysis 1, NMAI054, summer term 2021/22

Lecturer: Martin Klazar. Lectures are in contact form. If you are quarantined or cannot attend, send me an e-mail
and you will get the pdf of the lecture (and somewhat later it will be posted here).
Tutorial:
Mykhaylo
Tyomkyn (Tue 14:00 in N6, Tue 15:40 in N6). tutorials link

Exam: go to SIS to register for exams. Information on the exam. I will add two more exam terms in September.

Lecture 1 - 2/16/2022 Sets, functions, real numbers.

Lecture 2 - 2/23/2022 Theorems about the existence of limits of real sequences. (June 6, 2002 - an
explicit proof of Bolzano--Weierstrass theorem added.)

Lecture 3 - 3/2/2022 Arithmetic of limits. Limits and ordering. Series.

Lecture 4 - 3/9/2022 More about series. Limits of functions. Elementary functions.

Lecture 5 - 3/16/2022 Properties of limits of functions. Continuity of a function at a point.

Lecture 6 - 3/23/2022 Properties of continuous functions.

Lecture 7 - 3/30/2022 Derivatives of functions. (The derivative of a function at a point
is now defined at any limit point in the definition domain of the function!)

Lecture 8 - 4/6/2022 Mean value theorems and their consequences.

Lecture 9 - 4/13/2022 Taylor polynomials and series. Primitive functions.

Lecture 10 - 4/20/2022 Area under G_f. Newton's integral. Integration by parts and by substitution.

Lecture 11 - 4/27/2022 More about Newton's integral. Computing primitives of rational functions.

Lecture 12 - 5/4/2022 The Riemann integral.

5/11/2022 - Rector's day. (Something like Bloomsday.)

Lecture 13 - 5/18/2022 Riemann integral and its upgrade Henstock - Kurzweil integral. Use of integrals.

**(new!)** The honest answer to questions about **literature and references for MA 1** is that a textbook which I could recommend (and which
I would like to read myself) does not exist, as far as I know. Therefore you have to rely on the lectures published above. But
I will post here (version of May 25, 2022) from time to time my attempts to write such textbook. Since
this will be translation of the Czech version, I am afraid that progress here will be slow.

June 2022