Introductory Course in Mathematics 2025
for new students of the bachelor program Science

Basic information

The aim of this course is primarily to help new students of the bachelor program Science with transition from high school to university, to refresh their high school knowledge of mathematics just before the first semester starts, and maybe even learn a little bit of something new.

Last year, this course was a concise version of the introductory course for new students of bachelor programs in Czech, see Úvodní kurz z matematiky.

In year 2023 and 2024, we solved several problems in maths and physics (see the scanned notes below).

This course is optional and it is not necessary to register for it. You can just show up. If you are interested in any particular topic you would like to hear during the course, let us know (see Contact at the end)

Lecturer:
Karel Houfek from Institute of Theroretical Physics MFF UK
Time and place:
Probably 22-23 September 2025 starting at 9 AM
Lecture room T2 in Campus Troja, MFF UK, V Holešovičkách 2, Prague 8

Click on the map to get to mapy.cz.

Time schedule of the course - preliminary

Examples and notes from the year 2025

For notes on projectile motion see below the year 2024. Moreover, here are notebooks for Jupyter Lab with Pythod codes generated by claude.ai to demonstrate its capibilities and topics we were discussing:
numerical approximation of the first derivative,
numerical solution of the projectile motion (comparison with the exact soltion),
numerical solution of the projectile motion with the drag force (comparison with the soltion without the drag force)

Furthermore, here are my not very clean notes on basics of calculus with some worked examples. For a very nice summary of derivatives and integrals, visit https://tutorial.math.lamar.edu/, where you can find more nice summaries from mathematics.

Examples and notes from the year 2024

The first part of my hand-written notes on projectile motion. At the end, there is a not-so-easy problem to solve.

The solution to the last problem: hand-written notes, notebook in Mathematica, and pdf version if you cannot open the Mathematica notebook.

Examples and notes from the year 2023

Here are examples of problems which were explained during the course in 2023.
Summary of formulas for some topics and solutions to all problems above are available as hand-written notes.


By the way, if you are not familiar or confident with mathematical terms, phrases, and pronunciation in English, then you can find useful very nice booklet English for Mathematics by Muhammad Subhan Mukhlis. If the link would not work anymore, please let us know.

Contact

Do not hesitate to contact the lecturer Karel Houfek, email: Karel.Houfek@mff.cuni.cz, if you have any questions or would like discuss some topics further.

K. Houfek, September 2024