Notes 1 sept 2025
What to do with self study?
- Read sections in textbook/slides
- Do homework, online exercises and additional exercises on topics you find chalanging
Tips
- Show up
- Practise whats difficult
- Do homework with other students
- Try before you look at the awnser
- If stuck -> Get help from other students, tutur, lecturer or Discord
Why should you learn calculus
Something with rockets and faster code and understanding different scaling of algorithms.
How to compare two algoritms
Using limits! $$ \lim_{n\to \infty }{\frac{f}{g}} = 0 \to g\text{ grows faster} $$
P1 Real numbers and the real line
Math notation.
$\mathbb{N}$ natural numbers: 0, 1, 2, … (sometimes without 0)
$\mathbb{z}$ integer numbers: …,-2,-1,0,1,2,…
$\mathbb{Q}$ rational numbers (fractions): $\frac{p}{q}$ with p, q $\in$ $\mathbb{z}$
Decimal expantion
Rational numbers has a repeating pattern
$\frac{1}{2} = 0.50000\overline{0}$
$\frac{1}{3} = 0.3333\overline{3}$
Intervals
| Interval | Alternative notation |
|---|---|
| $(0,1)$ | $ 0 < x < 1 $ |
| $[0,1)$ | $0 \le x < 1$ |
| $(0,1]$ | $0 < x \le 1$ |
| $[1,\inf)$ | $1 \le x < \inf $ |
Symbols
$\cup$ union
$\cap$ intersection
$\in$ element of
$\vee$ or
$\wedge$ and