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! $$\underset{n\to \mathrm{\infty }}{lim}\frac{f}{g}=0\to g\text{ grows faster}$$

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
$\frac{1}{2}=0.50000\bar{0}$
$\frac{1}{3}=0.3333\bar{3}$

Intervals

Symbols

$\cup$ union
$\cap$ intersection
$\in$ element of
$\vee$ or
$\wedge$ and