Weekly outline

  • 5. oktober - 11. oktober

    Predavanja: $\mathbb{N}$, matematična indukcija, $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$, sup, inf, max, min, absolutna vrednost v $\mathbb{R}$, kartezični zapis $\mathbb{C}$ in računanje v kartezičnem zapisu.

    Lectures - pages in ($\cdot$) refer to this book: $\mathbb{N}$, mathematical induction (pages 39-42); $\mathbb{Z}$, $\mathbb{Q}$, $\mathbb{R}$ (p. 67-68, proof of Theorem 2.30 not required); sup, inf, max, min (p. 64-66, 69); absolute value in $\mathbb{R}$ (last paragraph of p. 61-63; proof of Theorem 2.25 not required); $\mathbb{C}$ in cartesian coordinates and basic operations in cartesian coordinates (last paragraph of p. 79-81).

  • 12. oktober - 18. oktober

    Predavanja: polarni zapis kompleksnega števila, računanje v polarni obliki, Eulerjeva formula, transformacije kompleksne ravnine.

    Lectures - pages in ($\cdot$) refer to this book: polar form of a complex number, basic operations in a polar form, Euler formula, transformations in a complex plane (from Theorem 2.15 on page 422-425).

  • 19. oktober - 25. oktober

    Predavanja: Algebraične enačbe, osnovni izrek algebra. $n$-ti koreni enote. Zaporedja (definicija, eksplicitni, rekurzivni zapis). Lastnosti zaporedij (omejenost, natančna zgornja/spodnja meja, monotonost). Limita zaporedja. Naraščanje/padanje prek vseh meja. 

    Lecture: Algebraic equations and fundamental theorem of algebra (pages 428-432; proof of Theorem 15.5 not required). $n$-th roots of unity (pages 427-428). Sequences: definition, explicitly and recursively determined sequences, limit of a sequence, growing over all bounds (up to Theorem 1 in this notes). Properties of sequences: boundedness supremum/infimum, increasing sequences (link).