Mathematik 1 | Die geometrische Folge und die endliche geometrische Reihe

Die geometrische Folge beschreibt exponentielle Wachstumsprozesse (z. B. die Entwicklung von Corona-Infektionszahlen bei konstanter Reproduktionszahl R).

Mathematik 1 | Arithmetische Folgen und Reihen und wo sie vorkommen

Wir erklären, was arithmetische Folgen und Reihen sind und wie man letztere mit dem "kleinen Gauß" explizit berechnen kann.

Mathematics 1 | Integration by Substitution

We explain integration by substitution, both for definite and indefinite integrals, and work out several examples.

Mathematics 1 | Integration by Parts: Halfway to the Solution

We explain the method of integration by parts and work out several examples.

Mathematics 1 | Definite Integrals and Area Functions

Finding area functions and finding derivatives are inverse processes of each other. We explain this close link in detail, revealing one of the most fundamental relationships in calculus.

Mathematics 1 | Indefinite Integrals, Primitives, and Antiderivatives

Three names, one idea: For a given function f find another function F, such that f is the derivative of F.

Mathematics 1 | Single Variable Optimization: A Rather Lengthy Story

We perform a complete walk-through of a single variable optimization of an example function.

Mathematics 1 | De l’Hôpital’s Rule featuring Hart-Und-Trocken-Män

De l'Hôpital's rule helps to find limits of functions in certain "pathological" cases. The Hart-Und-Trocken-Män does not help at all.

Mathematics 1 | Limits of Functions: Leaving the Comfort Zone

How does a function behave if the independent variable stretches towards the boundary of the domain?

Mathematics 1 | Continuity: Know Your Limits

We explain what a continuous function is and how we precisely define continuity using limits of sequences.