# What is higher math

## Analysis | higher mathematics

That was a brief introduction to the subject.
So that you understand it completely, watch more clearly explained math videos here:

### A.51 Multi-dimensional functions

Of course, functions do not necessarily have to depend on only one variable (ie only on "x"). A function can also have several "x-values"; they are then also called "multi-dimensional functions". These x-values ​​are then either x, y, z, .. or "x1", "x2", "x3", ... Most of the time you are interested in extreme points, tangents (which are not straight lines, but a tangential plane ( !) or something else). We will derive (that is, then “partially derive” according to the various, multiple variables), for the extreme points we will set the first derivatives to zero, ... we will then see the details in the sub-chapters.

### A.52 Various things worth knowing about functions with which one can write even better exams

"Diverses" is a hodgepodge of different topics. However, with topics that are a little more difficult and belong in the upper range of the upper school or lower range of the university. In the first sub-chapter we deepen the topic of vertical asymptotes (continuation of chapter A.43.06), the second sub-chapter contains an "easy" rule for difficult calculations of limit values. The third sub-chapter contains nested (= chained) functions and in the last sub-chapter we dedicate ourselves to the great terms “injective, surjective and bijective.

### A.53 Differential equations: what is a differential equation and how do you calculate with it?

A differential equation (different notation: differential equation) (short: DGL) is an equation in which derivative and function appear. A DGL therefore describes a relationship between the change in the stock and the stock itself. The level of difficulty begins “relatively easy” (→ Section 4.3.1). Then the level rises very quickly. We have left the school material by chapter 4.3.3 at the latest.

### A.54 Complex Numbers

An imaginary number is obtained by taking the square root of a negative number (or imagining that it would work). The root of “-1” is denoted by “i” (some also use “j” instead of “i”). If you add real numbers to imaginary numbers, you get complex numbers. For example, “z = 3 + 5i” is a complex number. The "3" is the real part of it and is abbreviated as re (z) => re (z) = 3. The “5” in front of the “i” is the imaginary part of z and is abbreviated as im (z) => im (z) = 5. Drawing in complex numbers: of course a number line is not enough, you need two axes. This is called the “complex number plane” or “Gaussian number plane”.

### A.55 Financial Mathematics

Financial math, of course, is concerned with calculating various financial math problems. In this chapter we consider: 1. compound interest calculations, 2. pension calculation (installment savings), 3. annuity calculation (repayment calculation), 4. cash and final values ​​(with terms such as in advance and in arrears)