Analysis describes a sub-area of mathematics that, to put it simply, deals with the study of functions. The other three major areas of mathematics taught in school are geometry, algebra, and stochastics.
In this article, we explain what calculus involves and some of its basics.
Have fun with your studying!
What is analysis?
Analysis deals extensively with functions, their properties and their limit values, with differential calculus and integral calculus. Analysis allows us to describe the changes in a function. You may already know this from school as growth and decay processes.
Fundamentals of Analysis
In order to give you a good overview of this very extensive topic, the basics are explained below.
functions
A function is a direct assignment between two sets, in which each element of the definition set is assigned exactly one element of the value set. There are several types of functions, such as linear functions, quadratic functions, power functions, root functions and many more.
If you want to learn more about functions, then the best thing to do is read the articles in the Functions chapter!
differential calculus
Behind the terms derivation and differentiation hides the generic term differential calculus. No panic! The differential calculus is used to describe the changing behavior of a function at a certain point. The derivative of a function, especially in the case of non-linear functions, indicates how much a function increases or decreases at each point.
Exact definitions, derivation rules and the derivation of important functions can be found in the chapter Derivation and Differentiation!
integral calculus
Integral calculus deals with the calculation of area and volume between two functions or a function and an axis of the coordinate system. In addition, integral calculus is the opposite of differential calculus! In order to calculate the integral, the corresponding functions are integrated using integration rules, then these are also called antiderivatives.
If you want to learn more about integral calculus, you will find many articles in the integral calculus chapter!
curve discussion
The curve discussion is one of the most important topics in school mathematics. This deals with the properties of the function such as the definition and value range, zeros, extreme values and the behavior at infinity. The curve discussion builds on differential and integral calculus, so you should be comfortable with these two topics before engaging in the curve discussion.
A large number of summaries can be found in the chapter discussion of curves!
growth and decay
Many natural processes of growth or decay in populations of living beings are dependent on the existing composition of the population. These processes are then represented by corresponding functions.
If you want to learn more about growth and decay, then read the articles in the Growth and Decay chapter!
The most important of analysis at a glance!
- Analysis is the part of mathematics that deals extensively with functions, their properties and their limit values, with differential calculus and integral calculus.
- Different sub-disciplines can be distinguished, such as differential and integral calculus, the discussion of curves, and growth and decay processes.
- Analysis lets you examine functions more closely, so you can find out geometric properties or the changes at any point.