# Content

## Arithmetics

### Fractions

Compilation of calculation rules for fractions with examples. Example calculator for determining the least common multiple (LCM) and the greatest common divisor (GCD).

Fraction Arithmetic Reducing Addition Subtraction Multiplication Division Power Roots Number Systems

### Calculator

Fraction Calculator Mean Value Calculator

### Combinatorics

Description of the combinatoric tasks and the basic functions. With help of examples and calculators is the using of combinatoric issues illustrated.

Combinatorics Faculty Binomial coefficient Polynomial coefficient Permutations Variations Combinations

### Calculator

Binomial Mean Value Calculator Fraction Calculator

### Complex Numbers

Calculation rules and definitions for complex numbers. Addition, multiplication and division of complex numbers. Powers and relations of complex conjugate numbers. Trigonometric and exponential representation of complex numbers. Example computer.

Calculation rules

Complex Numbers

### Graphical

Complex numbers Addition complex numbers Multiplication complex numbers Division complex numbers Power complex numbers

### Curve fit

The regression analysis is used for determining or estimating model parameters. Determining a best-fit line using the least squares method with example computer.

Regression Linear fit Power function Fourier series

Curve fit

### Interest

Interest, percentage and per mille calculation.

Percentage calculation Per mille calculation Interest calculation Rule of three calculation

### Calculator

Percentage calculator

## Functions

### Basic Functions

Elementary mathematical functions graphically with computer for characteristic values ​​of the function. Description of the following elemental functions with graphic display and computer example: linear function, quadratic function, sine function, exponential function, error function and normal distribution.

Basic Functions Linear Functions Quadratic Functions Sin function (sin) Exponential Function (exp) Error Function exp(-x2) Normal Distribution

### Grafical plot

Function Plot Function 3d-Plot Surface 3d-Plot Parabola Plotter Cubic Plotter Normal Distribution Plot Damped Vibration Plot

### Complex Functions

Complex Functions: Linear and quadratic functions, trigonometric and exponential functions plotted with domain colouring method.

Complex Functions

### Linear Equations

Linear equations with one and two unknowns, calculator and graphical presentation.

Linear Equations

### Linear Equation Systems

General representation. Solving methods: Addition method, Gauss method,... calculator and graphical presentation.

Linear Equation Systems

### Calculator

Systems 2x2 Systems 3x3 NxN Cramer's rule NxN Gauss method

General representation. pq-Formula. Examples with calculation steps. Calculator with calculation steps.

### Calculator

Quadratic Equation Normal form to vertex form

### Differential equations

Linear differential equation first order and first order models.

Differential equations Exponential growth Logistic growth

### Online ODE Calculator

ODE first order General first order ODE General second order ODE ODE second order ODE-System 2x2 ODE-System 3x3 Collection 1. order y'+ay=b y'+ay=ce^bx y'+2xy=xe^(-x^2) y'+xy=x y'+y=x y'=y^2 y'+y^2=1 y'=(Ay-a)(By-b)

## Derivative / Calculus

### Derivative

Explanation of the derivation rules with examples and calculation method: factor rule, sum rule, product rule, quotient rule, chain rule.

### Calculus

Explanation of the integration rules for definite and indefinite integrals with examples and calculation method.

Integration Rules

## Matrix / Determinants

### Matrix, Determinant and Vector

Matrix addition, subtraction, multiplication each with calculator and calculation method. Rules for computing determinants explained with examples. Calculator with calculation method. Leibniz formula. Vector addition, subtraction, multiplication each with calculator and calculation method.

Matrix rules Determinant rules Vector calculation Vector scalar Vector addition Vector subtraction Inner product Cross product Length Matrix Eigenvalues

### Graphical

Vector addition Vector subtraction Matrix-Vector product Inner product

### Calculator

Sum and dif of MxN matrices Multiplication of matrices Matrix-Vector Multiplication Adjugate matrix QR decomposition Inverse Matrix Determinant 2x2 Determinant 3x3 Determinant 3x3 symbolic Determinant 4x4 Determinant 4x4 symbolic Determinant 5x5 Determinant NxN

## Geometrics

### Trigonometry

Calculations on rectangular and the general triangle. Sine and cosine rule application.

Trigonometry Angle, opposite cathetus Angle, adjacent cathetus Cathetus Cathetus, hypotenuse 2 sides, 1 angle 2 angles, 1 side 3 sides Tower height Cross bearing Triangle of forces Hansens task Trigonometric function tables Power and n-th argument

### Graphical

Triangle Circle Ellipse Trapeze Parallelogram Rectangle

### Numeric

Numeric algorithms.

Newton Method Horners Method Fourier-Series Taylor-Series Lagrange Interpolation Newton Interpolation

### Basic calculators

Logaritm Sine, Cosine, Tangent Roots: square, cubic, ...

## Tools

### MathML

Using MathML to mathematical expressions on web pages can be displayed. On the following pages the MathML code is on examples explained.

MathML Examples Integral Sum Brackets Indices Fracture Roots Tables Matrix Determinant Vector Indentation Style Operators Differential / Integral Points Geometric Set Logic Vector Greek Letter

### JSXGraph

JSXGraph is a web-browser library for interactive geometry, function plotting, charting and data visualization in a Web browser. The library is completely implemented in JavaScript and uses SVG, VML, or canvas.

JSXGraph is developed at the Department of Mathematics and Didactics at the University of Bayreuth.

JSXGraph University Bayreuth JSXGraph Example: ODE with direction field

### Other languages

Spain France Italy Germany Poland Chinese