# eMath: 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).

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

#### 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.

#### Graphical

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.

#### Calculator

Interest Interest, percentage and per mille calculation.

### 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.

#### Grafical plot

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

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

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

#### Calculator

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

#### Calculator

Differential equations Linear differential equation first order and first order models.

### 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.

### 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.

### Geometrics

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

### Body Index

In order to determine whether a body model deviates from the norm or also involves a health risk, various indices have been developed. These indices can indicate whether there is an overweight or underweight or a health risk.

### Numeric

Numeric algorithms.

### Tools

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

#### 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.