icon-Mathe Math Tutorial: Content

Math tutorial on specific topics calculation method, examples and calculator. In each case, attempts to explain the essential and fundamental rules of calculation example and comprehensible way to represent in their respective steps. For a more complete representation is on every page, a link to the respective Wikipedia article. The pages include JavaScript calculators for sample tasks. The calculator gives for better understanding the single calculation steps.

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.

Content

Arithmetics

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

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

Complex Numbersicon-komplexe-Zahl 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.

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

Interesticon-Regression Interest, percentage and per mille calculation.

Functions

Basic Functionsicon-Funktion 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.

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

Equations

Linear Equationsicon-lineare-Gleichung Linear equations with one and two unknowns, calculator and graphical presentation.

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

Quadratic Equationsicon-quadratische-Gleichung General representation. pq-Formula. Examples with calculation steps. Calculator with calculation steps.

Differential equationsicon-Dgl Linear differential equation first order and first order models.

Derivative / Calculus

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

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

Matrix / Determinants

Matrix, Determinant and Vectoricon-Matrix 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

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