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 SystemsDescription 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 CombinationsCalculation 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 rulesThe 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 seriesInterest, percentage and per mille calculation.

Percentage calculation Per mille calculation Interest calculation Rule of three calculationElementary 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(-xComplex Functions: Linear and quadratic functions, trigonometric and exponential functions plotted with domain colouring method.

Complex FunctionsLinear equations with one and two unknowns, calculator and graphical presentation.

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

Linear Equation SystemsGeneral representation. pq-Formula. Examples with calculation steps. Calculator with calculation steps.

Quadratic EquationsLinear differential equation first order and first order models.

Differential equations Exponential growth Logistic growthExplanation of the derivation rules with examples and calculation method: factor rule, sum rule, product rule, quotient rule, chain rule.

Derivation rules Derivative calculator Gradient calculator Gradient 2d PlotExplanation of the integration rules for definite and indefinite integrals with examples and calculation method.

Integration RulesMatrix 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 EigenvaluesCalculations 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 argumentUsing 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 LetterJSXGraph 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