Maths online Gallery
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The Gallery consists of interactive multimedia learning units on various issues that shall facilitate understanding. Technically, most units are Java applets, some are graphical supplements or other programs (JavaScript). For practice and (self) control, visit the collection of interactive tests.

A more systematic outline of the underlying mathematical background is included in the German version of maths online. (It is one of our future plans to translate this part into English language).

The Gallery is under construction since March 1998, and new learning units are added continuously. We appreciate feedback about your experience with our material.



 

 

The learning units of the Gallery



You may call the learning units directly by clicking the respective icon

for applets,
for graphics or sequences of graphics, and
for other programs

A click on a hyperlink leads you to a page collecting and briefly describing all learning units of a chapter. Occasionally, remarks on additional material and further information on the web are made.




Sets

 

Definition of sets


Drawing plane and coordinate system

 

Cartesian coordinates
Coordinate system
Polar coordinates
Oblique coordinates


Variables, terms, formulae, and identities

 

Recognize structures 1 (use abbreviations)
Recognize structures 2 (formal properties of expressions)
Recognize structures 3 (numerical properties of expressions)


Equations

 

Equivalence transformations
Quadratic equations 1 (Proof of solution formula)
Quadratic equations 2 (Three solution methods)


Vectors 1

 

Introducing 3-vectors


Analytic geometry 1

 

The slope of a straight line
Spatial coordinates
Straight lines in 3-space


Functions 1

 

Function and graph
Graphs of simple power functions
Recognize functions 1 (simple polynomial functions)
Recognize graphs 1 (functions of at most second order)
Polynomial of third order (cubic polynomial)
Function plotter


Trigonometric functions

 

Definition of the trig functions


Trigonometry

 

Triangle and Law of Sines


Functions 2

 

Recognize functions 2 (functions containing negative powers)
Recognize graphs 2 (functions containing negative powers)
The graphs of sin, cos and tan
Graphs of elementary trigonometric functions
Graphs of some exponential and logarithm functions
Recognize functions 3 (sine and cosine functions)
Recognize graphs 3 (sine and cosine functions)
Function plotter


Limiting processes

 

Numerical computation of sequences
Numerical computation of series
What is a fault? A tale that makes you smile


Analytic geometry 2

 

Planes in 3-space


Differentiation 1

 

On the definition of the derivative
Derivative puzzle 1
Derivative puzzle 2
Derivative puzzle 3
First and second derivative


Applications of differential calculus

 

How to find a function's extremum


Power series

 

Power series 1 (input by scroll bar)
Power series 2 (numerical input)
Function plotter


Analytic geometry 3

 

Cycloids
Logarithmic spirals


Differentiation 2

 

Nowhere differentiable functions


Probability and statistics 1

 

The Gauss distribution


Integration

 

Intuitively understanding the integral


Mathematical structures and spaces

 

Lorentz transformation


Fourier series

 

Fourier series


 


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