Math != Calculating

This is an interesting talk:



Math >> Calculating

1. Pose the right questions.
2. Real world problem --> math formulation
3. Computation
4. Math formulation --> real world problem and verification

Maybe not spend so much time on step 3?  Use computer programming to nail down understanding!  These are very interesting ideas.

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Adding and Subtracting Rational Expressions

To simplify a rational expression:
Step 1:  Factor all denominators as a means to easily determine the LCD.
Step 2:  Multiply by the appropriate factors to obtain equivalent terms with a common denominator. 
Step 3:  Add or subtract the numerators and place the result over the common denominator. 
Step 4:  Simplify the resulting algebraic fraction.



A more involved example follows:

It is always a good idea to state the restrictions.  Remember that the restrictions are the values that produce zero in the denominator.

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Mandelbrot Explorer using Flash

Give the below flash movie a minute to download. Move the looking glass over the picture and release it to zoom.



The orbit is displayed, real time, in the corner.