Welcome of Trevor Pythagoras

Trevor Pythagoras contains tutorials on a range of mathematics topics at different levels, each topic can be found using the links across the top of every page. Each tutorial has a comments section where you can add comments, corrections or ask questions and I will try my best to respond to them. You can also use the request a post page to ask me to post a tutorial on a given topic.

Trevor Pythagoras should be useful to anyone who is currently study mathematics at school (whilst the content is based on the A Level and GCSE syllabus I studied in the UK it should still be relevant to you wherever you are reading this). However, I hope it is also useful to people have left school who want to expand or refresh their knowledge of maths.


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There a three ways of subscribing to this site so that you can read all the tutorials on the day they are posted without haveing to keep checking the site.

  • Email Subscription : each day I right a post, all the posts from that day will be emailed to you so you don't even have to leave you inbox (note that to see formulas correctly in emails you will need to make sure that images arn't being blocked)
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Recent Posts

Integrate cos and sin squared using double angles

January 27th, 2010 admin No comments

How to integrate sin and cos sqaured using the double cos (cosine) indentity

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Categories: Calculus Tags: , , , ,

Force, Mass and Acceleration

January 25th, 2010 admin No comments

When a (resultant) force is exerted on a body the (resultant) force, the mass of the body and the acceleration caused by the force can be summarised in the equation
F=ma
where f= (resultant) force, m=mass,a=acceleration.
Example
So for example if gravity is pulling down on a body of mass 2kg and is causing it to accelerate at 9.81ms-2 [...]

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Categories: Mechanics Tags: , , ,

Common Derivatives

January 23rd, 2010 admin No comments

Below is a table containing a list of common functions and their derivatives.

f(x)
f ‘(x)

c (constant)
0

xn
nxn-1

ln(x)
1/x

ex
ex

eax
aeax

sin(x)
cos(x)

cos(x)
-sin(x)

tan(x)
sec2(x)

cosec(x)
-cosec(x)cot(x)

sec(x)
sec(x)tan(x)

cot(x)
-cosec2(x)

sin-1(x)

cos-1(x)

tan-1

sinh(x)
cosh(x)

cosh(x)
sinh(x)

tanh(x)
sech2(x)

cosech(x)
-coth(x)cosech(x)

sech(x)
-tanh(x)sech(x)

coth(x)
-cosech2(x)

sinh-1(x)

cosh-1

tanh-1

a(x)b(x)
a’(x)b(x) + b’(x)a(x)

a(b(x))

If there any more standard derivatives that I have missed out please leave them in the comments section

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Monotonic (Increasing and Decreasing) Functions

January 22nd, 2010 admin No comments

Monotonic functions are functions on real numbers which are either always increasing or always decreasing. Monotonic is a collective name for increasing, strictly increasing, decreasing and strictly decreasing functions.
These can be defined as follows,
if for all x1 < x2

f(x1) ≤ f(x2) then f is increasing
f(x1 ) < f(x1 ) then f is strictly increasing
f(x1 [...]

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