Some subjects can be passed by 'learn and
regurgitate', but Engineering is all about
aptitudes. One of the tools that you must be
skilled at handling is mathematics.
Maybe you have learned these topics at school and
forgotten them. Maybe you are coming to them
afresh. But in any event you must be comfortable
using them to get answers to your engineering
problems.
At the end of each section you will find self-test
problems. Hammer away until the answers seem
obvious. If there are still problems email me
and tell me - I might need to revise the material to
make it clearer.
We tend to think of mathematics as a bundle of
different topics, as below, but they often fuse
together.
Algebra
Electrical engineers cannot live without complex
numbers! But for mechanical engineers, complex
numbers can save you a lot of tedious trigonometry!
Vectors and matrices are essential for 2- and 3-D
motion, transformations and lots more.
Trigonometry
Straightforward 'trig' can help you with the
geometry of robot arms, but when you consider
vibrations you are likely to get tangled in phase
angles. Angle formulae can come in very
handy. Complex numbers can make life easier!
Solving differential equations
In 'Calculus' you learned to integrate and
differentiate, so that you could turn acceleration
into speed and then into distance. With
dynamic systems, things are more complicated when
the rate-of-change of a variable depends on the
value of the variable itself. Then you wind up
with a differential equation, or maybe a whole array
of them.
