Further Maths

>>7811149
∫1/(a^2+x^2)dx= 1/2a tan^-1(x/a)

>>7811149
FP1:
Be familiar with inductive proof and matrices
FP2:
Be familiar with Taylor series expansions, usually with x0 = 0
FP3:
vectors, lines and planes in 3 dimensions.

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>>7811191
I have no material to go on with learning those though lol

>>7811196
Further maths is fuckin easy bro, wtf.

>>7811196
inductive proof:
prove basis case
assume k-th case
Find (k+1)-th case from k-th case
Since let k-th case = basis case
QED

Matrices:
Row multiplies columns

Taylor series:
approximate functions as (infinite) polynomials centred about a point x0. A special case is when x0 = 0. This can also be called a Maclaurin Series (dude was MLG, professor of Mathematics at Edinburgh at 19.)

Vectors in 3d space:
dot product:
u = ai + bj + ck
v = di +ej + fk

u.v = ad + be +cf
v is perpendicular to u if the dotproduct is zero.

cross product:
uxv = (bc - cb)i + (ca - ac)j + (ab - ba)k

Complex numbers & polar coordinates:
sqrt(-1) = i
a complex number is any number a + ib where a,b are real.
can be written in the form r(cos(x) + isin(x))
= rexp(ix) where r is the radius and x is the argument.

Hyperbolic functions:
literally trig functions with complex arguments.

The rest is bollocks.

By the time you hit uni this shit will be effortless.

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>>7811226
Some of this stuff I've learnt on my own - in Pure Mathematics 3 of normal Maths. Thanks tho.

Found Edexcel FP1 and FP2 textbooks using torrent sites btw, but not many seeders.