maths formulas or theory memorise

Vector cross product

a2b3-a3b2

A3b1-a1b3

A1b2-a2b1

Projection of U onto V

Proj v (U) = [(U•V)/|V²|] V

Taylor series

T_n(x) =f(a)+f’(a)(x-a)+f’’(a)(x-a)²/2…..+f^(n)(a)(x-a)²/n!

Maximums minimums and concavity

f’’(x)>0

f’’(x)>0 concave up minimum

f’’(x)<0 concave down maximum

f’’(x)=0 inflection

criteria for invertibility of a matrix

Determinant does not equal 0

Criteria if a matrix is diagnosable

Can be written in the form A=PDP^-1

N x N matrix has

N number of unique eigenvalues

What does P and D equal in A=PDP^-1

P = columns are the eigenvectors stacked on each other

D = eigen values as the diagonal of the matrix

How to calculate eigenvector/eigenspace

Lagranges formula

injective / Surjective

Injective - one to one (horizontal line test) distinctive outputs.

Surjective - range is equal to Codomain.

elementary limit

First principle differentiation

sum of infinite geometric series

Riemann sum

fundamental theorems of calculus

Fundamental theorem of calculus for a differentiable limit

Length of a graph formula

Disc Method

x axis ,

Shell method

y axis

Four forms of vector

Matrix invertible theorem

Eigenvalue/Eigenspace

Algebraic/geometric multiplicity

prove sqrt of 2 is irrational

Taylor series for e^x, cosx, sinx, coshx, sinhx, ln(1+x)