MATH 256 Memorize

MATH256 at UBC

linear first order equation

y = 1/i * integral( iq(x) ) + C/i

what is the guess:

e^nx

de^nx

polynomial degree n

Axⁿ + Bx^n-1 … C

coswx or sinwx

Acoswx + Bsinwx

e^nx(coswx or sinwx)

e^nx(Acoswx + Bsinwx)

e^nx(polynomial degree n)

e^nx(Axⁿ + Bx^n-1 … C)

homo sol

Axf(x)

xⁿcoswx or xⁿsinwx

(Axⁿ + Bx^n-1 … C)coswx + (Dxⁿ + Ex^n-1 … F)sinwx

notation for imaginary roots

r = α ± β

(Acos(βx) + Bsin(βx))*e^alphax

combining from cosβx + sinβx to cosβx

(Acos(βx) + Bsin(βx))*e^alphax

Ae^alphax(cos(βx+B))

y'' + 2αy' + Ω^2 = αcoswt

α > Ω overdamped

α < Ω underdamped

α = Ω critically damped RESONANCE

α = 0 no damping

resonance

at resonance α = Ω

w0 = (K/M - (D/(2M)²)^(1/2)

w0 = ( Ω² - α² )^(1/2)

period / frequency equation

T = 2pi/w

T = 1/f

w = 2*pi*f

makes cosine zero for pde

makes sine zero for pde

laplace integral

dirac delta