1. function must be periodic 2. it must be single values and continuous except at finite number within each period of finite discontinuities 3. finite number of extrema in one period 4….
work done in moving an object distance r by force F: dW = F.dr
describes a non relativistic particle of mass m in potential V
b^2 – 4ac < 0 ie wave equation
Energy of magnetic dipole: U = -mB Energy of electric dipole: U = -pE (potential energy is minimal when aligned with field work done given by W=Fd
div . D = ro (electric displacement and charge density) this integrated over a volume should give the charge
b^2 – 4ac = 0 ie diffusion equation
reexpressing the position in the new coordinates converting the unit vectors for differential operators: expressing the operators in the new basis system (may affect unit vectors) for integration: converting the limits and…
first few terms of fourier series overshoot the value for small n For larger n the overshoot does not disappear but the position of each overshoot has moved closer to the discontinuity.
The curl of a vector field integrated over any surface is equal to the contour integral over the boundary of the surface.