513.160 Microelectronics and Micromechanics

## Graphical solutions

An equation of the form y1(x) = y2(x) can be solved graphically by ploting both y1(x) and y2(x). The solutions are the points where the two graphs intersect. By zooming in to the intersection, the solutions can be determined with reasonable accuracy.

 y1(x)y2(x) x
 y1(x) = y2(x) =

from x =  to x = .

The mathematical functions that can be used are list below. Multiplication must be specified with a '*' symbol, 3*cos(x) not 3cos(x). Powers are specified with the 'pow' function: x² is pow(x,2) not x^2.

 abs(x) - absolute value acos(x) - inverse cosine acosh(x) - inverse hyperbolic cosine asin(x) - inverse sine asinh(x) - inverse hyperbolic sine atan(x) - inverse tangent atanh(x) - inverse hyperbolic tangent cos(x) - cosine exp(x) - ex H(x) - Heaviside Function pi = 3.141592653589793 log(x) - natural logarithm pow(x,y) - compute xy round(x) - round to the nearest integer sin(x) - sine sinh(x) - hyperbolic sine sqrt(x) - square root tan(x) - tangent tanh(x) - hyperbolic tangent