## Electronic Machines and Control: Revision

$$V = IR$$ $$Q = IT$$ $$W = I^2 RT$$ $$P = \frac{I^2 RT}{T} = I^2 R$$ Kirchoff's Current Law Conservation of charge: sum of current entering a point is zero. $$\sum_{k=1}^{n} I_k = 0$$ Kichoff's Voltage Law Sum of voltage in a closed loop is zero;

## Taylor Series and the Newton-Raphson Method

Taylor Series For a function $$f(x)$$ where $$a$$ is a solution. The difference between the initial guess $$x$$ and the solution is denoted by $$\delta x$$. $$f(x + \delta x)$$ is then the zeroth order Taylor series approximation. Zeroth Order $$f(x + \delta x) \approx f(x)$$ First Order

## Iterative Methods for Numerical Analysis

Jacobi Iteration Method For a system $$ax_1 + bx_2 + cx_3 = A$$ Rearrange for each $$x$$: $$x_1 = \frac{1}{a}(A -bx_2 -cx_3)$$ $$x_2 = \frac{1}{b}(A -ax_1 -cx_3)$$ $$x_3 = \frac{1}{c}(A -ax_1 -bx_2)$$ Start with initial