User:Emote





Click here to access Samuel Rutherford's Letters, available as a PDF download.



Work documentation

 * Overhaul the Alexander Stephens page
 * Status: in progress


 * Expand the biographical information on Asahel Nettleton
 * Status: in progress


 * Expand the biographical information on Robert Lewis Dabney
 * Status: not started


 * Create a page for Linton Stephens
 * Status: not started

Control equations
$$e^{At} \triangleq \mathcal{L}^{-1} [(sI - A)^{-1}]$$

$$\mathbf{}x(t) = e^{At}x(0)$$

CMOS equations
$$I_D = \frac{1}{2}k_n'\frac{W}{L}(V_{GS}-V_t)^2$$

$$r_o = \frac{ \left| V_A \right| }{I_D}$$

$$V_A = \frac{1}{\lambda}$$

$$g_m = \frac{i_d}{v_{gs}} = k_n'\frac{W}{L}(V_{GS}-V_t)$$

$$g_m = \sqrt{2k_n'}\sqrt{W/L}\sqrt{I_D} = \frac{2I_D}{V_{OV}}$$

$$A_v = \frac{v_d}{v_{gs}} = -g_mR_D$$

C code
void main {   int outcome; float a, b, Ea, Eb, Sa, Sb; printf("Enter player A's initial rating: "); scanf("%f", &a); printf("Enter player B's initial rating: "); scanf("%f", &b); printf("Did player A win(1), lose(2), or draw(3)? "); scanf("%i", &outcome); while((outcome != 1) && (outcome != 2) && (outcome !=3)) {      printf("\nERROR -- must choose 1, 2, or 3\n\n"); printf("Did player A win(1), lose(2), or draw(3)? "); scanf("%i", &outcome); }   Ea = 1 / (1 + pow(10,((b-a)/400))); Eb = 1 / (1 + pow(10,((a-b)/400))); if ( outcome == 1 ) {      Sa = 1; Sb = 0; }   else if ( outcome == 2 ) {      Sa = 0; Sb = 1; }   else {      Sa = 0.5; Sb = 0.5; }   printf("\nPlayer A has a new rating of %f\n", a + 32*(Sa - Ea)); printf("Player B has a new rating of %f\n\n", b + 32*(Sb - Eb)); return; }
 * 1) include 
 * 2) include 

Sandbox
Natural log integral: $$ \int \frac{1}{x} \, dx = \ln x $$

Pulse function: $$ \prod (t) = u(t+\frac{1}{2}) - u(t-\frac{1}{2}) $$

Fourier transform of double-sided exponential: $$ e^ \frac{-\left | t \right |}{\tau} \iff \frac{2 \tau}{1+(2 \pi f \tau)^2} $$

Absolute value interpretation: $$ x < \left| 5 \right|    \rarr     -5 < x < 5 $$

Other
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