New Mexico TechHyd 510
Hydrology ProgramQuantitative Methods in Hydrology
Summary of functions to be plotted from calculus review
in the lecture notes(see the notes for details):
(on the same plot) / Domain
Preview / / Graph the function C/C0vs. timet at a one more locations, x, and vs. spacex at one or more times, t. Choose parameter values.
Trig functions / sin x, cos x, tan x / -4π≤ x ≤+4π
Sine with frequencyb, phase lag c, and amplitudea / a sin(bx + c) / -4π≤ x ≤+4π; various values of a, b, c
Products of functions / exp(-|x|) sin x, / -4π≤ x ≤+4π
Function and its inverse / f (x) = 3xf -1(x) = x/3;
and y=x / 1≤ x≤25
“ / x2 √x ; and y=x / 0 ≤ x≤ 1.2
Exponential functions / 3x, 2x and (1/2)x / -3≤ x≤+3 (linear & semilog plots)
“ / exp(x), 3x, 2x / -3≤ x≤+3
“ / e-x,. (1/2)x, x-1 , x-2 / 0≤ x ≤+2
Log functions / ln x / 0 ≤ x ≤+3
Log and expfcns. / ln x and its inverse, ex;
and y=x / -3≤ x ≤+3
Ratio of functions / (x + 1)/(x - 1) / choose
Sums of functions / sin(x), cos (x), and their sum / -4π≤ x ≤+4π
Error functions / erf x and erfc x / -2≤ x≤+2
Exponential integral / Ei(x) and –Ei(-x) / 0≤ x≤+2
Bessel functions / J0(x) andK0(x) ( / 0 < x≤ 10
Exponential decay / e-k t for k= 0.5, 1, 2 / 0 ≤ t ≤ 5
Exponential growth / e+k t for k= 0.5, 1, 2 / 0 ≤ t ≤ 5