New Mexico Tech
Hydrology Program
Hyd 510
Quantitative Methods in Hydrology
Summary of functions to be plotted from calculus review
in the lecture notes (see the notes for details):
Topic
Function(s)
(on the same plot)
Domain
Preview
x

C
D
 erfc 

C0
 B v ( vt  x ) 
Trig functions
sin x, cos x, tan x
Graph the function C/C0 vs.
time t at a one more
locations, x, and vs. space x
at one or more times, t.
Choose parameter values.
-4π ≤ x ≤+4π
Sine with frequency b,
a sin(bx + c)
phase lag c, and amplitude a
Products of functions
exp(-|x|) sin x,
Function and its inverse
“
-4π ≤ x ≤+4π; various
values of a, b, c
-4π ≤ x ≤+4π
f (x) = 3x & f -1(x) = x/3;
and y=x
x2 & √x ; and y=x
1≤ x ≤25
3x, 2x and (1/2)x
0 ≤ x ≤ 1.2
“
exp(x), 3x, 2x
-3≤ x ≤+3 (linear &
semilog plots)
-3≤ x ≤+3
“
e-x,. (1/2)x, x-1 , x-2
0≤ x ≤+2
Log functions
ln x
0 ≤ x ≤+3
Log and exp fcns.
ln x and its inverse, ex;
and y=x
(x + 1)/( x - 1)
-3≤ x ≤+3
-4π ≤ x ≤+4π
Error functions
sin(x), cos (x), and their
sum
erf x and erfc x
Exponential integral
Ei(x) and –Ei(-x)
0≤ x ≤+2
Bessel functions
J0(x) and K0(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
Exponential functions
Ratio of functions
Sums of functions
choose
-2≤ x ≤+2