Below you find a listing of when the different Maple commands first are used in the works-sheets accompanying the lectures. The listings are much more sparse for the solutions to the problem sets. Generally these involve applications of material already introduced in the lecture material. There are some exceptions and these are given near the bottom of the file.
Complex
variables:
:= versus =
clearing memory: restart
complex variables: abs, argument, evalc, I, Im, polar, Re
evaluating as a floating point expression: evalf
exponential exp
hyperbolic functions: cosh, sinh
Pi
termination with/without output: ; :
trigonometric functions: arctan, cos, sin
Summing
series:
creating a simple plot: plot
defining functions: ()->expr
differentiating a function: diff
factorial: !
infinity
loading plots library package: with(plots)
plotoptions: axes, BOXED, color,
labels, title, tickmarks
power: ^
range of plot or sum: x=a..b
summing a series:
sum
Differential equations
differentiation
using D vs diff
defining functions : unapply vs ->
differential equation solutions: dsolve
dsolve options:
numeric, output=listprocedure,
plotting solutions generated by dsolve: odeplot
specifying a set of equations or variables: {}
substituting into an equation: subs
using part of an equation: rhs
sequences, sets and lists, seq, { }, [ ]
draw a curve through set of points: listplot
solve a system of equations: solve
union of two sets: union
Fourier coefficients:
integrating a function: int
numpoints
piecewise
plot3d
solving transcendental equations numerically:fsolve
tan
LCR-circuit:
Fast
Fourier Transform:
library package: with(stats)
array
FFT
iFFT
log
print
randomize
stats[random,normald]
stats[random,uniform]
Vibrating
membrane:
library package: with(geometry)
plot objects: display
animate3d
axes=none
circle
coords
draw
dsegment
frames
point
z_cylindrical
Heat equation:
spherical bessel functions
Fourier
transforms:
library
package with(inttrans)
fourier
invfourier
Delta
function:
if....then ... else
...fi
Solutions
to problems
(Commands
only listed if not in worksheets accompanying lectures)
square root: sqrt
limits of 0/0 expressions: limit
more hyperbolic functions: coth
natural logarithm: ln
sum
vs Sum
manipulating algebraic expressions: simplify
putting several curves in same plot: display
text in plot:
textplot
aligning text in plot : align=LEFT, align=RIGHT
Using mouse to read off values of points in plot
Manipulating algebraic expressions: expand
turning an expression into an operator: unapply
animate,
frames, numpoints
do-loop: for ... from ... to ...do
...
od
(end do)
matrixplot