Here's a question I was asked very recently: "When creating a plot, is it possible to specify the points at which the input expression should be evaluated?" The answer is "yes" for 2-D plots, and this is done with the 'sample' option.
Use the command plot(f(x), x=a..b, sample=[x1, x2, ..., xn]) to have f(x) evaluated at points x1, x2, ..., xn. Note this produces a plot that includes points with x-values x1, x2, ..., xn. To produce a plot that contains only these points, you need to add the adaptive=false option as well.
Waterloo Region, where our head office is located, has been called "The Quilt Capital of Canada". So a couple of years ago, I'd created a worksheet to generate a traditional "Log Cabin" quilt. I've made some minor updates to the example and added a "Trip Around the World Quilt". Having made a few quilts by hand myself, I can definitely say that it's easier to create a Maple one!
Here's a tip for people new to Maple or to 2-D input: always use a space for implied multiplication. 2-D math input in Maple allows for implicit multiplication, which is writing a multiplication operation without an explicit multiplication operator. An example is x y.
The space is not always required in cases where there is no ambiguity. However, it is highly recommended that you include it. An example that catches many new users (and some experienced ones as well) is s(t+u). This does not mean s times t+u, but the function s applied to t+u
One issue that often confuses users is local versus global optimization in Maple. I'm just going to give an overview here and will explore specific optimization topics more deeply in future blog entries. Please note that I'm covering only the numeric optimization methods here. I'll leave discussion of the exact methods in Maple to others more knowledgeable about those areas.
The Optimization package is built into Maple and is available to all users. This is primarily...
Question: How do I generate tickmarks in multiples of Pi? The answer has been posted before but this question comes up often enough that it is worth repeating.
In Maple 10 and earlier versions, you had to build a custom list of tickmarks, and the only way you could get the Greek pi symbol was to use the Symbol font.
In Maple 11, you can use the new 'spacing' structure with the 'tickmarks' option. To get tickmarks in multiples of Pi, use:
> plot(sin(x), x=0..8*Pi, tickmarks=[spacing(Pi), default]);
To get tickmarks spaced by 2*Pi, replace spacing(Pi) with spacing(2*Pi). To get the tickmarks occuring on the odd multiples of Pi, use spacing(2*Pi, Pi). The second argument is a fixed value from which the other tickmarks are determined.