Mathematics for Chemistry with Symbolic Computation

J. F. Ogilvie

            This interactive electronic textbook, in the form of Maple worksheets, is released in its sixth edition, 2021 August.  This book has two major divisions, mathematics for chemistry -- the mathematics that any instructor of a course in chemistry would wish a student thereof to understand and to be able to implement, and mathematics of chemistry, in the sense of the classic volumes by Margenau and Murphy -- mathematical treatments of particular topics in chemistry from an introductory post-secondary level to a post-graduate level. The content, which includes not only chapters in previous editions that have been revised but also additional chapters on quantum mechanics, molecular spectrometry and advanced chemical kinetics, has been collected during two decades, with many contributions from other authors, acknowledged in particular locations.  Each chapter includes not only explanatory treatments but also illuminating examples and exercises with chemical applications where practicable.

Mathematics for chemistry      0  introduction to Maple commands

                                                 1  numbers, symbols and elementary functions

                                                 2  plotting, geometry, trigonometry and functions

                                                 3  differential calculus

                                                 4  integral calculus

                                                 5  multivariate calculus

                                                 6  linear algebra

                                                 7  differential and integral equations

                                                 8  probability, statistics, regression and optimisation

Mathematics of chemistry       9  chemical equilibrium

                                                10  group theory

                                                11  graph theory

                                                12  quantum mechanics in three parts -- models, atoms and molecules

                                                13  molecular spectrometry

                                                14  Fourier transforms

                                                15  advanced chemical kinetics

                                                16  dielectric and magnetic properties

The content freely available at https://www.maplesoft.com/applications/view.aspx?SID=154267 includes also a published report on teaching mathematics with symbolic software and an interactive periodic chart that yields information about particular chemical elements and their isotopic variants.

            The nature of this electronic interactive textbook makes it applicable with an instructor in a traditional setting, or computer laboratory, for which the material of mathematics for chemistry could be reasonably covered in three or four semesters, but even for self study.  The chapters on quantum mechanics and Fourier transforms are available as separate textbooks in the same format.

Hi!

I have created a procedure for the so-called "Chaos Game" for the generation of Fractals. The file is the following:

Fractals_ChaosGame.mw

On the other hand, for a given day set D:={(x0,y0,(x1,y1),...., (xN,yN)}, for simplicity we assume D is contained in [0,1]x[0,1], one can to construct an "Iterated Functions System" such that its attractor set contains the set D. A detailed exposition of this topic can be found in the famous Barnsley's book "Fractals Everywhere". Also, in the following paper (sections 2.5 and 4-A):

https://arxiv.org/pdf/2102.09855.pdf

I have tried to implement in Maple 17 a procedure to create such Iterated Function System:

IFF_v2.mw

But, I feel that there is something wrong...After plot (with the Chaos Game procedure) a lot of points of the Iterated Functions System (i.e., an approximation of its attractor set), I have a "set of points", instead of a figure similar to a curve (which I feel that must be the correct).

Please, Somebody can have a look to the attached files?

Many thanks in advance for your comments.

Dear Sirs, 
I was with my students today, and attempting to do a Math Maple exercise. The assignment contained the requirement to plot three graphs in one plot f,g,h. Those with windows pc and maple were able use the proper command. 

plot({f(x),g(x),h(x)}) or plot([f(x),g(x),h(x)])  however some of those with MacOS would inside Maple 2021 get an error which said "GNU compiler not found", when using the same command. For those there was no other way (that I knew off) than to do a 

p1:=plot(f(x)): 

p2:=plot(g(x)): 

p3:=plot(h(x)):

and then plots:-display([f(x),g(x),h(x)]):  which work.

But why the MacOS error ? Any idea?

I have a printed book copy of Derek Richards' book, Advanced Mathematical Methods With Maple and would like to get the solutions to the problems in the book. Unfortunately the web download is no longer available. I have not been able to locate a copy or to contact Derek Richards directly. 

Can anyone please help?

Thanks

Joe Ladish

Hi! Do you know how can we make more transparent code for this animation plot? I want something similar to this but only for one spot:

my code:

restart;
with(plots);
with(plottools);
display(plot([cos(x), sin(2*x), x = 0 .. 2*Pi]), animate(pointplot, [[[cos(a), 0], [0, sin(2*a)], [cos(a), sin(2*a)]], color = [red, green, green], symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), 0], [cos(a), sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[0, sin(2*a)], [cos(a), sin(2*a)]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), implicitplot(x = cos(t), x = -1 .. 1, t = 0 .. 2*Pi), animate(plot, [[[0, a], [cos(a), a]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[0, a], [cos(a), a]], color = green, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), implicitplot(y = sin(2*t), t = 0 .. 2*Pi, y = -1 .. 1), animate(plot, [[[a, 0], [a, sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[a, 0], [a, sin(2*a)]], color = red, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [a, sin(2*a)]], linestyle = dash, color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [cos(a), a]], linestyle = dash, color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100));
 

Maybe some expert can help me with this.

I am trying to improve oeis.org/A156104. It is pairs of prime numbers p and p+36.
According to the k-tuple conjecture, this should be potentially an infinite list. I want to make the database .b file larger - from 1,000 to 10,000.

The virtual clipboard was too large to copy to notepad.  I could not figure out how to write this to a file.  I tried fopen() and fclose().

See my efforts

pairs_p_and_p+36_2.mw

pairs_p_and_p+36_2.pdf

Let me know.

Matt

restart;
with(Physics);
with(Physics[Vectors]);
with(geom3d);
with(LinearAlgebra);
with(ColorTools);
with(plots);

When I define a vector with Physics[Vectors] as:

a1 := a/2*(0*_i + _j + _k)

Maple returns:

a1:= a/2*(_j + _k)

Which is fine but if you try to take the cross product it won't work because the command expects a vector in R3 but interprets a1 as a vector in R2.

How do I ensure Physics[Vectors] understands a1 is a vector in R3

zero_component_problem.mw

The worksheet below contains an example of the tiling of the hyperbolic plane.

I would like to produce this and other hyperbolic plane tilings from Maple worksheets, but I don't know the math technique for doing so.

Please direct me to a source of the requisite knowledge or an example worksheet which I can study and imitate.

Hyperbolic_Plane_Tiling.mw

On virtually any webpage is a mixture of images and text. I can go to the page, select all contents, copy the contents into an Excel spreadsheet, save the spreadsheet file and then use the ExcelTools:-Import function to read the file into a DataFrame. At that point, I can work with the data.   All the text on the webpage, even if it is embedded in some HTML command, is copied as text into the spreadsheet which eventually can be read as text by Maple.

My quesiton is, what is the method for me to bypass Excel and import the webpage directly into Maple, striped of the HTML code? Can someone point me to an example? (The only examples I have seen use the Sockets package, but I thought this mode has been superceded with Import.)

Here is an example. Why not apply the minus sign to the numerator?
Is there a simple way to change this behavior.

t__FET_TurnOff := solve(-C__iss2*V__gs_th2 + Q__total = i__GateDriveN*t__off, t__off);



Preferred result

Programatically assigning colors to points in geom3d not working.  I just want all the points drawn by the draw command, to be the same color.  The output does not respond to programatic specification of the object color.

Maple 2021 Help says: "

geom3d: draw command

calling sequence:
draw(obj,...)
draw([obj_1,...,obj_n],...)

A typical call to the draw function is draw([ obj_1(localopts_1),...,obj_n(localopts_n) ], globalopts) where obj_1, ..., obj_n are geometric objects, localopts_1, ..., localopts_n are local options for a particular object, and globalopts are  options which apply to all of the objects.

localopts_i is a sequence of type equation. The set of options allowed for localopts_i is color = red."

I tried: color = "Red", color = "red", color = Red, color=red.  The command goes through but the colors remain distinct per point.  You can use the context menu to change the color after the command goes through but it is inefficient for my purposes. 

Here is an image of it not working:

Hello, There seems to be a bug in the int() routine when CPV is being used i.e.

restart;
f1 := (int(t^(2*a - 1)/(-t^2 + 1), t = 0 .. infinity, CPV = true) assuming (0 < a, a < 1));

the result given is

f1 := Pi/(2*sin(Pi*a)*(-1)^(1 - a))

but the correct result is

f1 := Pi/2*cot(Pi*a).

I need to use a remote machine with an outdated Maple 2016. But I have written my own package in Maple 2019 / 2020 on my laptop. When I try to load my code in Maple 2016, I got the error

Error, unexpected export declaration in module body

What are the main changes to the module system in the Maple language since the 2016 version? How should I modify the code to run it successfully? (I encounter no errors for other code which only contains procedures but not modules.)