Symbolic Mathematics for Chemists

A Guide for Maxima Users
 
 
Wiley (Verlag)
  • 1. Auflage
  • |
  • erschienen am 27. September 2018
  • |
  • 400 Seiten
 
E-Book | ePUB mit Adobe-DRM | Systemvoraussetzungen
978-1-119-27326-4 (ISBN)
 
An essential guide to using Maxima, a popular open source symbolic mathematics engine to solve problems, build models, analyze data and explore fundamental concepts Symbolic Mathematics for Chemists offers students of chemistry a guide to Maxima, a popular open source symbolic mathematics engine that can be used to solve problems, build models, analyze data, and explore fundamental chemistry concepts. The author -- a noted expert in the field -- focuses on the analysis of experimental data obtained in a laboratory setting and the fitting of data and modeling experiments. The text contains a wide variety of illustrative examples and applications in physical chemistry, quantitative analysis and instrumental techniques. Designed as a practical resource, the book is organized around a series of worksheets that are provided in a companion website. Each worksheet has clearly defined goals and learning objectives and a detailed abstract that provides motivation and context for the material. This important resource: * Offers an text that shows how to use popular symbolic mathematics engines to solve problems * Includes a series of worksheet that are prepared in Maxima * Contains step-by-step instructions written in clear terms and includes illustrative examples to enhance critical thinking, creative problem solving and the ability to connect concepts in chemistry * Offers hints and case studies that help to master the basics while proficient users are offered more advanced avenues for exploration Written for advanced undergraduate and graduate students in chemistry and instructors looking to enhance their lecture or lab course with symbolic mathematics materials, Symbolic Mathematics for Chemists: A Guide for Maxima Users is an essential resource for solving and exploring quantitative problems in chemistry.
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1
Fundamentals


The most powerful single idea in mathematics is the notion of a variable.

- K. Dewdney [1]

Maxima is a general-purpose computer algebra system (CAS) that can be used to perform numerical and symbolic calculations, simplify complicated expressions, solve algebraic and differential equations, analyze and plot data, differentiate and integrate functions, compute statistics, perform matrix and vector operations, and more. Maxima in various forms has been in use for half a century. Development on Maxima's predecessor Macsyma began in the late 1960s at MIT. In 1998, the U.S. Department of Energy released Macsyma's source code into the public domain, and the program became Maxima. Today, Maxima is actively supported and updated by an international community of users and developers [2].

Maxima differs in several important ways from commercial CASs like Mathcad, MATLAB, Maple, and Mathematica:

  • Maxima is open-source software, distributed under the the Free Software Foundation's GNU General Public License [3].
  • Maxima is available for Windows, Mac OS, Linux, and Android tablets and phones. Commercial software is usually available on a limited number of platforms. For example, Mathcad works only under Windows; Mathematica and Maple are not available for Android tablets or phones, or on non-Intel-based Macs.
  • Most commercial CASs provide a single interface, while Maxima is a computational "back end" that can use several different interfaces. Think of Maxima as an automobile engine; it runs unseen under the hood of the car. It is controlled through a graphical "front end" or user interface, analogous to the steering wheel, dashboard, and pedals of the car. Some front-ends and software systems that use Maxima as a back end are wxMaxima [4], XMaxima [5], Euler Math Toolbox [6], Sage [7], TeXmacs [8], SMath Studio [9], and Cantor [10]. Websites can also perform symbolic calculations and plot graphs interactively using Maxima as a back end [11].

1.1 Getting Started With wxMaxima


Maxima comes bundled with two front-ends: Xmaxima and wxMaxima. wxMaxima is the more powerful of the two. It displays typeset mathematical expressions and plots, and it provides menus, toolbars, and dialogs to access most important Maxima functions. It also saves an entire session with Maxima including text, headings, and calculations in a single printable document. In this book, we'll focus exclusively on Maxima running under wxMaxima.

In wxMaxima, commands are typed into input cells. To create a new cell, click on an empty space anywhere. A horizontal line will appear. This is the cell cursor; typing will create a new input cell at that point. You can click between cells or before the first cell to move the cell cursor to at any point in the worksheet.

Start wxMaxima and type 2+2;. To execute the command, press ?+?. The result will like this:

Commands end with either a semicolon (;) or a dollar sign ($). The semicolon shows output from the command; the dollar sign hides it. wxMaxima adds the semicolon automatically to the last command in a cell if you forget to type it.

Linebreaks, tabs, and spaces are ignored in Maxima commands. You'll get an error message if you try to separate commands only with a linebreak instead of a semicolon or dollar sign.

1.1.1 Input Cells


Let's take a closer look at the way wxMaxima displays a command and its output in input cells:

Maxima labels both input and output within the cell. The first command is labeled with (%i1). Each additional command you type will be labeled with %i followed by the number of the command. The output is labeled with (%o1). Every output is labeled with %o followed by the number of the corresponding input command.

Notice the glyph on the left edge of the cell (Figure 1.1). It shows the division between input and output in the cell, and also provides a way to hide the output (click on the triangle on top of the glyph). Clicking on the glyph itself selects the cell. Dragging the mouse over multiple glyphs selects them all. You can then cut, copy, or delete the selected cell or cells:

  • To copy, press ?+? or click on the Copy Selection icon on the tool bar (it's just to the right of the scissors icon).
  • To delete, press the key.
  • To cut (which copies the cell and then deletes it), press ?+? at the same time or click on the scissors icon on the toolbar.

Figure 1.1 An input cell in wxMaxima divides the cell into input and output sections, with a glyph on the left that provides a way to hide output or select the cell for copying, cutting, or deleting.

Cells that have been cut or copied can be pasted back into the worksheet. Click on the space where you'd like to insert the cell or cells and press ?+?.

Cells are executed by pressing ?+?. While a cell is executing, the glyph is outlined in black, and the message Maxima is calculating appears in the status bar at the bottom of the window.1 The black outline will not go away if you've made an error in the cell.

You can place multiple commands into a single input cell, as long as each ends with a semicolon or a dollar sign. This is useful in showing intermediate results or for grouping commands. Press after each command to keep the input readable. Maxima executes commands within a cell the order that you type them, and it numbers the output for each line automatically.

1.1.2 The Toolbar


The toolbar provides shortcuts for storing, loading, editing, and managing sessions in wxMaxima (Figure 1.2).

Figure 1.2 The wxMaxima toolbar.

The crossed tool icon is used to set program options and flags, and also to set styles for fonts and colors. We'll look at it in more detail in Section 1.1.3.

The triangle, square, and slider icons are used to play, stop, and step through animated plots. This is an advanced feature that we'll use in one of the worksheets for Chapter 4.

The blue question mark icon on the right will display the Maxima manual in a separate window. To see the help page for a particular command, select the command in your worksheet and click on the Help icon (the question mark on the far right side of the toolbar). Clicking the icon without first selecting a command brings up the wxMaxima manual. You can also press the key or select to bring up help pages for a selected command.

1.1.3 The Menus


Many Maxima functions can be accessed through the menus above the toolbar. The menus also let you configure wxMaxima and control the execution of cells.

  • The menu has items for creating, opening, saving, and printing wxMaxima documents. can load special-purpose code packages into Maxima. can load and execute a series of commands that have been previously saved as a file with the .mac extension.2 can save your wxMaxima file as an HTML file or as a LATEX file.3
  • The menu has items for undoing and redoing changes; cutting, copying, and pasting commands and output; finding and selecting text; zooming in and out; and setting preferences. The item is equivalent to the crossed-tool icon on the toolbar. Select to change wxMaxima's default behavior. Most of the options are self-explanatory.
    • - Check Match parenthesis in text controls so wxMaxima will automatically type a closing parenthesis after you type an open parenthesis, and so that clicking on a closing parenthesis automatically highlights the matching opening parenthesis.
    • - Check Show long expressions if you'd like to see results when Maxima displays a message like?<?< Expression too long to display! >?>?.
    • - Check Enter evaluates cells if you'd rather not execute cells with ?+? (the default). This isn't recommended, because it will keep you from breaking long commands up into a series of easy-to-read lines.
    Select to change the fonts and colors that wxMaxima uses.
  • The menu is used to evaluate, copy, insert, and hide different types of cells. In addition to input cells containing Maxima commands, you can organize your wxMaxima document by inserting text, titles, section titles, subsection titles, images, and page breaks.
  • The menu is used to interrupt or restart Maxima. Several useful floating toolbars can be shown using . You can also use the menu to show and delete functions and variables that have been defined in the current session, and change the way math is displayed in output.
  • The , , , , and menus start dialogs that build Maxima commands.
  • The menu has items that are useful for setting the precision of calculations and displayed numeric results.
  • The menu provides context-sensitive help. Selecting a command and then selecting brings up the manual page for that command. can...

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