Introduction to Maple
Maple is a symbolic computation system or computer algebra system (CAS) that manipulates information in a symbolic or algebraic manner. You can use these symbolic capabilities to obtain exact, analytical solutions to many mathematical problems. Maple also provides numerical estimates to whatever precision is desired when exact solutions do not exist.
Maple 2019 and higher is different from previous versions of Maple. With Maple 2019 you can create profession quality documents, presentations, and custom computational tools. You can access the power of the Maple computational engine through a variety of interfaces: standard worksheet, classical worksheet, command line version, graphing calculator (Windows only), or Maple applications. Although you type in the commands in a very similar manner as in previous versions of Maple, the statement appears in a “pretty print” format on the screen; that is, the statement appears more like typeset mathematics.
This is a full-featured graphical user interface offering features that help to create documents that show all assumptions, the calculations, and any margin of error in your results. You can even hide the computations to focus on problem setup and final results.
The basic worksheet environment works best for older computers with limited memory.
Command-line interface, without graphical user interface features, is used for solving very large, complex problems or batch processing.
Maplesoft™ Graphing Calculator
The graphical interface to the Maple computational engine allows you to perform simple computations and create customizable, zoomable graphs. The Graphing Calculator is only available in the Windows version.
The graphical user interface containing windows, textbox regions, and other visual features gives you point-and-click access to the power of Maple. It allows you to perform calculations and plot functions without using the worksheet or command-line interfaces.
Maple’s extensive mathematical functionality is most easily accessed through all these interfaces. Previous older versions relied on its advanced worksheet-based graphical interface. A worksheet is a flexible document for exploring mathematical ideas or mathematical alternatives and even creating technical reports.
Experimental mathematical modeling, a natural stepping stone to statistical analysis, has an obvious coupling with computers, which can quickly solve equations, and plot and display data to assist in model test and evaluation. The software computer algebra system, Maple, is a powerful tool to assist in this process. When dealing with real-world problems, data requirements can be immense. When evaluating immigration trends, for example, and the political, social, and economic effects of these trends, thousands of data points are used; in some cases, millions of data points. Such problems cannot be analyzed by hand, effectively or efficiently. The manipulation required to plot, curve fit, and statistically analyze with gooclness-of-fit techniques, cannot feasibly be done without the assistance of a computer software system.
The Maple system is easy to learn and can be applied in many mathematical applications. While these demonstrate its versatility, Maple is also an extremely powerful software package. Maple provides over 5000 built-in definitions and mathematical functions, covering every mathematical interest: calculus, differential equations, linear algebra, statistics, and group theory to mention only a few. The statistical package reduces many standard time-consuming statistical questions into one-step solutions, including mean, median, percentile, kurtosis, moments, variance, standard deviation, and so forth. There are many references for Maple, and a short list would include:
This chapter presents a quick review of some basic Maple commands. It is not intended to be a self-contained tutorial for Maple, but will however provide a quick review of the basics prior to more sophisticated commands in the modeling chapters. There are many good references for those new to Maple. Additionally, there is a collection of self-contained tutorials accessed by clicking the “Getting Started” button on Maple’s opening screen. See Figure 1.1.