Mathematica, Maple, Matlab, IDL
Brief description, with links
Each of these popular symbolic and/or numerical mathematics software packages has its own strong points. All are available on some computers on the C.U. campus, though rarely all on a single computer.
Mathematica
is the premier all-purpose mathematical software package. It integrates swift and accurate symbolic and numerical calculation, all-purpose graphics, and a powerful programming language. It has a sophisticated ``notebook interface'' which is great for documenting and displaying work. It can save individual graphics in any graphics format. Its functional programming language (as opposed to procedural) makes it possible to do complex programming using very short concise commands; it does, however, allow the use of basic procedural programming constructs like Do and For. Drawbacks: steeper learning curve for beginners used to procedural languages; more expensive links: BASICS, Local resources, Wolfram Inc., Wolfram technical FAQs
Matlab
Matlab combines efficient computation, visualization and programming for linear-algebraic technical work and other mathematical areas. It is widely used in the Engineering department. Drawbacks: Not for analytical/symbolic math links: MathWorks Matlab home page
Maple
Maple is powerful analytical and mathematical software which does the same sorts of things that Mathematica does, with similar high quality. Maple's programming language procedural -- like C or Fortran or Basic -- although it has a few functional programming constructs. Drawbacks: Worksheet interface/typesetting not as developed as Mathematica's, but it is less expensive links: Waterloo Maple web site
IDL
(Interactive Data Language) excels at processing real-world data, especially graphics, and has a reasonably simple syntax, especially for those familiar with Fortran or C. IDL makes it as easy as possible to read in data from files of numerous scientific data formats. IDL is very popular at NASA, universities and research facilities, and especially at C.U. where it was originally developed and is free (see site license). Drawbacks: Does not do symbolic math links: basic IDL, RSI IDL home page
Friday, September 15, 2006
What Is Mathematica?
What Is Mathematica?
You probably know Mathematica by name. Or you may be one of nearly two million users. But do you really know the breadth of capabilities Mathematica can offer you? Whatever you're working on--calculating, programming, learning, documenting or developing--Mathematica is equipped to help.
Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. It is this range of capabilities--many world-leading in their own right--that makes Mathematica uniquely capable as a "one-stop shop" for you or your organization's technical work.
Wide Range of Uses
Handling complex symbolic calculations that often involve hundreds of thousands or millions of terms
Loading, analyzing, and visualizing data
Solving equations, differential equations, and minimization problems numerically or symbolically
Doing numerical modeling and simulations, ranging from simple control systems to galaxy collisions, financial derivatives, complex biological systems, chemical reactions, environmental impact studies, and magnetic fields in particle accelerators
Facilitating rapid application development (RAD) for engineering companies and financial institutions
Producing professional-quality, interactive technical reports or papers for electronic or print distribution
Illustrating mathematical or scientific concepts for students from K-12 to postgraduate levels
Typesetting technical information--for example, for U.S. patents
Giving technical presentations and seminars
Works at All LevelsUsually Mathematica is used with its notebook interface directly as it comes out of the box. However, it is increasingly being used through alternative interfaces such as a web browser or by other systems as a back-end computational engine.
Some of these uses require in-depth Mathematica knowledge, while others do not. Mathematica is unusual in being operable for less involved tasks as well as being the tool of choice for leading-edge research, performing many of the world's most complex computations. It is Mathematica's complete consistency in design at every stage that gives it this multilevel capability and helps advanced usage evolve naturally.
Take a tour of Mathematica.
Fully Featured, Fully Integrated
At a superficial level, Mathematica is an amazing, yet easy-to-use calculator. The world's most comprehensive set of mathematical, scientific, engineering, and financial functions is ready-to-use--often with just one mouse click or command. However, Mathematica functions work for any size or precision of number, compute with symbols, are easily represented graphically, automatically switch algorithms to get the best answer, and even check and adjust the accuracy of their own results. This sophistication means trustworthy answers every time, even for those inexperienced with the mechanics of a particular calculation.
While working through calculations, a notebook document keeps a complete report: inputs, outputs, and graphics in an interactive but typeset form. Adding text, headings, formulas from a textbook, or even interface elements is straightforward, making online slide show, web, XML, or printed presentation immediately available from the original material. In fact, with notebook document technology, a fully customized interface can easily be provided so that recipients can interact with the content. The notebook is a fully featured, fully integrated technical document-creation environment.
Easy Programming, Powerful Results
The move from immediate calculations to programmed computations can occur evolutionarily. Just one line makes a meaningful program in Mathematica--the methodology, syntax, and documents used for input and output remaining as they are for immediate calculations.
Mathematica is also a robust software development environment. Mathematica packages can be debugged, encapsulated, and wrapped in a custom user interface, all from within the Mathematica system. Alternatively, Java, C, or links to a proprietary system can use Mathematica's power behind the scenes.
One Unifying Idea
Symbolic programming is the underlying technology that provides Mathematica this unmatched range of abilities. It enables every type of object and every operation--be they data, functions, graphics, programs, or even complete documents--to be represented in a single, uniform way as a symbolic expression. This unification has many practical benefits from ease of learning to broadening the scope of applicability of each function. The raw algorithmic power of Mathematica is magnified and its utility extended.
You probably know Mathematica by name. Or you may be one of nearly two million users. But do you really know the breadth of capabilities Mathematica can offer you? Whatever you're working on--calculating, programming, learning, documenting or developing--Mathematica is equipped to help.
Mathematica seamlessly integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. It is this range of capabilities--many world-leading in their own right--that makes Mathematica uniquely capable as a "one-stop shop" for you or your organization's technical work.
Wide Range of Uses
Handling complex symbolic calculations that often involve hundreds of thousands or millions of terms
Loading, analyzing, and visualizing data
Solving equations, differential equations, and minimization problems numerically or symbolically
Doing numerical modeling and simulations, ranging from simple control systems to galaxy collisions, financial derivatives, complex biological systems, chemical reactions, environmental impact studies, and magnetic fields in particle accelerators
Facilitating rapid application development (RAD) for engineering companies and financial institutions
Producing professional-quality, interactive technical reports or papers for electronic or print distribution
Illustrating mathematical or scientific concepts for students from K-12 to postgraduate levels
Typesetting technical information--for example, for U.S. patents
Giving technical presentations and seminars
Works at All LevelsUsually Mathematica is used with its notebook interface directly as it comes out of the box. However, it is increasingly being used through alternative interfaces such as a web browser or by other systems as a back-end computational engine.
Some of these uses require in-depth Mathematica knowledge, while others do not. Mathematica is unusual in being operable for less involved tasks as well as being the tool of choice for leading-edge research, performing many of the world's most complex computations. It is Mathematica's complete consistency in design at every stage that gives it this multilevel capability and helps advanced usage evolve naturally.
Take a tour of Mathematica.
Fully Featured, Fully Integrated
At a superficial level, Mathematica is an amazing, yet easy-to-use calculator. The world's most comprehensive set of mathematical, scientific, engineering, and financial functions is ready-to-use--often with just one mouse click or command. However, Mathematica functions work for any size or precision of number, compute with symbols, are easily represented graphically, automatically switch algorithms to get the best answer, and even check and adjust the accuracy of their own results. This sophistication means trustworthy answers every time, even for those inexperienced with the mechanics of a particular calculation.
While working through calculations, a notebook document keeps a complete report: inputs, outputs, and graphics in an interactive but typeset form. Adding text, headings, formulas from a textbook, or even interface elements is straightforward, making online slide show, web, XML, or printed presentation immediately available from the original material. In fact, with notebook document technology, a fully customized interface can easily be provided so that recipients can interact with the content. The notebook is a fully featured, fully integrated technical document-creation environment.
Easy Programming, Powerful Results
The move from immediate calculations to programmed computations can occur evolutionarily. Just one line makes a meaningful program in Mathematica--the methodology, syntax, and documents used for input and output remaining as they are for immediate calculations.
Mathematica is also a robust software development environment. Mathematica packages can be debugged, encapsulated, and wrapped in a custom user interface, all from within the Mathematica system. Alternatively, Java, C, or links to a proprietary system can use Mathematica's power behind the scenes.
One Unifying Idea
Symbolic programming is the underlying technology that provides Mathematica this unmatched range of abilities. It enables every type of object and every operation--be they data, functions, graphics, programs, or even complete documents--to be represented in a single, uniform way as a symbolic expression. This unification has many practical benefits from ease of learning to broadening the scope of applicability of each function. The raw algorithmic power of Mathematica is magnified and its utility extended.
Subscribe to:
Posts (Atom)
Facebook Badge
Subscribe To
Posts
All Comments
