Graphical lnterface
Package for Calculus Education
Support for Researchers, Scientists and Engineers
List of New Features and Benefits

Graphical Interface

Make Maple easier to use – your way
With the Maplets™ package, you can create your own graphical user interfaces to Maple. Maplets give users access to your Maple applications through buttons, text areas, menus, and other graphical elements that you specify. Your Maple code recedes safely into the background, sparing users from having to understand its syntax or enter Maple commands.

Hands-on tutorials for students
The Maplets package provides a natural medium for creating tutorials for math and science classes. For example, you can use maplets to create interactive tutorials on the e-d definition of a limit, the Doppler effect, or the iterations of a fractal. The only boundary is your imagination.

Interactive Plot Builder
You can create plots through a built-in maplet that prompts you for all relevant plotting options in text areas and menus. No more remembering plot commands and their plethora of options!

Package for Calculus Education

Step-by-step calculus computations
Maple 8 can guide students through differentiation, integration, and limit problems. At any step of a problem, a student can apply a calculus rule or ask Maple for a hint. For example, Maple might recommend “Substitute u=tan(x)” or “Use the chain rule”. The student can then apply the hint and proceed to the next step of the problem.

Instant visual aids for calculus lessons
Want to examine a surface of revolution from different angles? Watch Newton’s method converge? Annotate the graph of a function with its intervals of concavity? Visual aids designed specifically for calculus lessons are now built into Maple 8 as high-level commands.

Examples include:
& Tangent lines and secant lines
& Graphs labeled with slope, concavity, extrema, roots, and asymptotes
& Surfaces and volumes of revolution
& Animations of Taylor series and Newton’s method
& Approximate integration (Simpson’s Rule,
Trapezoidal Rule, and more)

Support for Researchers, Scientists and Engineers

Scientific constants
Never again must you consult reference books or the Web to perform scientific computations. Maple 8 includes Avogadro’s number, the proton magnetic shielding correction, and over 13 000 other scientific constants from physics and chemistry.
If you need to look up the ionization energy of iodine, don’t get up, because Maple 8 already knows the Periodic Table. With a single Maple command, you can access the basic chemical properties of any element or isotope.
If the Maple 8 database of constants doesn’t suffice for your application, you can easily extend or change it.

Numeric PDEs
Heat equation, wave equation, Poisson equation – they all yield to the new Maple 8 numeric PDE-solver. Maple 8 can now solve linear systems of PDEs with boundary conditions.

Java™ code generation and external calling
Maple 8 has added Java™ to its repertoire of connectivity with other programming languages. You can exploit the flexibility of Java classes by automatically translating your Maple results into Java code. You can also call static Java methods externally from Maple 8 applications.

Vector calculus
Maple 8 provides a new package of functions for vector calculus. —-operations, surface integrals, differential geometric properties, and many other computations can be performed using any basis and in any coordinate system that you specify. The package is fully compatible with the Maple LinearAlgebra package.

Calculus of variations
You can now compute geodesics and other optimal functionals with ease using the new Maple 8 VariationalCalculus package.

Differential equations
The Waterloo Maple research team has enriched the Maple ODE solvers with more powerful algorithms in Maple 8. Maple remains the most extensive computational environment in the world for working with differential equations.

List of New Features and Benefits

MATHEMATICAL

Education

Maplets™
& A revolutionary package called Maplets™ provides tools to create custom Java™-based graphical user interfaces – called maplets – to the thousands of routines in the Maple library, as well as to your routines. Maplets allow users to perform Maple calculations and display graphics without knowledge of Maple syntax.
& You can embed a full range of GUI elements
into your maplets, including text areas, buttons, equation editors, drop-down menus, scroll bars, and plot regions.
& Several predefined maplets are available in the Examples subpackage, which you can modify and reuse, including interfaces to several functions in the LinearAlgebra package.
& There are predefined dialog maplets that prompt the user to enter an expression, find a file, and answer a question.

The Student Package
& The new Student package assists educators and students in teaching and learning first year calculus.
& An intuitive set of tools allows students to work through limit, differentiation, and integration problems step-by-step. At any step of the problem, the student can obtain a hint from Maple.
& Numerous visualization commands graphically illustrate the Mean Value Theorem, volumes and surfaces of revolution, Newton’s method, Taylor approximations, and more.

Differential Equations

Numerical Solutions to PDEs
& You can solve linear systems of bivariate PDEs and PDE-boundary value problems numerically using the new numeric option to pdsolve.
& You can view numeric PDE solutions as plots, animations, and numerical values.

Nonlinear ODEs
& Enhancements to dsolve include a new implementation of integrating factor methods that can systematically determine integrating factors of varied types and perform multiple reductions of order in one step when more than one integrating factor is found.
& Improvements to symmetry algorithms provide simpler solutions for second order nonlinear ODEs.
& New routines are available for solving two
parameterized Abel ODE classes
& All routines for solving equivalence problems can handle fractional or abstract powers systematically.

Linear ODEs
& There are new algorithms for computing
hypergeometeric solutions for second order
linear ODEs in which the equivalence between an ODE and one having 2F1, 1F1, or 0F1 hypergeometric solutions can be resolved.
& Kovacic’s algorithm has been extended to
handle fractional and abstract powers.
& Three new algorithms have been incorporated for higher order linear ODEs to work in the presence of non rational objects.

Enhancements in the DEtools Package
• New routines to DEtools include the ability to
solve a rational ODE using power transformations of the independent variable composed with linear transformations of the dependent variable.
& The intfactor command has been enhanced
to compute integrating factors for nonlinear ODEs when the integrating factor depends on many variables.
& A new set of linear ODE families can compute hypergeometric solutions.
& You can solve an ODE admitting many different integrating factors simultaneously using the new redode routine.
& The convertODE facility has been extended to convert to ODEs of type linear, Ricatti, and Abel to normal form.

Numerical Solution to ODEs
• The default stiff and non-stiff methods are enhanced to produce a numerical solution over a range in terms of piecewise polynomial functions.
& plots[ODEplot] can produce multiple solution curves and animations of solutions to ODE systems.
& rkf45, dverk78, gear, and classical methods have been enhanced to compute numerical solutions to ODE problems in which the initial point has a removable singularity.
& An option to dverk78 provides a choice of local error computation strategies, resulting in reduced running time.

New Mathematics Packages

Vector Calculus
• The VectorCalculus package provides a full suite of routines to perform calculations in multivariate and vector calculus, including — operations, surface integrals, and differential geometric properties. You can perform these calculations in any coordinate system and in any basis.

Scientific Constants
• The ScientificConstants package provides access to the values of over 13000 physical constants that occur in chemistry and physics, including the speed of light in a vacuum and the melting point of sodium.
& You can extend and modify the database with constants and chemical properties.

Calculus of Variations
• You can construct the Euler-Lagrange equation and first integrals, the Jacobi differential equation and the Weierstrass excess function with the new VariationalCalculus package.

Symbolic-Numeric Algorithms for Polynomials (SNAP)
• New tools for the algebraic manipulation of numerical polynomials include computation of an epsilon gcd, a quasi gcd, and the last numerically stable Euclidean reduction.

Matrix Polynomial Algebra
• You can determine special forms of matrix polynomials, perform basic polynomial operations, find bases for the kernel of a matrix polynomial, and compute algebraic operations using the new MatrixPolynomialAlgebra package.

Sum Tools
& The SumTools package provides functions for finding closed forms of definite and indefinite sums of hypergeometric type.

Enhanced Mathematics Packages

CurveFitting
• The Spline routine now accepts boundary conditions such as natural, not-a-knot, periodic, clamped, and generalized end conditions.
& The Spline function has a more efficient algorithm for degree 2 and degree 3 cases in the presence of floating-point data.
& A built-in maplet provides a graphical interface to the CurveFitting package.

Linear Algebra
& The LinearAlgebra package has a new subpackage for performing linear algebra operations modulo a prime or composite over a positive range.
& A new EigenConditionNumbers routine computes any of the eigenvalues, eigenvectors, condition numbers of the eigenvalues, or the condition num bers of the eigenvectors for real or complex, generalized or nongeneralized problems.
& The MatrixInverse routine has been extended to compute the Moore-Penrose pseudo-inverse for floating-point and exact matrices.
& The LeastSquares routine contains an indirect sparse real solver for floating-point problems.
& The new HermiteForm routine computes a reduced transforming matrix.
& A new algorithm makes generation of sparse random matrices faster.

Plots
• You can visually compare the real and imaginary parts of two functions to see where they differ on a given domain, using the new plotcompare routine.

Slode Package
& You can construct formal solutions of differential equations in which the series coefficients satisfy homogenous or nonhomogeneous recurrences with more than two terms.

Solve Tools
& New routines in SolveTools allow inverse functions to be canceled, parts of expressions containing logarithms, exponentials and powers to be combined, and systems of linear equations with various coefficients to be solved.

Enhanced Symbolic Capabilities
• A flexible new network of conversion routines for mathematical functions permits the expression of any mathematical function in terms of another. These routines allow you to convert among any of the 58 mathematical functions. Simplifying definite integrals or sums uses the integrating range.
& The simplify command has been extended for generalized hypergeometric MeijerG functions, confluent hypergeometric Kummer functions, and Legendre functions of integer degree and order to elementary form.

GRAPHICAL USER INTERFACE

Maplets
• You can design graphical user interfaces to access the Maple library and your Maple routines using the new Maplets package. Graphical elements that you can place in your maplets include buttons, text areas, equation editors, pop-up menus, menubars, tables, and MathML viewers.

Maplet Viewer
• The MapletViewer facility launches a standalone maplet outside a Maple session.

Saving a Worksheet as a Maplet or Maple Input
• Worksheets saved as maplets can be displayedusing the MapletViewer feature.
& Worksheets saved as Maple input can be loaded into command-line versions of Maple.

Interactive Plot Builder
• You can create plots and build plot commands using a new graphical user interface to Maple basic plotting routines and plot options. This feature is accessible through the context menus and the plots interactive routine.

Pretty-Printer Enhancements
• Numerous pretty-printer enhancements include improved derivative display, control of numeric display precision, added symbols for the set and membership operators, basis notation for vectors, and improved expression layout.

Spell Check
• The Spellcheck facility searches text regions from among thousands of words including commonly used mathematical terms and Maple words. Users can add words to the dictionary or select a preferred dictionary.

E-mail Worksheets
• Worksheets can be emailed directly from the Maple environment.

Importing and Exporting XML
• You can export a worksheet in the Extensible Markup Language (XML) format and load XML documents.

Web Resources Links
• You have direct and easy access to the Maple Application Center, the Maple Student Center, and the Waterloo Maple Corporate home page from the Maple Help menu.

Mixed Kernel Mode
• Mixed kernel mode allows users to specify the mode (shared or parallel) in which each worksheet window runs.

File Preferences Dialog
& The settings available from the Options menu are available in the File Preferences dialog box from the File menu.

PROGRAMMING & CONNECTIVITY

Java Code Generation
• The new CodeGeneration package translates Maple routines to Java code.

Enhanced C and Fortran Code Generation
• The CodeGeneration package provides enhanced C and Fortran code generation. Several options give you greater control over the translation of types, and improvements have been incorporated when translating to Fortran.

Software Metrics
& You can analyze the code complexity of a Maple procedure or module by computing McCabe’s cyclomatic complexity metric, Halstead’s software science metrics, or metrics that provide details about the nesting depth of selection and repetition structures.

Library Tools
• The new LibraryTools package simplifies the creation and maintenance of Maple libraries.

Type Tools
• You can extend the existing list of types in Maple by allowing users to add, delete, or display user-defined types.

Worksheet
• The Worksheet package provides a set of functions to generate and manipulate Maple worksheets as XML data structures.

Enhanced packagesdefine_external for Java
• You can now call static Java methods externally with the define_external routine.

Process
• The Process package has expanded to include the ability to launch a process or software application outside Maple.
Sockets
& The new HostInfo routine retrieves platform specific data such as the platform, operating system, node, domain name, and pid.

StringTools
& The new FormatTime routine returns a formatted date and time using an optional list of conversion specifiers to display the string of your choice.
& The StringBuffer routine constructs long strings in pieces by appending the pieces one at a time.
& The Encode and Decode routines process strings by subjecting them to text encoding and decoding.XMLTools
& Several new utilities and a validating XML parser were added to this package.

Programming Facilities Changes

System Changes
• Maple repositories can be assigned unique names and saved in the same directory.
& You can list the contents of a directory and distinguish between files and subdirectories when navigating through directories using two new routines, isdir and listdir
& A new option for kernelopts greatly simplifies module debugging.

Higher Order Procedures
• Two new procedures, andmap and ormap, determine whether a predicate holds for some or all operands of an expression.
& The member procedure now accepts functions as a second argument.
& A new function, membertype, checks whether an object of the given type exists in the second argument.
& A maptype function maps a function to each operand of an expression of a given type.

Verifications
• You can compare 2-D plot data structures using two new verify routines, function_shells
and function_bounds.

New and Improved Conversions
• The float command accepts an option to specify the number of digits.
& The compose routine places any number of conversions on the expression.
& Convert to and from the atomic number of a chemical element and its temporary IUPAC name or symbol using the iupac routine.

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