What's New: Professionals
Linearization Tools
 Built-in tools for linearizing nonlinear differential algebraic equations support work in control design, calibration, and sensitivity analysis.
- Efficiently linearize a set of non-linear differential algebraic equations about a defined linearization point.
- Calculate the equilibrium point of a nonlinear system such that user-defined constraints are satisfied. If no such point exists, the algorithm returns a point that minimizes the state derivatives.
- If the linearized system is affine (that is, not linear time-invariant), Maple then automatically converts the system into a linear time-invariant system by performing a shift transformation. This transformation is performed whenever the linearization point is an equilibrium point that falls within user-specified tolerance levels.
- Provide the linearized system in state space or differential equation form.
- Support further analysis since the resulting linearized system is compatible with all the commands in the Dynamic Systems package.
Solvers for Algebraic Riccati Equations (CARE/DARE)
New solvers for continuous and discrete algebraic Riccati equations (CARE and DARE) let you apply more advanced techniques to control design problems. These solvers make it easy to rapidly design and implement sophisticated controllers, such as those used in optimal and robust control theory for linear and nonlinear plant models. These solvers are used to:
- Provide a greater degree of freedom to tune your linear quadratic regulators, linear quadratic Gaussian controllers, and Kalman estimators by including the three weighting matrices in the quadratic cost function.
- Guarantee the uniqueness and positive definiteness of solutions when certain conditions of the control design are met.
 Feature details:
- Solves continuous and discrete algebraic Riccati equations in matrix form
- Results are customizable and can include any or all of the following:
- The matrix that solves the equation
- The vector of closed-loop eigenvalues of the symplectic matrix
- The reciprocal of the condition number of the system
- The gain matrix
- Provides optional control over the data structures used to store the results, which can be used to increase efficiency of subsequent calculations when information about the structure of the problem is known in advance
 Control Design
The expanded suite of tools for control design provides greater insight into the dynamic behavior of your system.
- Generate a Nyquist plot for your continuous or discrete to gain more insight into the frequency response. The unit of frequency can be set to Hertz or radians. System definitions can be completely specified or contain symbolic variables as parameters.
- Compute step response properties of the system, which can include symbolic parameters, making it easier to verify your design requirement. The calculated properties are:
- Final-value
- 10%-point
- 33%-point
- 67%-point
- 90%-point
- Peak-point
- Settling-point
- Automatically determine the equivalent system representation of two or more interconnected system objects using serial, parallel, append, negative-feedback, positive-feedback, or feed-forward configurations.
- Using a new plot option, specify when frequency points on the axis should be generated adaptively, which can result in plots that are easier to interpret. This option is available for Bode, frequency response, magnitude, Nyquist, and phase plots.
Connectivity with MATLAB®
 Maple provides extensive connectivity with MATLAB®, including code translation, code generation, import and export of data files, and calls to MATLAB® from Maple. Maple 14 expands your connectivity options with the following features:
- The Maple Toolbox for MATLAB® is now included as part of Maple.
- Enhanced integration with MATLAB® provides direct access to all of the commands, variables, and functions of each product while working in either environment.
- Access Maple’s world-leading symbolic engine to handle the symbolic portions of your MATLAB® calculations and programs.
- If you are working in MATLAB®, you can still access Maple interactive assistants and tutors for rapid solution development.
 Gain arbitrary precision in your MATLAB® calculations, avoiding catastrophic cancellations in your MATLAB® code. - Fully compatible with code written using earlier versions of symbolic toolboxes from The MathWorks™.Enhanced integration with MATLAB® provides direct access to all the commands, variables, and functions of each product while working in either environment.
- Maple 14 supports the importing and exporting of MATLAB® binary files.
Improved Search Capabilities
Improved search capabilities mean that searches of the help system return more meaningful results faster, so you can get the information you need quickly.
- When the same function name appears in multiple packages, the most commonly used functions are presented first.
- Improvements to access speed mean results are presented quickly.
- The full standard help browser is available from all of the Maple interfaces, including the command-line version. You can access the search tools, table of contents, and hyperlinks of the fully featured help system while working in any Maple environment.
 Solve more problems with increased depth and breadth of math for engineering applications
Maple 14 gives you even more built-in mathematical tools to support your engineering applications.
- A new numerical differential equations solver, the Cash-Karp pair, is available for solving non-stiff and semi-stiff ODEs and DAEs.
- New world-leading techniques in solving differential equations mean that Maple can solve new classes of ODEs, which in turn expands the reach of the PDE solvers. These techniques also find particular solutions to an even wider class of ODE problems for which no general solution exists, solve PDEs with boundary conditions, and compute series solutions of PDEs.
- A new package for differential algebra works with systems of polynomial differential equations. Differential algebra techniques can be applied to a wide range of problems, such as optimizing interplanetary transfers and studying nonlinear behavior in beam physics.
- Users of the NAG® library now have seamless access to the full functionality offered by the NAG C Library routines from within Maple. Formerly available as a separate toolbox, this functionality is now integrated into Maple directly.
- Other areas of improvement include root finding and polynomial solving, linear algebra, and integration.
Enhanced performance lets you find solutions faster and tackle even larger problems
Performance enhancements in Maple 14 result in speed increases for both Maple routines and your own code, so you find your solutions faster and can tackle even larger problems.
- Performance improvements were made in key fundamental routines, such as core polynomial operations and fundamental linear algebra, in many cases adopting new parallel algorithms. Not only are these routines faster, but the performance of operations that depend on these routines is also increased.
- Linear algebra routines can be accelerated using CUDA™ technology from NVIDIA®, on computers with a CUDA-enabled graphics card. Matrix multiplication can be greatly accelerated for a variety of matrix datatypes and shapes. Since matrix multiplication is fundamental to most linear algebra calculations and linear algebra techniques are used extensively throughout Maple, the result is increased performance across a variety of mathematical operations.
- Enhancements to programmatic manipulation routines mean that custom code can be even faster and more efficient. Improvements include in-place substitution into arrays, matrices, and vectors; eliminating overhead by providing direct access to polynomial solvers; efficient new commands for working with lists; and new benchmarking tools for optimizing code.
See Performance Improvements in Maple 14 for examples of speed-ups in fundamental operations.
 New tools and resources improve the work environment
Additions to Maple 14 improve the work environment for interactive exploration, document creation, and constructing programmatic solutions.
- Maple 14 provides a single integrated environment for creating, distributing and receiving technical documents through the MapleCloud™ Document Exchange. Access to the MapleCloud is seamlessly integrated into the Maple environment. You can easily and instantly share your work among a group of colleagues or with Maple users worldwide, without the need for separate tools or cumbersome uploading and downloading.
- Maple documents can now be executed programmatically and the results can be returned to the calling code. As a result, key calculations and components of designs can be created and documented separately in a rich technical document environment, and then called programmatically as part of a larger solution.
 Enhanced tables provide built-in facilities for captions, table numbering, and cross-references. When a new table is inserted, table numbers are updated automatically and references are adjusted as required.- Improved plotting of 2-D functions with discontinuities provides the ability to highlight removable discontinuities and greater control over the appearance of plots.
- The enhanced point probe tool lets you explore the coordinates of a 2-D plot. In addition to displaying the current cursor location, the point probe can find the point on the curve closest to your cursor, or even the closest point that Maple actually calculated to produce the plot. It also provides the ability to extract the coordinates of the cursor and paste them anywhere in the document, in the form of a valid Maple object.
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