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 Maple
15 allows you to study and tackle a large range of problems in
computational physics, including problems in classical mechanics,
quantum physics,
and relativistic field theory. It also provides material of use
in a first course in field theories at the graduate level
- The Physics package extends the standard computational domain
with operations over anticommutative and noncommutative variables and
functions and related product and power operations, appropriate for
quantum physics formulations; tensor indices of spacetime, spinor and/or
gauge types, functional differentiation, differentiation with respect
to anticommutative variables, differentiation and simplification of
tensorial expressions using the Einstein summation convention for
repeated indices. In this way, you can take advantage of the
computational power of the Maple environment without having to change
the flexible notation used when computing with paper and pencil.
- The extension of the computational domain includes the Vectors subpackage, to perform standard abstract vector calculus.
The package includes representations for non-projected 3-D vectors,
inert and active representations for the non-projected differential
operators nabla, gradient, divergent, curl and the Laplacian, as well as
algebraic (non-matricial) representations for projected 3-D vectors in
the Cartesian, cylindrical, and spherical vector basis. It is then
possible to compute using coordinate-free vectorial formulations,
exploring the coordinate-free properties of the vectors and vectorial
operations involved, without specifying the vector basis until that is
desired, and to input /work with vectorial expressions involving both
non-projected and projected vectors using essentially the same notation
found in textbooks that you use when computing by hand.
- All the conventions for a given computation can be easily set using a compact and versatile interactive assistant.
In order to perform this extension of the computational domain, a set
of conventions for distinguishing between commutative, anticommutative
and noncommutative variables, 3-D vectors, tensors, etc. are
established. An advanced default setup of conventions is loaded when you
load the Physics package. You can change these conventions using the
Setup assistant.
- Textbook mathematical notation:
Anticommutative and noncommutative variables are displayed in different
colors, non-projected vectors and unit vectors are respectively
displayed with an arrow and a hat on top, the vectorial differential
operators Nabla and Laplacian with
 and  are displayed as in textbooks, as are most of the other Physics commands/operations.
- Extensive documentation with examples for each Physics command, as well as examples illustrating the use of the package to tackle problems in analytical Geometry, mechanics, electrodynamics and quantum mechanics, are provided.
- A complete set of computational tools for advanced general relativity is provided within the Differential Geometry package. With Maple 15, seventeen new commands have been introduced in this area.
- Maple is the leading system in terms of computing closed-form solutions to ODEs and PDEs, relevant in many areas of physics. Maple 15 further enhances this area with a large number of new solving algorithms.
- Special functions, used to represent solutions in computational physics, are another strong area for Maple,
which has seen further improvements in Maple 15. In particular, a new
class of special functions, the Bell polynomials, have been introduced
with this latest release.
Some examples of computations in Physics
Mechanics: Lagrangian for a pendulum
The Lagrangian is defined as
b) The steps are the same as in part a:
Electrodynamics: Magnetic field  of a rotating charged disk
Problem
Solution
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Datasheet
