Examples and case studies utilize Mathematica 7's newest tools, such as dynamic manipulations and adaptive three-dimensional plotting.Emphasizes the breadth of Mathematica and the impressive results ...of combining techniques from different areas.Visualization is emphasized throughout, with finely crafted graphics in each chapter.All Mathematica code is included as Extras through Springer, saving the reader hours of typing. Access Extras here: http://extras.springer.com/2010/978-0-387-75366-9.
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic ...theory to recently published research material.
Mathematica is today's most advanced technical computing system, featuring a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful ...programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility."The Mathematica GuideBook for Numerics" (text and code fully tailored for Mathematica 5.1) concentrates on Mathematica's numerical mathematics capabilities. The available types of arithmetic (machine, high-precision, and interval) are introduced, discussed, and put to use. Fundamental numerical operations, such as compiling programs, fast Fourier transforms, minimization, numerical solution of equations, ordinary/partial differential equations are analyzed in detail and are applied to a large number of examples in the main text and solutions to the exercises.
Mathematica is today's most advanced technical computing system. It features a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful ...programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface, and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility. The Mathematica GuideBook for Symbolics (code and text fully tailored with Mathematica 5.1) deals with Mathematicas symbolic mathematical capabilities. Structural and mathematical operations on single and systems of polynomials are fundamental to many symbolic calculations and they are covered in considerable detail. The solution of equations and differential equations, as well as the classical calculus operations (differentiation, integration, summation, series expansion, limits) are exhaustively treated. Generalized functions and their uses are discussed. In addition, this volume discusses and employs the classical orthogonal polynomials and special functions of mathematical physics. To demonstrate the symbolic mathematics power, a large variety of problems from mathematics and phyics are discussed.
We have developed a Mathematica program package SpaceGroupIrep which is a database and tool set for irreducible representations (IRs) of space group in BC convention, i.e. the convention used in the ...famous book “The mathematical theory of symmetry in solids” by C.J. Bradley & A.P. Cracknell. Using this package, elements of any space group, little group, Herring little group, or central extension of little co-group can be easily obtained. This package can give not only little-group (LG) IRs for any k-point but also space-group (SG) IRs for any k-stars in intuitive table form, and both single-valued and double-valued IRs are supported. This package can calculate the decomposition of the direct product of SG IRs for any two k-stars. This package can determine the LG IRs of Bloch states in energy bands in BC convention and this works for any input primitive cell thanks to its ability to convert any input cell to a cell in BC convention. This package can also provide the correspondence of k-points and LG IR labels between BCS (Bilbao Crystallographic Server) and BC conventions. In a word, the package SpaceGroupIrep is very useful for both study and research, e.g. for analyzing band topology or determining selection rules.
Program title:SpaceGroupIrep
CPC Library link to program files:https://doi.org/10.17632/3vm4g32t4d.1
Developer's repository link:https://github.com/goodluck1982/SpaceGroupIrep
Licensing provisions: GNU General Public Licence 3.0
Programming language: Mathematica
External routines/libraries used:spglib (http://spglib.github.io/spglib)
Nature of problem: Space groups and their representations are important mathematical language to describe symmetry in crystals. The book—“The mathematical theory of symmetry in solids” by C.J. Bradley & A.P. Cracknell (called the BC book)—is highly influential because it contains not only systematic theory but also detailed complete data of space groups and their representations. The package SpaceGroupIrep digitizes these data in the BC book and provides tens of functions to manipulate them, such as obtaining group elements and calculating their multiplications, identifying k-points, showing the character table of any little group, determining the little-group (LG) irreducible representations (IRs) of energy bands, and calculating the direct product of space-group (SG) IRs. This package is a useful database and tool set for space groups and their representations in BC convention.
Solution method: The direct data in the BC book is used to calculate the LG IRs for standard k-points defined in the book. For a non-standard k-point, we first relate it to a standard k-point by an element which makes the space group self-conjugate and then calculate the LG IRs through the element. SG IRs are obtained by calculating the induced representations of the corresponding LG IRs. The full-group method based on double coset is used to calculate the direct products of SG IRs. In addition, an external package spglib is utilized to help convert any input cell to a cell in BC convention.
Essay/Review: Vita Mathematica Luis Radford
Revista Brasileira de História da Matemática,
11/2020, Letnik:
4, Številka:
7
Journal Article
Recenzirano
Odprti dostop
Historical Research and Integration with Teaching. Ronald Calinger, Editor. Washington DC: The Mathematical Association of America. xii + 359 pp. ISBN 0-88385-097-4
Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and ...reflects the author's decades-long teaching experience.
•Overview: The analytical derivation are carried out for fifth-order asymptotic geometric aberrations of electron lenses.•Core findings: All analytical expressions are found out for fifth-order ...asymptotic geometric aberrations of electron lenses.•Essence of the work: To analytically derive the expressions of fifth-order asymptotic geometric aberrations of electron lenses.•Distinctive highlight: The derived formulae are numerically cross-validated with the differential algebraic method.
In this article the analytical expressions of the fifth-order asymptotic geometric aberrations of electron lenses are derived by Mathematica. The process of the derivation is analogous to the method described in “Principles of Electron Optics” by P.W. Hawkes and E. Kasper. All the analytical formulae for asymptotic aberration coefficients in polynomials in the reciprocal magnification are numerically cross-validated with the differential algebraic (DA) method. The results indicate that the derived formulae are doubtless correct.
The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background ...needed for understanding the examples and how to compute in Mathematica(R) will also be discussed.
Computing with Mathematica, 2nd edition is engaging and interactive. It is designed to teach readers how to use Mathematica efficiently for solving problems arising in fields such as mathematics, ...computer science, physics, and engineering. The text moves from simple to complex, often following a specific example on a number of different levels. This gradual increase incomplexity allows readers to steadily build their competence without being overwhelmed. The 2nd edition of this acclaimed book features:* An enclosed CD for Mac and Windows that contains the entire text as acollection of Mathematica notebooks* Substantive real world examples* Challenging exercises, moving from simple to complex* A collection of interactive projects from a variety of applications "I really think this is an almost perfect text." -Stephen Brick, University of South Alabama
* Substantive real world examples * Challenging exercises, moving from simple to complex examples * Interactive explorations (on the included CD-ROM) from a variety of topics using a multitude of interesting mathematical applications
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