Maple

Maple
Maple
Type of	computer mathematics system
Developer	Waterloo Maple Inc.
Written on	C , Java, language Maple
operating system	Windows (10, 8.1 and 7), mac OS, Linux
Interface languages
First edition
Latest version	2019 ( April 2019 )
Readable file formats
License	Commercial software
Site	maplesoft.com

Maple - software package, computer algebra system (more precisely, computer math system). It is a product of Waterloo Maple Inc. , which since 1984 has been producing software products focused on complex mathematical calculations, data visualization and modeling. The Maple system is intended for symbolic computations , although it has a number of means for numerically solving differential equations and finding integrals . It has advanced graphic tools. It has its own interpreted programming language , with a syntax partially reminiscent of Pascal .

Content

Basics of the Maple Language

Standard Math Functions

Math notation	Maple Record
$e^{x}$ ${\ displaystyle e ^ {x}}$	exp (x)
$\ln x$ ${\ displaystyle \ ln x}$	ln (x)
$\lg x$ ${\ displaystyle \ lg x}$	lg (x)
$\log _{a}x$ ${\ displaystyle \ log _ {a} x}$	log [a] (x)
${\sqrt {x}}$ ${\ displaystyle {\ sqrt {x}}}$	sqrt (x)
$\|x\|$ ${\ displaystyle \| x \|}$	abs (x)
$\sin x$ ${\ displaystyle \ sin x}$	sin (x)
$\cos x$ ${\ displaystyle \ cos x}$	cos (x)
$\operatorname {tg} \,x$ ${\ displaystyle \ operatorname {tg} \, x}$	tan (x)
$\operatorname {ctg} \,x$ ${\ displaystyle \ operatorname {ctg} \, x}$	cot (x)
$\sec x$ ${\ displaystyle \ sec x}$	sec (x)
$\csc x$ ${\ displaystyle \ csc x}$	csc (x)
$\arcsin x$ ${\ displaystyle \ arcsin x}$	arcsin (x)
$\arccos x$ ${\ displaystyle \ arccos x}$	arccos (x)
$\operatorname {arctg} \,x$ ${\ displaystyle \ operatorname {arctg} \, x}$	arctan (x)
$\operatorname {arcctg} \,x$ ${\ displaystyle \ operatorname {arcctg} \, x}$	arccot (x)
$\sinh x$ ${\ displaystyle \ sinh x}$	sinh (x)
$\cosh x$ ${\ displaystyle \ cosh x}$	cosh (x)
$\tanh x$ ${\ displaystyle \ tanh x}$	tanh (x)
$\coth x$ ${\ displaystyle \ coth x}$	coth (x)
$\delta (x)$ ${\ displaystyle \ delta (x)}$ - Dirac function	Dirac (x)
$\theta (x)$ ${\ displaystyle \ theta (x)}$ - Heaviside function	Heaviside (x)

Identical transformations and simplification of expressions

Act	Code example
Brace expansion	expand (( x + 1 ) * ( x - 1 ) * ( x ^ 2 - x + 1 ) * ( x ^ 2 + x + 1 ));
Polynomial factorization	factor ( x ^ 5 - x ^ 4 - 7 * x ^ 3 + x ^ 2 + 6 * x );
Expression simplification	simplify ( sin ( x + y ), trig );
Combine the exponents of power functions or reduce the degree of trigonometric functions	combine ( 4 * sin ( x ) ^ 3 , trig );

Solving equations and inequalities

To solve equations in Maple, there is a universal command solve (eq, x), where eq is an equation, x is a variable. An example of solving the equation:

  solve ( a * x ^ 2 + b * x + c = 0 , x );

An example of solving inequality:

  solve ( 5 * x > 2 * x - 1 , x );

For the numerical solution of the equation, there is a function fsolve (eq, x). Example:

  fsolve ( x ^ 5 - 4 * x + 2 = 0 , x );

Plotting functions

For plotting function $f(x)$ ${\ displaystyle f (x)}$ use the command plot (f (x), x = a..b, y = c..d, p), where p is the image control parameters. Example:

  plot ( x ^ 2 , x = - 5 .. 5 , color = " red " );

Function graph $f(x,y)$ ${\ displaystyle f (x, y)}$ You can build with the command plot3d (f (x, y), x = a..b, y = c..d, p), where p is the image control parameters. Example:

  plot3d ( sin ( x ) + sin ( y ), x = - 5 .. 5 , y = - 5 .. 5 );

Sample Code

An example of three-dimensional graphics created in Maple

The following code calculates the solution of a linear differential equation

${\frac {d^{2}y}{dx^{2}}}-3y(x)=x$ ${\ displaystyle {\ frac {d ^ {2} y} {dx ^ {2}}} - 3y (x) = x}$

with initial conditions:

$y(0)=0,\quad \left.{\frac {dy}{dx}}\right|_{x=0}=2$ ${\ displaystyle y (0) = 0, \ quad \ left. {\ frac {dy} {dx}} \ right | _ {x = 0} = 2}$

  dsolve ({ diff ( y ( x ), x , x ) - 3 * y ( x ) = x , y ( 0 ) = 0 , D ( y ) ( 0 ) = 2 }, y ( x ));

Versions

Maple 2018 March 21, 2018
Maple 2017.3 October 3, 2017
Maple 2017.2 August 2, 2017
Maple 2017.1 June 28, 2017
Maple 2017 May 25, 2017
Maple 2016.1a April 27, 2016
Maple 2016.1 April 20, 2016
Maple 2016 March 2, 2016
Maple 2015.1 November 2015
Maple 2015 March 5, 2015
Maple 18.02 November 2014
Maple 18.01a July 2014
Maple January 18 , 2014
Maple 18 March 7, 2014
Maple January 17, 2013
Maple 17 March 13, 2013
Maple 16.01 May 16, 2012
Maple 16 March 28, 2012
Maple 15.01 June 21, 2011
Maple 15 April 13, 2011
Maple 14.01 October 28, 2010
Maple April 14 , 2010
Maple February 13 , 2009
Maple January 13, 2009
Maple 13 April 24, 2009
Maple 12.02 December 2008
Maple 12.01 October 2008
Maple 12 May 13, 2008
Maple 11.02 November 10, 2007
Maple 11.01 July 6 , 2007
Maple 11: February 21 , 2007
Maple 10: May 10 , 2005
Maple 9.5: April 15 , 2004
Maple 9: June 30 , 2003
Maple 8: April 16 , 2002
Maple 7: July 1 , 2001
Maple 6: December 6 , 1999
Maple V R5: November 1 , 1997
Maple V R4: January 1996
Maple V R3: March 15 , 1994
Maple V R2: November 1992
Maple V: August 1990
Maple 4.3: March 1989
Maple 4.2: December 1987
Maple 4.1: May 1987
Maple 4.0: April 1986
Maple 3.3: March 1985 (First widely available version)
Maple 3.2: April 1984
Maple 3.1: October 1983
Maple 3.0: May 1983
Maple 2.2: December 1982
Maple 2.15: August 1982
Maple 2.1: June 1982
Maple 2.0: May 1982
Maple 1.1: January 1982
Maple 1.0: January 1982

Accessibility

Maplesoft sells both student, academic and professional versions of Maple, with a significant price difference ($ 124, $ 1,555 and $ 2,845, respectively). Also available is a version for personal use at a price of $ 299, whose license agreement does not imply the use of the system for commercial, scientific and educational purposes.

Recent student versions (starting with the sixth) did not have computational limitations, but were supplied with a smaller amount of printed documentation. The student and professional versions of the Mathematica package also differ.

Notes

↑ NationMaster - Encyclopedia: Maple (software)

Literature

Govorukhin V.N., Tsybulin V.G. Introduction to Maple. A math package for everyone. - M .: Mir , 1997. - p. 208. - ISBN 5-03-003255-X .
Diakonov V.P. Mathematical system Maple V R3 / R4 / R5. - M .: SOLON = Press , 1998. - p. 400. - ISBN 5-85954-081-7 .
Dyakonov V.P. Computer Mathematics. Theory and practice. - M .: Knowledge, Peter , 1999, 2001. - P. 1296. - ISBN 5-89251-065-4 .
A. Tsyganov. Course of lectures Quantum mechanics with Maple. St. Petersburg, 2000. http://www.exponenta.ru/educat/systemat/tsiganov/00.asp
Dyakonov V.P. Maple 6 Training Course. - SPb. : Peter , 2001. - p. 608. - ISBN 5-318-00183-1 .
A. Matrosov. Maple 6: Solving Problems of Higher Mathematics and Mechanics: A Practical Guide. 2001 528 p. ISBN 5-94157-021-X
Diakonov V.P. Maple 7 Training Course. - SPb. : Peter , 2002. - p. 672. - ISBN 5-318-00719-8 .
Dyakonov V.P. Maple 8 in mathematics, physics and education. - M .: SOLON = Press , 2003. - p. 656. - ISBN 5-98003-038-7 .
Vasiliev A.N. Maple 8. Tutorial. - Moscow : Dialectics , 2003. - p. 352. - ISBN 5-8459-0452-8 .
Goloskokov D. P. Equations of mathematical physics. Solving problems in the system Maple. Publishing house: "Peter" , 2004. 544с. ISBN 5-94723-670-2
Dyakonov V.P. Maple 9.5 / 10 in mathematics, physics and education. - M .: SOLON = Press , 2006. - P. 720. - ISBN 5-98003-258-4 .
B. Popov. Rossiating of problems in the system of computer algebras Maple V. - Kiev: ViP, 2007. - 312 p.
Kirsanov MN Graphs in Maple. - M .: Fizmatlit , 2007. - 168 p. - ISBN 978-5-9221-0745-7 . http://vuz.exponenta.ru/PDF/book/GrMaple.pdf http://eqworld.ipmnet.ru/ru/library/books/Kirsanov2007ru.pdf
Charles Henry Edwards, David E. Penny. Differential equations and boundary value problems. Simulation and calculation using Mathematica, Maple and MATLAB. Per. from English Ya. K. Schmidsky = Differential Equations and Boundary Value Problems: Computing and Modeling. - 3rd ed. - M .: Williams, 2008. - 1104 p. - ISBN 978-5-8459-1166-7 ( ISBN 0-13-065245-8 ).
Dyakonov V.P. Encyclopedia of Computer Algebra. - M .: DMK-Press , 2009. - p. 1264. - ISBN 978-5-94074-490-0 .
Dyakonov V.P. Maple 10/11/12/13/14 in mathematical calculations. - M .: DMK-Press , 2011. - p. 800. - ISBN 978-5-94074-751-2 .
Kirsanov MN Maple and Maplet. Solving mechanical problems. - SPb. : Lan, 2012. - p. 512. - ISBN 978-5-8114-1271-6 .
Taranchuk V. B. The main functions of computer algebra systems . - Minsk: BSU, 2013. - 59 p.
Egorov A. I. Ordinary differential equations and the Maple system. - M .: SOLON-Press, 2016. - 392 p. - ISBN 978-5-91359-205-7 .
Kirsanov M.N. , Kuznetsova O.S. Algebra and Geometry. Collection of problems and solutions using Maple. - M .: Infra-M, 2016. - 272 p. - ISBN 978-5-16-012325-7 .

English Literature

Richard H. Enns, George C. McGuire, Nonlinear Physics With Maple for Scientists and Engineers. ISBN 0-8176-4119-X
Jon H. Davis, Differential Equations With Maple: An Interactive Approach. ISBN 0-8176-4181-5
Martha L. Abell, James P. Braselton, Differential Equations with Maple V. ISBN 0-12-041560-7
Franco Vivaldi, Experimental Mathematics with Maple. ISBN 1-58488-233-6
Ronald L. Greene, Classical Mechanics With Maple. ISBN 0-387-94512-1
Stephen Lynch, Dynamic Systems with Applications using Maple. ISBN 0-8176-4150-5
John F. Putz Maple Animation. 2003. ISBN 1-58488-378-2

Links

[1] NationMaster - Encyclopedia: Maple (software)