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Introduction to Mathematica презентация, доклад

What is Mathematica?“A system for doing mathematics by computer”Also for modeling, simulation, visualization, development, documentation, and deployment.Available on all public computer clusters.Can be installed on any GT-owned computerCurrent version: 6.0.3Versions for:Windows

Слайды и текст этой презентации

Слайд 1Introduction to Mathematica
AE6381 Special Lecture
Prof. J. Craig
Fall 2008

Introduction to MathematicaAE6381 Special LectureProf. J. CraigFall 2008

Слайд 2What is Mathematica?
“A system for doing mathematics by computer”
Also for

modeling, simulation, visualization, development, documentation, and deployment.
Available on all public

computer clusters.
Can be installed on any GT-owned computer
Current version: 6.0.3
Versions for:
Windows XP, Vista
Mac OS-X
Unix/Linux
What is Mathematica?“A system for doing mathematics by computer”Also for modeling, simulation, visualization, development, documentation, and deployment.Available

Слайд 3Why consider Mathematica?
Powerful system for symbolic mathematical but also handles

numerical mathematics, graphics, data visualization, simulation.
Larger community of users

than Maple.
Versatile Notebook and Player for flexible documentation & distribution.
CONS:
VERY steep learning curve
Proprietary
Why consider Mathematica?Powerful system for symbolic mathematical but also handles numerical mathematics, graphics, data visualization, simulation. Larger

Слайд 4What is this introduction?
I’ve been using Mathematica in AE3125 Aerospace

Structural Analysis in order to simplify tedious calculations and solve

problems not readily doable by hand.
All homework solutions are in Mathematica.
I’ll try to provide a simple and very basic introduction using this as my reference.
I’ll suggest other uses and point to the Wolfram web pages and ScreenCasts.
What is this introduction?I’ve been using Mathematica in AE3125 Aerospace Structural Analysis in order to simplify tedious

Слайд 5References
Wolfram, S., “Mathematica,” 2nd Edition, Addison-Wesley, 1991.
http://www.wolfram.com is main web

site.
Built-in Mathematica documentation (all written in Mathematica Notebook code)
Tutorial screencasts

are an excellent source of helpful information and can be found at: http://www.wolfram.com/broadcast/screencasts/
Demonstration Project has great user demos at: http://demonstrations.wolfram.com/ (create your own using File>New>Demonstration)
Mathematica Journal at http://www.mathematica-journal.com
ReferencesWolfram, S., “Mathematica,” 2nd Edition, Addison-Wesley, 1991.http://www.wolfram.com is main web site.Built-in Mathematica documentation (all written in Mathematica

Слайд 6Launching Mathematica
User sees the Notebook interface.
An extensive online documentation system

is available.
Palettes
A separate kernel is used for all mathematical

processing

Launching MathematicaUser sees the Notebook interface.An extensive online documentation system is available. PalettesA separate kernel is used

Слайд 7Basic Notebook Operation
Type an expression; default style is Input
Press Enter

(in numeric pad) or Shift-Return which will send Input to

kernel
Result will appear on line below
Sequential line numbers are prepended by kernel
Style determines appearance and what happens to line(s). Input is always sent to kernel.
Styles define appearance of blocks of cells shown by brackets at right margin.
Click cell bracket to select (to change, cut, copy…)
Double-click cell bracket to collapse that cell
Can collapse an entire bracket to the first cell
Basic Notebook OperationType an expression; default style is InputPress Enter (in numeric pad) or Shift-Return which will

Слайд 8Notebooks
Provide a very readable display of code along with comments

to fully document
Can collapse/hide portions (styles are useful here)
Layout is

controlled by styles that can be modified by the user to change appearance
Can insert graphics, logos, etc.
Previous output can be saved in Notebook, including plots.
Use Evaluation>Evaluate Notebook to compute Notebook (send code to kernel).
Can also click on style bracket(s) and hit Enter (or Shift-Return) to compute that selected portion of Notebook.
NotebooksProvide a very readable display of code along with comments to fully documentCan collapse/hide portions (styles are

Слайд 9Notebook and Kernel Issues
Kernel retains state of computations and sequentially

numbers all input and output lines.
Must manually clear any previous

variables
Clear[variables] (* clears values of variables *)
x=. (* same as Clear *)
Remove[“Global`*”] (* removes all variables *)
May need to “quit” local kernel to reset counter. See Evaluation>Quit KernelMay also connect to remote kernel(s) for greater power.
Line numbers show calculation sequence…
Notebook and Kernel IssuesKernel retains state of computations and sequentially numbers all input and output lines.Must manually

Слайд 10Using Mathematica
Startup Palette opens in a window by default when

Mathematica is started. Go here for all documentation and help.
All

documentation is in “live” Notebook format and you can cut & paste into your own code.
Good tutorials available.
Using MathematicaStartup Palette opens in a window by default when Mathematica is started. Go here for all

Слайд 11Useful details…
Use of brackets:
[ ] =function arguments
{ } =defines a

list (can be nested)
[[n ]] =indexes a list (equiv to

Part[ ] )
( ) =groups mathematical operations
N[expr]=numeric value
expr// =operator postfix notation
expr/.x→2 =transformation rule (substitution)
% =previous result (%%=next to previous)
%n =result on Output line n
Useful details…Use of brackets:[ ] =function arguments{ } =defines a list (can be nested)[[n ]] =indexes a

Слайд 12Basic operations
Simple numerical computations
Simple symbolic computations
Using built-in Functions

Basic operationsSimple numerical computationsSimple symbolic computationsUsing built-in Functions…

Слайд 13Useful Algebraic Manipulation
Can use Algebraic palette:
Click to apply directly to

current expression
Type function and execute
Some functions have optional arguments
Simplify[ expr,assum]

= Simplify to expression with smallest number of terms. Optional: assumptions, i.e, x>0.
FullSimplify[ ]= same but with more effort…
Expand[ expr]= Expand numerators, keeping denominator
ExpandAll[expr]= Expand numerators and denominators
ExpandNumerator[expr]= Expand only numerator (like Expand[ ])
ExpandDenominator[ ]= Expand only denominator
Factor[expr] = Factor a polynomial
Together[expr] = Puts terms in a sum over a common denominator and cancels factors in the result.
Apart[expr] = Rewrites a rational expression as a sum of terms with minimal denominators.
Cancel[expr] = Cancels out common factors in the numerator and denominator of expr.
Collect[expr,[x1,..}]= Collect together terms with same powers of objects matching x1 …
Useful Algebraic ManipulationCan use Algebraic palette:Click to apply directly to current expressionType function and executeSome functions have

Слайд 14Examples from AE3125
Shear flow in a thin-wall cross-section beam.
Function definitions
Symbolic

integration
Plotting
Bending-shear-torsion in a complex thin-wall cross-section beam.
Solve ODE with boundary

conditions
Rotational transformation using matrices
Examples from AE3125Shear flow in a thin-wall cross-section beam.Function definitionsSymbolic integrationPlottingBending-shear-torsion in a complex thin-wall cross-section beam.Solve

Слайд 15Another example…
Needed to explain to undergrad what happens to structural

dynamics when you add a tip mass to a cantilever

beam:
Set up PDE and use separation of variables
Solve spatial ODE
Compute eigenvalues and modeshapes
Animate?
Another example…Needed to explain to undergrad what happens to structural dynamics when you add a tip mass

Слайд 16Graphics
Large and sophisticated collection of graphics functions and objects.
Easy functional

evaluation as well as basic numeric data plotting.
Many interesting examples

available in Document Center and in “Demonstration Project.”
Screencasts: http://www.wolfram.com/broadcast/screencasts/
GraphicsLarge and sophisticated collection of graphics functions and objects.Easy functional evaluation as well as basic numeric data

Слайд 17Data Manipulation
Easy to import data in many different file formats.
Many

data sources (lots of new ones in 6.0).
Computation as well

as plotting.
Screencast: http://www.wolfram.com/broadcast/screencasts/integrateddata/
Data ManipulationEasy to import data in many different file formats.Many data sources (lots of new ones in

Слайд 18Other topics…
Programming in Mathematica
Developing attractive Notebooks
Using Packages
Developing Packages
Creating Notebook Player

files (.nbp)

Other topics…Programming in MathematicaDeveloping attractive NotebooksUsing PackagesDeveloping PackagesCreating Notebook Player files (.nbp)

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