MATLAB Physics - Iuspas.fnal.gov/materials/14UNM/Matlab_1.pdf · MATLAB Physics - I MATLAB and...
Transcript of MATLAB Physics - Iuspas.fnal.gov/materials/14UNM/Matlab_1.pdf · MATLAB Physics - I MATLAB and...
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06/15/14 UPAS - MATLAB Physics 1
MATLAB Physics - I
● MATLAB and Symbolic Math should be installed on an accessible computer – you will execute the scripts.
● There is a textbook available■ The book is supplied by UPAS■ There is a CD with the .m file scripts for the
demonstrations used in the course● Lecture/class notes – email list for communication of
the class ● Distribute all scripts by data stick – 200 examples● Homework and “project”
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06/15/14 UPAS - MATLAB Physics 2
Programming in MATLAB
• Templates and demos available - local
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06/15/14 UPAS - MATLAB Physics 3
Matlab Windows
● Workspace, command history, command window and editor – desktop layout
■ Open .m files, editor color coded■ Debug options■ In command window – set path to scripts
(.m files)● Setup toolbars, status busy/ready. Help● Use product help and function browser● Use demos – e.g. getting started, quick
start
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06/15/14 UPAS - MATLAB Physics 4
Desktop Layout
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06/15/14 UPAS - MATLAB Physics 5
MATLAB Startup
● Getting Started■ Functions■ Examples■ Demos
● Quick start■ Language■ Math■ Graphics■ Programming
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06/15/14 UPAS - MATLAB Physics 6
Help Page – Top of Tree
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06/15/14 UPAS - MATLAB Physics 7
Demos and Getting Started
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06/15/14 UPAS - MATLAB Physics 8
Drill Down in HELP - Examples
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06/15/14 UPAS - MATLAB Physics 9
Programming - GUI
• Demo exists – many tools supplied
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06/15/14 UIC – MATLAB Physics 10
MATLAB Displays
● MATLAB has a suite of displays● 2d
■ Errorbar, plot, loglog, semilogx, semilogy, polar, bar, pie, hist, scatter
■ title, xlabel, ylabel, legend, grid, hold, axis● 3d
■ Contour, surface, mesh, quiver
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06/15/14 UIC – MATLAB Physics 11
Help - Graphics
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06/15/14 UIC – MATLAB Physics 12
Help – 3 d
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06/15/14 UIC – MATLAB Physics 13
Plot details, Axis definition
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06/15/14 UIC – MATLAB Physics 14
plot(x,y) –
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06/15/14 UIC – MATLAB Physics 15
3-d Plots
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06/15/14 UIC – MATLAB Physics 16
Mesh and Meshc
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06/15/14 UIC – MATLAB Physics 17
Surfc and quiver
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06/15/14 UIC – MATLAB Physics 18
MATLAB Symbolic Tools
● MATLAB has many, many tools. You will have to browse through the options.
■ Diff, int (calculus)■ Matrix inversion■ Eigenvalues■ Taylor■ Fourier – our scripts
● Other examples and script in the textbook
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06/15/14 UIC – MATLAB Physics 19
SM_Diff and SM_Int
● Use MATLAB diff, intyou need neverdo another integral
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06/15/14 UIC – MATLAB Physics 20
SM_Diff Script “loop” -blue
● ~ standard “loop”● Use “while”
“break”“for”“if”“end”
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06/15/14 UIC – MATLAB Physics 21
Eigenvalues
You need neversolve anothereigenvalueproblem
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06/15/14 UIC – MATLAB Physics 22
Eigen Script
● Used diff and int for the 2 previous examples● Now use MATLAB matrix tools, det, inv and eig
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06/15/14 UIC – MATLAB Physics 23
Taylor Series
● See convergence of the series graphically – select the number of terms
ftay = taylor(sym(fin),x,aoff,'Order',nterm); yy = simple(ftay); pretty(yy)
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06/15/14 UIC – MATLAB Physics 24
Fourier - 1
● Examples worked out already – square, triangle and sawtooth. See convergence with number of terms
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06/15/14 UIC – MATLAB Physics 25
Fourier - 2
● Use int, sym and eval to do a general Fourier series. Any analytically solvable series!
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06/15/14 UIC – MATLAB Physics 26
Fourier - 3
● Example for f(t) = t*cos(t), 5 terms
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06/15/14 UIC – MATLAB Physics 27
Numeric Tools - I
● Most problems must be solved numerically● Numeric tools for a vector x
■ Length■ Min■ Max■ Mean■ Std■ sort
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06/15/14 UIC – MATLAB Physics 28
Numeric Tools- II
● MATLAB utility “quad” does numeric integration. Try “int” first – default to “quad” if it fails.
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06/15/14 UIC – MATLAB Physics 29
MATLAB Equation Solvers
● MATLAB has several ways to solve equations
■ Symbolic solutions should be tried first■ Define symbolic variables using “syms”■ “solve” is for algebraic equations■ “dsolve” is for ordinary differential equations■ “ode45” is for numerical solutions to ODE■ “pde” is for partial differential equations in 1
space (x) and 1 time (t) dimension
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06/15/14 UIC – MATLAB Physics 30
Help for solve – has examples
● Use help and search for solve
● Symbolic solution
● You need never solve another ODE
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06/15/14 UIC – MATLAB Physics 31
solve -2
● Use command window to define a simple quadratic
● Use “simple” and “pretty for visualization
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06/15/14 UIC – MATLAB Physics 32
dsolve
● Solves ODE symbolically with IC
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06/15/14 UIC – MATLAB Physics 33
Dsolve - example
● Use symbolically for ODE. Initial conditions
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06/15/14 UIC – MATLAB Physics 34
SM_ODE3
● SM_ODE2 allows a choice of a few well known equations. SM_ODE3 is free form.
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06/15/14 UIC – MATLAB Physics 35
ode45
● Numerical solution of ODE
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06/15/14 UIC – MATLAB Physics 36
ode45 - 2
Need to define a function which specifies the ODE
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06/15/14 UIC – MATLAB Physics 37
ode45 - 3
● The physics is all in the function specified. The boundary conditions are specified in the ode45 call as is the time evolution of the system. We do examples later.
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06/15/14 UIC – MATLAB Physics 38
pde
● PDE solver in MATLAB
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06/15/14 UIC – MATLAB Physics 39
pde-2
● Example from 1-d Quantum Mechanics
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06/15/14 UIC – MATLAB Physics 40
Special Functions
● You need never again look up a special function! Search MATLAB help (mfun)
● Run script DG/SM ” Matlab_Functions”