Using Numerical Computing with MATLAB in the Classroom: powersin(x) - File Exchange

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Highlights from
Using Numerical Computing with MATLAB in the Classroom

bigscreen(arg) BIGSCREEN Set graphics properties for large audiences.
bizcard BIZCARD Future version of The MathWorks business card.
blackjack(N) BLACKJACK. Use random numbers in Monte Carlo simulation.
brownian.m BROWNIAN Two-dimensional random walk.
censusgui(callbackarg) CENSUSGUI Try to predict the US population in the year 2010.
circlegen(h) CIRCLEGEN Generate approximate circles.
eigsvdgui(A,job) EIGSVDGUI Demonstrate computation of matrix eigenvalues and singular values.
fern FERN MATLAB implementation of the Fractal Fern
fftgui(y) FFTGUI Demonstration of Finite Fourier Transform.
fftmatrix(varargin) FFTMATRIX Plot columns of the Finite Fourier Transform matrix.
finitefern(varargin) FINITEFERN MATLAB implementation of the Fractal Fern.
flame FLAME A stiff ordinary differential equation.
floatgui(callbackarg) FLOATGUI Show structure of floating point numbers.
fzerogui(F,ab,varargin) FZEROGUI Demonstrate the zero finding algorithm used by FZERO.
greetings(phi) GREETINGS Seasonal holiday fractal.
imagesvd(varargin) IMAGESVD Principle component analysis of monochrome and color images.
interp2dgui(arg1,arg2) INTERPGUI Behavior of periodic parametric curves.
interpgui(arg1,arg2) INTERPGUI Behavior of interpolating functions.
lorenzgui LORENZGUI Plot the orbit around the Lorenz chaotic attractor.
lugui(A,pivotstrat) LUGUI Gaussian elimination demonstration.
ncmgui NCMGUI Master GUI for Numerical Computing with MATLAB.
pdegui(action) PDEGUI Demonstrate solution of model partial differential equations.
pennymelt(delta) PENNYMELT Heat a penny.
pivotgolf(course,pivotstrat) PIVOTGOLF Pivot Pickin' Golf.
primespiral(n,c) PRIMESPIRAL Ulam's prime number spiral.
quadgui(F,a,b,tol,varargin) QUADGUI Demonstrate numerical evaluation of a definite integral.
randgui(randfun) RANDGUI Monte Carlo computation of pi.
randncond.m RANDNCOND Condition of random matrices
rungeinterp(arg) RUNGEINTERP Runge's polynomial interpolation example.
stegano(p,q) STEGANO Investigate steganography in the default image.
swinger(x,y,orbitval) SWINGER Classic double pendulum.
threenplus1(n)
touchtone(arg) TOUCHTONE Use FFT to synthesize and analyze telephone dialing
walker WALKER Human gait.
waves WAVES Wave equation in one and two space dimensions.
bslashtx(A,b) BSLASHTX Solve linear system (backslash)
crypto97(x) CRYPTO97 Cryptography example.
digraph(file) DIGRAPH Generate and analyze text digraph frequency matrix.
encrypt(filein,fileout) ENCRYPT Apply the CRYPTO function to a text file.
ffttx(x) FFTTX Textbook Fast Finite Fourier Transform.
fibnum(n) FIBNUM Fibonacci number.
fibonacci(n) FIBONACCI Fibonacci sequence
fmintx(F,a,b,tol,varargin) FMINTX Textbook version of FMINBND
fzerotx(F,ab,varargin) FZEROTX Textbook version of FZERO.
goldfract(n) GOLDFRACT Golden ratio continued fraction.
golub(n) GOLUB Badly conditioned integer test matrices.
inregion(x,y,xv,yv) INREGION True for points inside or on a polygonal region.
lutx(A) LUTX Triangular factorization, textbook version
membranetx(k,m,n,np) MEMBRANETX Textbook version of MEMBRANE, eigenfunctions of L-membrane.
ode23tx(F,tspan,y0,arg4,varar... ODE23TX Solve non-stiff differential equations. Textbook version of ODE23.
pagerank(U,G,p) PAGERANK Google's PageRank
pagerankpow(G) PAGERANKPOW PageRank by power method with no matrix operations.
pchiptx(x,y,u) PCHIPTX Textbook piecewise cubic Hermite interpolation.
piecelin(x,y,u) PIECELIN Piecewise linear interpolation.
polyinterp(x,y,u) POLYINTERP Polynomial interpolation.
powersin(x)
qrsteps(A,b) QRSTEPS Orthogonal-triangular decomposition.
quadtx(F,a,b,tol,varargin) QUADTX Evaluate definite integral numerically.
randmcg(p,q) RANDMCG Multiplicative congruential uniform random number generator.
randntx(varargin) RANDNTX Text book version of RANDN
randssp(p,q) RANDSSP Multiplicative congruential uniform random number generator.
randtx(arg1,arg2) RANDTX Text book version of RAND
splinetx(x,y,u) SPLINETX Textbook spline function.
surfer(root,n) SURFER Create the adjacency graph of a portion of the Web.
tridisolve(a,b,c,d) TRIDISOLVE Solve tridiagonal system of equations.
vandal(n) VANDAL Symbolic Vandermonde matrix.
Contents.m
goldrect.m
sunspotstx.m
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from Using Numerical Computing with MATLAB in the Classroom by Cleve Moler
M-files used in the webinar held on April 27, 2004.

powersin(x)

function s = powersin(x)
%POWERSIN  Power series for sin(x).
%  y = POWERSIN(x) tries to compute sin(x) from its power series.
s = 0;
t = x;
n = 1;
while s+t ~= s;
   s = s + t;
   t = -x.^2/((n+1)*(n+2)).*t;
   n = n + 2;
end

Highlights from Using Numerical Computing with MATLAB in the Classroom

Highlights from
Using Numerical Computing with MATLAB in the Classroom