MATLAB Mathematics - SERC - Index of

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2 Polynomials and Interpolation Polynomials This section provides • A summary of the MATLAB polynomial functions • Instructions for representing polynomials in MATLAB It also describes the MATLAB polynomial functions that • Calculate the roots of a polynomial • Calculate the coefficients of the characteristic polynomial of a matrix • Evaluate a polynomial at a specified value • Convolve (multiply) and deconvolve (divide) polynomials • Compute the derivative of a polynomial • Fit a polynomial to a set of data • Convert between partial fraction expansion and polynomial coefficients Polynomial Function Summary MATLAB provides functions for standard polynomial operations, such as polynomial roots, evaluation, and differentiation. In addition, there are functions for more advanced applications, such as curve fitting and partial fraction expansion. The polynomial functions reside in the MATLAB polyfun directory. Polynomial Function Summary Function conv deconv poly polyder polyfit polyval Description Multiply polynomials. Divide polynomials. Polynomial with specified roots. Polynomial derivative. Polynomial curve fitting. Polynomial evaluation. 2-2
Polynomials Polynomial Function Summary (Continued) Function polyvalm residue roots Description Matrix polynomial evaluation. Partial-fraction expansion (residues). Find polynomial roots. The Symbolic Math Toolbox contains additional specialized support for polynomial operations. Representing Polynomials MATLAB represents polynomials as row vectors containing coefficients ordered by descending powers. For example, consider the equation px ( ) = x 3 – 2x – 5 This is the celebrated example Wallis used when he first represented Newton’s method to the French Academy. To enter this polynomial into MATLAB, use p = [1 0 -2 -5]; Polynomial Roots The roots function calculates the roots of a polynomial: r = roots(p) r = 2.0946 -1.0473 + 1.1359i -1.0473 - 1.1359i By convention, MATLAB stores roots in column vectors. The function poly returns to the polynomial coefficients: p2 = poly(r) p2 = 1 8.8818e-16 -2 -5 2-3
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MATLAB® The Language of Technical
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Revision History June 2004 First pr
Page 6 and 7: 2 Polynomials and Interpolation Pol
Page 8 and 9: Introduction to Initial Value ODE P
Page 10 and 11: vi Contents
Page 12 and 13: 1 Matrices and Linear Algebra Funct
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Page 58 and 59: 2 Polynomials and Interpolation pol
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Page 94 and 95: 3 Fast Fourier Transform (FFT) Intr
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Page 104 and 105: 4 Function Functions Function Summa
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4 Function Functions You can also c
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4 Function Functions 25 20 15 10 5
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4 Function Functions Minimizing Fun
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4 Function Functions To try fminsea
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4 Function Functions Plotting the R
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4 Function Functions The number of
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4 Function Functions and displays t
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4 Function Functions end function s
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4 Function Functions States of the
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4 Function Functions 100 80 60 40 2
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4 Function Functions You can verify
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4 Function Functions Troubleshootin
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4 Function Functions A three-dimens
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4 Function Functions Parameterizing
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4 Function Functions “Anonymous F
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5 Differential Equations Initial Va
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5 Differential Equations odephas3 o
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5 Differential Equations This secti
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5 Differential Equations The basic
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5 Differential Equations 2 Code the
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5 Differential Equations function.
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5 Differential Equations One way to
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5 Differential Equations y0, yp0 Ve
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5 Differential Equations For exampl
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5 Differential Equations 1 0.8 0.6
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5 Differential Equations 2.5 Soluti
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5 Differential Equations To run thi
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5 Differential Equations 2 u′ i =
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5 Differential Equations dydt(i+1,:
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5 Differential Equations refine = 4
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5 Differential Equations Example: A
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5 Differential Equations function [
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5 Differential Equations Note The R
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5 Differential Equations 1 Robertso
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5 Differential Equations The MATLAB
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5 Differential Equations Summary of
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5 Differential Equations Problem Si
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5 Differential Equations Error Tole
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5 Differential Equations Troublesho
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5 Differential Equations Function d
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5 Differential Equations dde23 prod
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5 Differential Equations The exampl
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5 Differential Equations solution y
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5 Differential Equations Example: C
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5 Differential Equations Changing D
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5 Differential Equations BVP Functi
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5 Differential Equations two-point
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5 Differential Equations The input
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5 Differential Equations 2 Pass the
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5 Differential Equations Finding Un
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5 Differential Equations vectorized
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5 Differential Equations There is a
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5 Differential Equations 3 Solve on
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5 Differential Equations hold off T
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5 Differential Equations Note The d
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5 Differential Equations legend('An
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5 Differential Equations Here, v(1-
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5 Differential Equations solution v
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5 Differential Equations Note The D
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5 Differential Equations After disc
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5 Differential Equations The output
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5 Differential Equations The exampl
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5 Differential Equations and the ri
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5 Differential Equations u1(x,t) 1
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5 Differential Equations Selected B
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6 Sparse Matrices Function Summary
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6 Sparse Matrices Function Summary
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6 Sparse Matrices This matrix requi
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6 Sparse Matrices S = (3,1) 1 (2,2)
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6 Sparse Matrices Now F = full(S) d
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6 Sparse Matrices Importing Sparse
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6 Sparse Matrices west0479 west0479
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6 Sparse Matrices The find Function
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6 Sparse Matrices of the rows and c
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6 Sparse Matrices The vertices of o
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6 Sparse Matrices 0 10 20 30 40 50
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6 Sparse Matrices 0 500 1000 1500 2
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6 Sparse Matrices simply sparse(m,n
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6 Sparse Matrices Similarly, S(:,p)
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6 Sparse Matrices The following MAT
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6 Sparse Matrices 0 Original 0 Reve
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6 Sparse Matrices QR Factorization
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6 Sparse Matrices shows that A has
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6 Sparse Matrices Functions for Ite
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6 Sparse Matrices set up the five-p
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6 Sparse Matrices Manipulating Spar
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6 Sparse Matrices Selected Bibliogr
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Index comparing sparse and full mat
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Index H hb1dae demo 5-35 hb1ode dem
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Index nonstiff ODE examples rigid b
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Index LU factorization 6-30 minimum
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Index twobvp demo 5-63 two-dimensio
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