## Matlab Programs

### Matlab Programs for Math 4457

Main routines
• dspr.m — normal modes of oscillation of linear mass & spring system
• gspr.m — graph oscillations of linear mass & spring system
• cspr.m — show oscillations of linear mass & spring system
• mspr.m — show oscillations and normal components of linear mass & spring system
• dyst.m — dynamical modes of oscillation of 2D or 3D structure
• network.m — finds potentials and currents in electrical networks
• strut.m — graphs a structure in two or three dimensions, and determines its stability
• graph.m — finds incidence matrix and plots a graph
• quasi.m — plot quasi—periodic function (2 modes)
• quasi3.m — plot quasi—periodic function (3 modes)

Computational subroutines

• incidence.m — computes incidence matrix from edge matrix
• ngon.m — finds coordinates for unit polygon
• solids.m — edge matrices and vertices for regular solids
• house.m — edge matrices and vertices for houses
• tr3.m — linear transformations of multiple points

Graphics subroutines

• button.m — sets up buttons for interacting with dynamical graphics
• circle.m — draws circles
• triangle.m — draws triangles
• linevec.m — draws lines using vector coordinates
• arrowvec.m — draws directed lines using vector coordinates
• textvec.m — writes text at specified coordinates

### Matlab Programs for Math 5457

Main routines
• Qplot.m — for graphing quadratic functions
• ellipse.m — graphs ellipses and their principal axes
• ellipsoid.m — graphs ellipsoids and their principal axes
• network.m — finds potentials and currents in electrical networks
• strut.m — graphs a structure in two or three dimensions, and determines its stability
• graph.m — finds incidence matrix and plots a graph
• cgraph.m — finds incidence matrix and plots complete graph
• ograph.m — finds incidence matrix and plots circular graph

Computational subroutines

• incidence.m — computes incidence matrix from edge matrix
• cedge.m — finds edge matrix for complete graph
• oedge.m — finds edge matrix for circular graph
• cgon.m — finds edge matrix and vertex coordinates for complete graph
• ogon.m — finds edge matrix and vertex coordinates for circular graph
• ngon.m — finds coordinates for unit polygon
• solids.m — edge matrices and vertices for regular solids
• house.m — edge matrices and vertices for houses
• tr3.m — linear transformations of multiple points

Graphics subroutines

### Matlab Programs for Math 5458

Main routines
• phase3.m — phase portrait of 3D ordinary differential equation
• heat.m — numerical solution of 1D heat equation (Crank—Nicholson method)
• wave.m — numerical solution of 1D wave equation (finite difference method)
• go2.m — graph solutions to planar linear o.d.e.'s
• go3.m — graph solutions to three—dimensional linear o.d.e.'s
• dspr.m — normal modes of oscillation of linear mass & spring system
• gspr.m — graph oscillations of linear mass & spring system
• cspr.m — show oscillations of linear mass & spring system
• mspr.m — show oscillations and normal components of linear mass & spring system
• dyst.m — dynamical modes of oscillation of 2D or 3D structure
• phase.m — phase portrait of 2D ordinary differential equation
• phaseg.m — phase portrait plus graph of second order ordinary differential equation
• phasem.m — phase portrait plus movie of pendulum motion

Computational subroutines

• o3.m — a simple 3D differential equation
• fset.m — set up for Fourier sine series
• fsine.m — plot Fourier sine series
• fset2.m — set up for Fourier series
• fouri.m — plot Fourier series
• lo2.m — general planar linear first order o.d.e.
• lo3.m — general three—dimensional linear first order o.d.e.
• button.m — sets up buttons for interacting with dynamical graphics
• quasi.m — plot quasi—periodic function (2 modes)
• quasi3.m — plot quasi—periodic function (3 modes)
• pendulum.m — nonlinear pendulum differential equations
• dpendulum.m — damped nonlinear pendulum differential equations
• fpendulum.m — forced nonlinear pendulum differential equations
• fdpendulum.m — forced damped nonlinear pendulum differential equations

### Matlab Programs for Math 5485

• rn.m — rounding function
• iter.m — function iteration
• secant.m — secant method
• newton.m — Newton's method
• gauss.m — regular Gaussian elimination
• gaussr.m — alternative regular Gaussian elimination
• back.m — back substitution
• trid.m — generate tridiagonal matrices
• specr.m — compute spectral radius of a matrix
• miter.m — matrix iteration
• jacobi.m — Jacobi iteration
• gs.m — Gauss—Seidel iteration
• sor.m — SOR iteration
• sorw.m — optimal SOR parameter
• newton3.m — solve z^3 = 1 by Newton's method
• robot.m — position robot arms by Newton's method
• lagrangep.m — Lagrange interpolating polynomial
• lagrangeplot.m — Plot Lagrange interpolating polynomial
• ix2.m — the function 1/(1+x^2)

### Translations of this web page:

Professor Peter J. Olver
School of Mathematics
University of Minnesota
Minneapolis, MN   55455
USA