MATH 251
Name:
Examination II
April 4, 2011
Student Number:
FORM A
Section:
This exam has 12 questions for a total of 100 points. In order to obtain full credit for
partial credit problems, all work m
Chapter 7
Ordinary Differential
Equations
Matlab has several different functions for the numerical solution of ordinary differential equations. This chapter describes the simplest of these functions a
function rk4_systems(a, b, N, alpha)
0unction rk4_systems() approximates the solutions of systems of m
0ifferential equations that are written in the form
0y1/dt = f1(t,y1,y2,.,ym)
0y2/dt = f2(t,y1,y2
Introduction to Matlab
Ela Pekalska,
Marjolein van der Glas
,
Pattern Recognition Group, Faculty of Applied Sciences
Delft University of Technology
2001 - 2004
Send comments to [email protected]
Co
Chapter 8
Fourier Analysis
We all use Fourier analysis every day without even knowing it. Cell phones, disc
drives, DVDs, and JPEGs all involve fast finite Fourier transforms. This chapter
discusses b
function [xp, idid, lambda]=polyline(xc, fc, gc, d, ft, f, maxarm)
%
% C. T. Kelley, Dec 29, 1997
%
% This code comes with no guarantee or warranty of any kind.
%
% function [xp, idid]=polyline(xc, fc
function [x,histout,costdata] = gaussn(x0,f,tol,maxit)
%
% C. T. Kelley, Dec 14, 1997
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = gaussn(x0,f)
%
function hess = diffhess(x, f, gc, heps)
% compute a forward difference Hessian f'(x)
%
% uses dirdero.m to compute the columns, then symmetrize
%
% C. T. Kelley, March 17, 1998
%
% This code comes wi
function [sgr,fb,xb,sflag]=simpgrad(x,f,v,fc,fdiff)
%
% simplex gradient for use with implicit filtering
% also tests for best point in stencil
%
% set fdiff = 1 to get forward differencing, useful in
function z = dirdero(x,w,f,gc,epsnew)
% Finite difference directional derivative for optimization
% Approximate f'(x) w
%
% C. T. Kelley, Dec 20, 1996
%
% This code comes with no guarantee or warranty
Matlab tutorial
by Nick Aschenbach
In this tutorial you will learn a few of the basic functions of Matlab. First we will start
working with basic mathematical functions, setting variables, and generat
function [x, histout] = hooke(x0, f, budget, scales, tol, v)
%
% Nelder-Mead optimizer, No tie-breaking rule other than MATLAB's sort
%
% C. T. Kelley, July 10, 1998
%
%
% This code comes with no guar
function [xSmall, t, tau] = rka(x,t,tau,err,derivsRK,param)
% Adaptive Runge-Kutta routine
% Inputs
% x Current value of the dependent variable
% t Independent variable (usually time)
% tau Step size
function [x,histout,costdata] = ntrust(x0,f,tol,maxit,resolution)
%
%
% C. T. Kelley, Dec 15, 1997
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = nt
MATLAB
The Language of Technical Computing
Getting Started with MATLAB
Version 7
How to Contact The MathWorks:
www.mathworks.com
comp.soft-sys.matlab
www.mathworks.com/contact_TS.html
Web
Newsgroup
Te
function [x,histout,costdata] = bfgswopt(x0,f,tol,maxit,hess0)
%
% C. T. Kelley, July 17, 1997
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout] = bfgswopt(x0,f,t
function [x,histout,costdata] = projbfgs(x0,f,up,low,tol,maxit)
%
% C. T. Kelley, June 11, 1998
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = projb
function [x,lhist,histout] = imfil(x0,f,budget,scales,parms)
%
%
% C. T. Kelley, January 9, 1998
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,fcount,histout] = imfil(
function [x,lhist,histout,simpdata]=nelder(x0,f,tol,maxit,budget)
%
% Nelder-Mead optimizer, No tie-breaking rule other than MATLAB's sort
%
% C. T. Kelley, December 12, 1996
%
%
% This code comes wit
#
ME 681
MATHEMATICAL METHODS IN ENGINEERING
#
MATLAB Tutorial Session
Date : 03.08.2006
Day : Thursday
Venue: L2 Time: 17:00 - 18:00 Hrs.
=
1) PROGRAMMING IN MATLAB
=
- Done using command li
function [x,histout,costdata] = steep(x0,f,tol,maxit)
%
% C. T. Kelley, Dec 20, 1996
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = steep(x0,f,tol,m
function R = rombf(a,b,N,func,param)
% Function to compute integrals by Romberg algorithm
% R = rombf(a,b,N,func,param)
% Inputs
% a,b Lower and upper bound of the integral
% N Romberg table is N by N
function [x,histout,costdata] = levmar(x0,f,tol,maxit)
%
% C. T. Kelley, Dec 14, 1997
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = levmar(x0,f,tol
Chapter 11
Partial Differential
Equations
A wide variety of partial differential equations occurs in technical computing. We
cannot begin to cover them all in this book. In this chapter, we limit ours
Chapter 10
Eigenvalues and Singular
Values
This chapter is about eigenvalues and singular values of matrices. Computational
algorithms and sensitivity to perturbations are both discussed.
10.1
Eigenva
function [x,histout,costdata] = gradproj(x0,f,up,low,tol,maxit)
%
% C. T. Kelley, June 11, 1998
%
% This code comes with no guarantee or warranty of any kind.
%
% function [x,histout,costdata] = gradp
MATH 251
Exam I
September 26, 2011
ANSWER KEY (Form A)
1.
(a) No
(b) Yes
(c) No (also acceptable: Yes, it can be rewritten
into an exact equation because the equation is separable.)
(d) No
2.
D
3.
A
4
MATH 251
Name:
Final Examination
August 10, 2011
Student Number:
FORM A
Section:
This exam has 10 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all w
MATH 251
Name:
Final Examination
April 30, 2012
Student Number:
FORM A
Section:
This exam has 15 questions for a total of 150 points. In order to obtain full credit for
partial credit problems, all wo