SyDe312  Numerical Methods Assignments and Solutions 
Stephen
Birkett

Research
Teaching
Linear Algebra
Numerical Methods Topics and Lectures Assignments Tests Computational Mathematics Musical Instruments Music

Assigned problems are listed below for each unit. References are to Atkinson/Han 3rd Edition. The links to solutions will become active when they are available for downloading. Try doing the problems before looking at the solutions!  
UNIT 0  NUMERICAL COMPUTATION  
2.1 1acd 2.2 1bde 5bde 6adg 9 10 14 16 18 19. Find the IEEE 754 standard single precision floating point values representing the decimal numbers: 666.7523, 3.1415926535, 3.0E127, 3.0E127 1.1 2bc 7 8 1.2 5 8 1.3 9 10 11 [resources: IEEE Standard 754 Floating Point Numbers IEEE 754 Floating Point chop.m expSeriesPlot.m fidiff.m]  
UNIT I  LINEAR ALGEBRA  
6.1 4 5 6 6.2 (7) 9 10 6.3 1 2 5 [explore these with limiting precision using GEdemo.m ] 6.5 1 3 4 6.4 2a [hand calc and solve the system] 1 [hand calc  use strict partial pivoting] 2bc [use Matlab] 5 6 Suppl. Cholesky problems 8 [use Matlab] 9 10 [tridiag.m can be downloaded from the publisher's website] 6.6 1b 3 4 5 6 14[resources: cholesky.m] 7.2 1a 12 14 Suppl. SVD problems  
UNIT II  ROOT FINDING AND NONLINEAR SYSTEMS  
3.4 3 4 7 3.1 bisect.m brackPlot.m 1 4 7* 8* 3.2 newton.m 1 2 10* 11* 3.3 1 5 6 [using both secant and regula falsi methods] 3.5 1* 2* 8* 7.3 newtonSys.m 2 3 5. For polynomial problems marked * repeat using: (a) the companion matrix method [use eig in matlab to get the eigenvalues] and (b) Laguerre's method, utilizing polynomial deflation where interesting / appropriate / desirable, e.g. in 3.58 where there is a quadruple root.  
UNIT III  CURVE FITTING AND INTERPOLATION  
7.1 1, 3 Extra curvefit problems 4.1 2, 3, 6, 7, 12, 24, 25, 28 4.3 1, 3, 7, 14 [explore solutions of these problems using the matlab spline function and basic curve fitting in the graphic screen and compare to hand solutions] Extra illustrative examples  
UNIT IV  NUMERICAL INTEGRATION AND DIFFERENTIATION  
5.1 2adef, 3adef, 4b, 5a, 6. 5.3 1 2adef 4b 5a Extra quadrature problems 5.4 1ac, 2ac, 3ac, 9ac, 13. Quassian quadrature mfiles  
UNIT V  DIFFERENTIAL EQUATIONS  
8.2
1abdg (also use midpoint method and RK4; compare the ratios as described).
8.5 10bd, 11bd, 12 bd odeEuler.m
odeMidpt.m
odeRK4.m
Extra illustrative examples  