
MATH 4721 / 6721 

Fall 2017 


Numerical Analysis 

Dwiggins 








Tuesdays 
Thursdays 


Aug 29 
§§ 5.12 
Aug 31 
§§ 5.23 


Numerical
Solutions to 
Euler's Method, 


Ordinary
Differential Equations: 
RungeKutta Methods, 


Initial Value
Problems 
and variations on those themes 


Sep 5 
§§ 5.4, 4.12 
Sep 7 
§§ 4.23 


MultiStep
Methods for ODEs, 
Simpson's Rule 


Introduction
to 
and Beyond 


Numerical
Integration 
HW # 1 due (Chapter 5) 


Sep 12 
§§ 4.56 
Sep 14 
§§ 4.89 


Gaussian
Quadrature, 
Improper Integrals, 


Adaptive
Quadrature, 
Techniques for 


Examples from
Physics 
Numerical Differentiation 


Sep 19 
§§ 1.13 
Sep 21 
§§ 1.35 


FloatingPoint
Arithmetic 
Error Analysis: 


and
Computational Error 
Estimating the total error, and 


HW # 2 due
(Chapter 4) 
algorithms for minimizing error 


Sep 26 
§§ 2.13 
Sep 28 
§§ 2.46 


Classical
Techniques of 
Newton's Method, 


Approximate
Computation 
Rates of Convergence, 


(e.g. the
Mechanic's Method) 
Müller's Method 


Oct 3 
§§ 3.12 
Oct 5 
§§ 3.23 


Polynomial
Interpolation, 
Organizing your work: 


the Lagrange
Polynomial 
Divided Difference 


HW # 3 due
(Chapters 12) 
Tables 


Oct 10 

Oct 12 




MidTerm Exam 


REVIEW 
Chapters 1, 2, 4, 5 






Oct 17 
FALL BREAK 
Oct 19 
§§ 3.45 



Hermite Polynomials, 


No classes
scheduled 
Introduction to 



Spline Theory 


Oct 24 
§ 3.5 
Oct 26 
§§ 6.12 


More on Spline
Theory, 
Solving Linear Systems: 


and why Cubic
Splines 
Gaussian Elimination 


are the best 
HW # 4 due (Chapter 3) 


Oct 31 
§ 6.3 
Nov 2 
§ 6.4 


Problems
involved with 
Matrix Inverses and 


Matrix
Inversion: 
Determinants, and why we 


Pivoting
Schemes 
often don't really need them 


Nov 7 
§ 6.5 
Nov 9 
§ 6.6 


Matrix
Factorizations 
Problems involving 


and their 
special types of matrices 


Applications 
(Band Matrices, Tridiagonal Matrices) 


Nov 14 
§§ 7.23 
Nov 16 
§§ 7.34 


Vector Norms
and 
Methods for estimating 


Matrix Norms 
Eigenvalues and 


HW # 5 due
(Chapter 6) 
Eigenvectors 


Nov 21 
§ 7.6 
Nov 23 
THANKSGIVING 


Matrix
Factorizations 



and their 
No classes scheduled 


Applications 



Nov 28 
§ 8.4 
Nov 30 
§§ 9.56 


Interpolation
using 
More on matrices: 


Orthogonal
Polynomials 
Householder's Method, 


HW # 6 due
(Chapter 7) 
the QR Decomposition 


Dec 5 

Dec 7 
STUDY DAY 






REVIEW 
No classes scheduled 






Dec 12 

Dec 14 



Final Exam 
Extra Credit 


Chapters 3, 6,
7, plus 
Assignments Due 


material from
MidTerm Exam 









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