Wed - November 22, 2006

Readings for Week 12. 


No new readings. 

Posted at 04:08 PM    

Fri - November 17, 2006

Readings for Week 11. 


Week 10
Topic: Numerical Solutions of Ordinary Differential Equations and Least Squares Curve Fitting

Rec Chapter 12. Sections 12.4 is about adaptive stepsize algorithms and section 12.5 is about coupled ODEs and higher order ODEs.

Class 31 of Ell is on least squares curve fitting. We will actually cover a bit more than Ell does, so this week reading Rec will be essential.

Chapter 9 of Rec is on least squares curve fitting. We will only cover the material up to the end of section 9.2.2. The salient topics are the line fitting, transformations for fitting apparently non-linear functions, and least squares fit to a linear combination of functions.  

Posted at 09:47 AM    

Fri - November 10, 2006

Readings for week 10: 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Week 9
Topic: Numerical Solutions of Ordinary Differential Equations

The classes 23, 24 and 25 of Ell are on solving ordinary differential equations.

This is the topic of Rec Chapter 12. Next week we will probably cover much of the material discussed in sections 12.1-12.3. 

Posted at 09:22 AM    

Thu - November 2, 2006

Readings for Week 9. 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Week 9:
Topics:- Gaussian Quadrature.

The Ell notes covers Gaussian quadrature very tersely in class 22.

A more thorough treatment of Gaussian quadrature is done in Rec, section 11.3, however, some of it does not pertain to the material I covered this term. In particular section 11.3.4 on computing the nodes and weights can be skipped. You will need to read section 11.3.5 on composite Gaussian quadrature (also known as Gauss Legendre quadrature) to do one of the homework questions. I will go over this with you when we do the solutions to the homework.  

Posted at 04:30 PM    

Fri - October 27, 2006

Readings for Week 8. 


Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab


Week 8: Topics:- Numerical quadrature

Ell covers this topic in classes 19,20, and 21.

In Rec chapter 11 is on numerical quadrature. You should read the whole chapter, but can skip over section 11.3 on Gaussian quadrature for now. We will cover that next week. 

Posted at 03:52 PM    

Wed - October 18, 2006

Readings for Week 7. 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab


Week 7:
Topics:- Piece-wise polynomial interpolation.


Ell covers piece-wise polynomial interpolation in classes 15 and 16. There is no mention in Ell, of solving the spline coefficients using a tri-diagonal matrix.

Rec covers Hermite and cubic spline interpolation in Chapter 10 sections 10.3 Section 10.4 discusses the built in Matlab interpolation routines.  

Posted at 02:51 PM    

Fri - October 13, 2006

Readings for Week 6. 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Week 6:
Topics:- Polynomial interpolation using the monomial, Lagrange, and Newton Bases.

Ell covers polynomial interpolation in classes 9, 10, and 11. There is no mention in Ell, of using Vandermonde matrices to interpolate with the monomial basis.

Rec covers the three methods of interpolation in Chapter 10 sections 10.1 and 10.2.  

Posted at 04:03 PM    

Fri - October 6, 2006

Readings for Week 5. 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab


Week 5:
Topics:- Norms and condition numbers.

Class 28 of Ell covers norms and condition numbers.

Vector and matrix norms are covered in Rec sections 7.1.2 and 7.2.4 respectively. Section 8.3 of Rec discusses conditioning and the effects of small perturbations on ill-conditioned systems.  

Posted at 11:12 AM    

Thu - September 28, 2006

Readings for Week 4. 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Class 26 in Ell is on Gaussian elimination, and class 27 is on pivoting. Class 29 of Ell discusses LU decomposition.

Chapter 7 in Rec is a review of linear algebra. This week you should read section 7.1 , 7.2 (7.2.4 vector norms will be on next weeks reading list and I will discuss it in class, so you can skip 7.2.4 for now.) 7.3.4, 7.3.5, 7.4.1, 7.4.2, 7.4.3. Sections 7.4.3 - 7.4.8 cover special types of matrices. It wouldn't hurt to read about these. I don't think we deal with positive definite matrices or orthogonal matrices. Of these special matrices we will look at permutation matrices when we do LUP decomposition, and tridiagonal matrices when we do cubic splines.

Most of this should be a review of the linear algebra you have already taken. I will not be actively lecturing on these topics, rather the expectation is that you can brush up on this material on your own.

Chapter 8 in Rec covers Gaussian elimination and LU decomposition. This week read 8.1 8.2 and 8.4.1. This is the material I will lecture on next week. 

Posted at 02:03 PM    

Fri - September 22, 2006

Readings for Week 3.  


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Ell class 7 covers some root finding algorithms that we won't be doing this term. So you don't need to read this as preparation for quiz 1. Similarly class 8 covers some partial explanations of the convergence rate of the different root finding methods, this too will not be examined in quiz 1.

Rec Chapter 3 is on Matlab programming. This chapter will be useful for some of the programming problems in the homework for week 2. My comments (see Readings Week 1.) on quickly reading through chapter 2 apply to chapter 3 as well.  

Posted at 01:10 PM    

Fri - September 15, 2006

Readings for Week 2 


Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Topics: - Taylor's theorem, Root finding algorithms

Taylor's theorem is covered in Ell Class 1.
Root finding algorithms relevant to this class are covered in Ell Classes 5 and 6.

Taylor's theorem is in Rec section 5.1. There is an interesting discussion of convergence in section 5.2. I won't explicitly cover this in class, but you will find reading this stuff now, useful for material we will be doing in the weeks to come.
Root finding algorithms relevant to this class are covered in Rec chapter 6 sections up to the end of section 6.6. 

Posted at 03:41 PM    

Mon - September 11, 2006

Readings for Week 1. 




Key:
Ell = Randy Ellis, Scientific Computing Notes
Rec = Gerald Recktenwald, Numerical Methods with Matlab

Rec Chapter 2 is a nice introduction to the interactive usage of Matlab. I would suggest that your first reading of this chapter can be done quickly, skipping over the details. You can always refer to this section when you need it.

Rec Chapter 5 scetions 5.1 and 5.2 goes over much of what I did today. Read it in detail as a support for your lecture notes.
Ell classes 2,3,4 cover floating point issues. The most relevant part to read are subsection FLOATING-POINT NUMBERS in Class 2 pages 7-10. I didn't go over base conversion methods. Most of you have probably seen this in a prior course. Furthermore, this is really not central to the rest of the course. I did an abridged version of class 3 when discussing arithmetic error. Thus you can safely skip this chapter.
Class 4 on error propagation discusses more that I am willing to do on this topic at this point of the course. Again reading this chapter is up to you and not required.  

Posted at 04:19 PM    

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