Applied Linear Algebra and Numerical Analysis

Course Description

Essential Initial Information on homework guidelines, and character of the course; Please READ description , hw guidelines and matlab use , mfiles use.

Textbook and lecture notes

• Gerald Recktenwald, Numerical Methods with MATLAB, Prentice Hall, 2000.
  
• This text is not required but highly recommended: Schaum's Outline of Linear Algebra by Seymour Lipschutz, Marc Lipson, ISBN: 0071362002 $17 paperback. on reserve in the Engineering lib (24h) or Math lib
  More advanced references:
• This is the text for AMATH 584 the graduate applied linear algebra course NUMERICAL LINEAR ALGEBRA Lloyd N. Trefethen and David Bau, III SIAM, 1997 (not required)

• Lecture notes and m-files for Ordinary differential equations dir
• m-file for July 6 lecture
• Lecture notes for interpolation dir

The matlab scripts that accompany this book are available on the PCs in the MSCC lab,
or can be downloaded from

• http://www.prenhall.com/recktenwald

  Syllabus

  (1) Review of Applied Linear Algebra: Basis, range, rank vector norms, matrix norms. Special matrices: symmetric, orthogonal, lower and upper triangular, tridiagonal. Mostly Chapter 7

  (2) Taylor series and error analysis. Chapter 5

  (3) Solution of a Single Nonlinear Equation: Bisection method. Newton's method. Convergence to a root. Chapter 6

  (4) Direct Methods for Solving Dense Systems of Linear Equations: Gaussian elimination with partial pivoting. Paragraphs: 8.1.2, 8.2, 8.2.3, 8.2.4 Solution of triangular systems, multiple right hand sides. Tridiagonal systems LU factorization 8.4.1 The condition number 8.3.2

  (5) Function approximation: Curve fitting, Least squares, Polynomial interpolation, Vandermonde, Lagrange, Newton basis. Cubic splines. Reading: 9.1,9.2,10.2,10.3

  (6) Ordinary Differential Equations - Initial Value Problems: Euler's method. Accuracy and stability. Implementation of ode23 and ode45 for solution of scientific problems.

  Matlab Resources

  • Matlab is available for use in the MSCC lab.
• The Matlab help desk where you can find useful introductory information under "Learning MATLAB"
• List of Matlab Resources at Mathworks site Moller's online textbook
• Matlab Hypertext Reference, Henri Gavin's list of tutorialsDuke University
• Many other Matlab tutorials can be found one the web with any search engine, e.g. Google.
• The Matlab help desk where you can find useful introductory information under "Learning MATLAB"

  Schedule and Homework

  Homework Format You may discuss and compare your results with other students in the class but you should provide your own answers.

  Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

  Teaching Assistant:	you may always send an e-mail to the TA at jszhou@amath.washington.edu to ask questions about the hw
  Homework and Exams	Homework Due Date	Homework Problem Sets	Homework Solutions
  First day of classes	Monday, June 20	Matlab orientation session	MSCC B027 12:00-13:00 (after class)
  2nd-4th day of classes	Tuesday June 19 AND Thurday June 21	Extra lecture	16:00 - 18:00 Condon Hall 101
  Homework#1	due Friday, June 22	Homework #1 ( .pdf )	HW #1 Solutions ( dir)
  Homework#2	due Friday, June 29	Homework #2( dir)	HW #2 Solutions ( dir)
  Independence Day	Wednesday, July 4	No class
  Homework#3	due Friday, July 6	Homework #3 ( dir )	HW #3 Solutions ( dir)
  Homework#4	due Friday, July 13	Homework #4 (.pdf))	HW #4 Solutions ( .pdf) )
  Homework#5	due Friday, July 20	Homework #5 ( dir))	HW #5 Solutions ( dir))
  Mid-term exam	Monday July 23 in class	review material	practice material, answers
  Homework#6	due Friday August 3	Homework #6 (dir)	HW #6 Solutions ( dir))
  Homework#7	due Friday, August 10	Homework #7 .pdf)	HW #7 Solutions ( dir)
  Final Examination	Monday August 13 10:50-11:50	final review
  project	Due Wednesday August 15 at noon	Turbulent round jet	interp1 example
  Week 7,8,9 detailed schedule		office hrs, project, exam

  Grading, Exams and Office Hours

  Your course grade will be calculated by weighing your Homework, Take-home Exam, Midterm Exam and Final Exam grades in the proportions 20%, 20%, 30% and 30% respectively. Homework problem sets will be assigned weekly, normally due on Friday. The TA will grade the majority but not all problems in your homework.
  Mid-term exam: Monday July 23
  This is a 50-minute written examination that will cover material as described in paragraphs (1), (2), (3) and (4) of the Syllabus. Because the linear algebra part is being tested in the GRE exams you will not be allowed notes on this subject so that you can prepare. You are allowed notes on numerical analysis though: Bring a one-sided sheet of notes on numerical analysis only.
  Take-home exam : It will cover material from paragraph (5) of the Syllabus and will require you to use Matlab.
  Final Exam: August
  The final exam will last 50-minutes, testing your understanding of the material we covered in sections (5), (6) of the syllabus and emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity. Bring with you: a double-sided sheet of notes that will exclude any linear algebra material. More info on this later in the quarter

  Important Note on Office hours
  Office hours are hours during which I am guaranteed to be in my office, answering your questions and dealing with problems you may have in this course. Office hours are not time during which you do your homework in my office. Rather, you should use this time to ask questions about problems which you have tried to work out, but got stuck at some point. In other words, you should come to office hours prepared, just like you should come to class prepared. On the other hand you can do your homework at the MSCC lab, during office hours if you prefer, with me or Justine.

  Extra credit
  (1) I will frequently assign some homework problems of extra difficulty for those wishing to explore the techniques further and test their understanding.
  (2) Since most of you come from diverse areas of science and engineering, economics etc. where numerical methods are frequently used, in every homework, you are strongly encouraged to explore your area further and find one (1) problem that uses the techniques of this week's homework (which I will be describing each week). You will get extra credit for a sound explanation of the origins of the problem and a full solution.

  What to do next Prof. Kutz offers AMATH 581 - Scientific Computing. A numerical linear algebra course is AMATH 584.

  You may view your homework and exam grades on-line.

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  <kirkinis@amath.washington.edu>

  Thu June 14 11:07:17 PDT 2007