Math 471 Home Page
Numerical Analysis

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MCS471 Course Data :

1. Semester Fall 2004 Section with Professor Hanson:

   °   Time Table:

   MCS 471 Numerical Analysis
   3 OR 4 hours. 3 undergraduate hours. 4 graduate hours.

   Prerequisite(s): Grade of C or better in MCS 275 or grade of C or better in CS 102 or grade of C or better in CS 108; or consent of instructor.

   12362 LCD 03:00 PM-03:50 PM MWF E112 2LCE Hanson, F
   3 hours Restricted to Undergrad - Chicago.

   20463 LCD 03:00 PM-03:50 PM MWF E112 2LCE Hanson, F
   4 hours Restricted to Graduate - Chicago, and Graduate Non-Degree Chicago.

   °   Fall 2004 Instructor: Professor Floyd Hanson, 718 SEO, hanson A T uic edu , (Email Is BEST, but phone is 1312-413-2142).

   °   Instructor Office Hours: 1pm-1:50pm, 718 2SEO MWF

   °   Class and Section Web Page: http://www.math.uic.edu/~hanson/mcs471 (current page)

2. Class Web Page: http://www.math.uic.edu/~hanson/mcs471/ (current page)

3. Course Coordinator: Professor F. B. Hanson, 718 SEO, hanson A T uic edu , (Email Is BEST, but phone is 1312-413-2142).

Syllabus :

• MCS 471 General Syllabus

• Prerequisites (REVISED*): A grade of C or better in
  
  MCS190 Introduction to Scientific Computing
  OR EECS 170 Fortran Programming for Engineers
  OR EECS 171 Introduction to Programming.
  OR MCS 260 Introduction to Computer Science I
  OR EECS 270 Introduction to Programming languages
  OR MCS 360 Structured Programming II
  (*REVISED: College Catalog is Out of Date)

• MCS 471 Topics by Lecture(Approximate & Dated from 1997, To Be Revised.)

Class Text :

1. Your Class Lecture Notes Taken From Professor Hanson's Lectures, if Fall 2004 class.
2. See also http://www.math.uic.edu/~jan/MCS471.html, Notes from Professor Verschelde Spring 2002 Class.
3. {For a 2nd Opinion:}
   C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 6th Ed., Addison-Wesley, 1999. Prior text or prior edition also could be used. Also, try getting a used copy, such as as www.amazon.com, to save lots of money.
4. {For a more advanced 3rd Opinion:}
   Michael T. Heath, Scientific Computing: An Introductory Survey, McGraw-Hill, 2nd Edition, 2002.
5. R. E. White, Computational Numerical Analysis: Methods and Analysis in UCES, Undergraduate Computational Engineering and Science (UCES) online HTML text, 1994.

Homework :

• Homework Problem#1 due Friday 10 September 2004 in Class

Computer Problems

There will be about 4-5 Computer Problems (using C or Fortran or other progamming language, MATLAB and also Maple symbolic computation) to be assigned as individual work, such as:
• Computer Problem 1: Floating Point Arithmetic Machine Epsilon  (Due 22 September 2004).

• Computer Problem 2: Zeros of Nonlinear Equations   (Due 18 October 2004).

• Computer Problem 3: Computational Linear Algebra - Newton's Multidim. Method  (Due 15 November 2004).

• Computer Problem 4: Integration using Maple Symbolically and Numerically   (Due 03 December 2004)..

Practice Problems :

• Practice Problems #1: Nonlinear Equations

• Practice Problems #2: Computational Linear Algebra

• Practice Problems #3: Interpolation

• Practice Problems #4: Numerical Integration

• Practice Problems #5: Numerical Solution of ODEs

• See Also Partial Answers ("PartAns") from old Computer Science Master's Exam, but there are only 2 Numerical Analysis Questions per CS Master's Exam, and the posted answers are almost all Professor Hanson's.

Examinations (Fall 2004) :

1. <Exam #1 (Fall 2004 First Triterm Exam): on Precision and Nonlinear Equations, Wednesday 13 October 2004
   
   °   Exam 1 Topics:
   • Floating Point Precision
   • Bisection Method
   • Secant Method
   • Newton's Method
   • Fixed Point Iteration Method
   • Golden Section Search
   • See also sample exam Practice Problems#1: Nonlinear Equations
   
   °   Formula Sheet of one side of an 8.5x11 sheet of paper will be allowed, IF it ONLY contains Formulas and NO examples and NO problems. Put your Name on the page since it will be collected with your exam, but even if you choose not to use a formula sheet you must hand in a blank sheet except with your name on it.
   • Sample Exam #1 Spring 99: exam1s99.pdf (Answers are not available: verified answers lost.)

2. Exam #2 (Fall 2004 Second Triterm Exam): on Computational Linear Algebra, Wednesday, 10 November 2004
   
   °   Exam 2 Topics:
   • Floating Point Arithmetic, Efficiency and Accuracy are part of all exams.
   • Forward Gaussian Elimination with Back Substitution
   • Virtual Row (Partial) Pivoting and Row Scaling
   • Linear Algebra Computational Complexity
   • Determinants, Inverse and Multiple RHSs by FGE
   • Norms, Condition Numbers
   • Multidimensional Newton's Method (Nonlinear Algebra)
   • See also sample exam Practice Problems#2: Compuational Linear Algebra
     Note that the first four problems of pp2.html are the questions and answers to the MCS471 2nd Exam of Fall 1999, but only the first question is really relevant for Fall 2004.
   
   °   Formula Sheet of one side of an 8.5x11 sheet of paper will be allowed, IF it ONLY contains Formulas and NO examples and NO problems. Put your Name on the page since it will be collected with your exam, but even if you choose not to use a formula sheet you must hand in a blank sheet with your name on it.

3. Final Exam (Fall 2004): on Linear Interpolation, Integration and ODEs, 1-3pm, Wednesday 08 December 2004, Room E2-LC
   
   °   Final Exam Topics: {Lectures are Primary, G&W Sections are Second Opinion}
   • Linear Interpolation.
   • Numerical Integration.
     • Left, Right, Midpoint Rectangular Integration Rules
     • Trapezoidal Rule
     • Simpson's Rule
     • Gaussian Quadrature {GR₁, GR₂, kXGR₁}
     • See also sample exam Practice Problems#4: Numerical Integration
   • Numerical Solution of ODEs
     • Euler Methods
     • Runge-Kutta Methods (RK2, RK4)
     • See also sample exam Practice Problems#5: Numerical Solution of ODEs

   °  Formula Sheet: You are allowed to prepare and bring a Formula Sheet - two sides of an 8.5x11 sheet of paper - which you must turn in with your exam to have your exam graded. The sheet may have the following information:

   • Required: Name, UI ID Number (optional if name is clearly printed).                                                    
   • Except Examples and problems are NOT allowed.
   • Sample Final S99: (PDF?*   OR   PS?*)   OR   (Sample MapleVr3 Answers?)

   • See Also: Master's Exam CS Option Partial Answers ("PartAns"), but there are only 2 Numerical Analysis Questions per Exam, and the posted answers are almost all Professor Hanson's.

   • Sample Answers (4a and 5a)for Spring 2001 Final Exam. Answers to Questions 4a and 5a

Grading Policy :

• Hour Exams* (2) ---- 33%
• Final Exam* ---- 34%
• Individual Computer Problems and Homework** ---- 33%
  
  °   Exams, homework and computer problems are INDIVIDUAL assignments, and NOT group work.
  °   *Cheating on Exams Results in Double Credit Deduction and Ultimately Failure for Both Copier and Copiee (person copied from, even if for not keeping work covered). Cheating on Final Exams may also Result in Dismissal from the University.
  °   **Credit for Problems NOT Handed in is the Negative of Full Credit.
  °   **Plagiarism or Copying of Computer Problems and Homework from someone else Will Result in Severe Penalties, starting with nearly identical problems sharing the credit for one problem only.

Help for MATLAB Labs :

• Prof. Hanson's MATLAB Help HomePage: http://www.math.uic.edu/~hanson/MATLABhelp.html

• Prof. Verschelde's MCS 320 Symbolic Computing with MATLAB (and Maple) Lectures

• Desmond J. Higham and Nicolas J. Higham, MATLAB Guide, SIAM, 2000.

• John Mathews, Numerical Analysis Page, Course material from the book "Numerical Methods: Using Matlab", such as Numerical Tutorials, MATLAB Code and more.

• Duane Hanselman and Bruce Littlefield, Mastering MATLAB 6: A Comprehensive Tutorial and Reference, Prentice Hall, 2001.

• Delores M. Etter, Engineering Problem Solving with MATLAB, Prentice Hall,1993.

• George Lindfield and John Penny, Numerical Methods Using MATLAB, Prentice Hall, 2000.

• Rudra Pratap, Getting Started with MATLAB, Saunders, 1996.

Help for Maple Labs :

• Beginner's Introduction to Maple in MathLab 200 SEO and also UIC PClabs

• Basic Help for Using UIC PCLabs

• MSCS Maple Resource Site

• MSCS Maple Labs Introduction to Maple

• Maple Reference Card.ps (2 page V5r5 postscript doc by Doug Mgade)

• Prof. Hanson's Help for Maple Symbolic Tools Archive

• Prof. Verschelde's MCS 320 Symbolic Computing with Maple Lectures

• Maple V Release 4 Student Edition: (Availability for Those Who Want Their Own Maple Copy.)

  °   Student Edition of MapleV (rel. 4.0) at Microstation, Software Price List, or just go to Microstation on the first floor of CCC at the North End near the Dorms, and ask for MapleV 4.0 Student Edition, about $60, Part No. 20-90-200-A, specify MacOS or Win9r/NT system. Also check for the New Improved Maple 6 too.

  °   Waterloo Maple Student Edition, BUT only a Limited Version for an Introductory Maple Course. $94.9 Full version. You Can Visit Epicenter Bookstore on 2nd Floor CCC since they are an official Springer Vendor.

Class Resources :

• Prior Semester MCS471 Courses:

• Supplementary References:

• Class Notes:

• PostScript Viewer Help for PCs

• Help for Numeric and Symbolic Computational Tools
  
  °   MATLAB Help HomePage.
  °   Octave Matrix Lab Help Page
  °   Maple Symbolic Computation Help Page