Status: December 8, 2001

Instructor:

Schedule:

Contents:

Numerical algorithms (called also sometimes scientific computing) is the topic concerned with the design and analysis of algorithms for solving mathematical problems that arise as real-world problems in many fields, especially science and engineering. The main feature that distinguishes numerical algorithms from most other parts of computer science is that they deal with quantities (like time, distance, temperature, density, pressure, etc.) that are continuous.

In this class we shall discuss a number of modern algorithms and approximation techniques for solving mathematical problems. The class will be of an introductory nature and it should provide a solid basis for further study of numerical algorithms and scientific computation. Special emphasize will be given to understanding of numerical algorithms.

The following are the main topics covered in the class:

• Errors in numerical algorithms
• Numerical solution of equations in one variable
• Interpolation and polynomial approximation
• Numerical differentiation and integration
• Numerical solution of ordinary differential equations
• Solving linear algebraic systems
• Approximation theory and Fast Fourier Transformation (tentatively)

Programming assignments (in C/C++) and homework sets will be given.

Prerequisite: completion of a 100-level GUR course in CIS. Additionally, a general knowledge of programming (C or C++) and algorithms is required. Basic background in mathematics (including linear algebra) is also neccessary. (If you don't satisfy these requirements, then contact the instructor immediately.)

Description from the NJIT undergraduate course catalog:
CIS 421: Numerical Algorithms
This course deals with fundamentals of numerical methods, including discussion of errors, interpolation and approximation, linear systems of equations, solution of nonlinear equations, and numerical solution of ordinary differential equations. The algorithmic approach and the efficient use of the computer are emphasized.

Grading and Policies:

• Grading will be based on 4-5 problems sets (homework and programming assignments in C/C++) - 32%, an in-class midterm - 25%, a final exam - 33%, participation - 5%, and instructor's overall impression - 5%.

• 1st Programming Assignment is available (updated version).
  The deadline has been extended once again. It is now Sunday, October 21, 2001.
  One should either (recommended) send source files to seung@homer.njit.edu by the due date or hand over a diskette with the source file(s) to the class on October 21, 2001.
  Additionally - it is allowed for students to work in teams of two.
  
  
• The first part in the course (solving the problem of finding roots of equations in one variable) has been finished. To summarize this part and to help students in working on most representative problems to this topic, a list of problems in this topic to self work is prepared. The list is in
  • postscript format and
  • pdf format.
  
  
• 1st Homework due 6:00 pm (sharp), Friday, October 19, 2001, is available
  • postscript format and
  • pdf format.
  
  Solutions to all problems are available.
  The main text with solutions is available in
  • postscript format and
  • pdf format.
  A more detailed tables with the data for solutions to Problems 1 and 2 are available in the following two files in html format:
  
  • Question 1 and
  • Question 2.
  
  
  
• Midterm exam took place place on October 26, 2001.

  Midterm exam took place from 6:30 pm till 8:30 pm.

  It was an open-textbook exam, which means that students could use class notes and both textbooks: Richard L. Burden and J. Douglas Faires, ``Numerical Analysis,'' and Michael T. Heath, ``Scientific Computing. An Introductory Survey.'' Of course, every student could use her/his calculator (and it's highly recommended for students to bring one, as good as possible). However, the use of any other material (including any other books, computers, etc.) was forbidden. No students' cooperation was allowed during the midterm exam.

  The following text contains practice problems for preparations for the midterm. The files are in postscript format and pdf format.

  Solutions to all problems from the midterm exam are available in postscript format and in pdf format.

  Grades are available.
  
  

• 2nd Homework is available in the following formats:
  • postscript format and
  • pdf format.
  
  Solutions to all problems are available in
  • postscript format and
  • pdf format.
  
  
  
• 2nd Programming Assignment is available.
  The FINALdeadline is December 18, 2001. No late assignments will be accepted.
  All questions should be directed to the TA (seung@homer.njit.edu).
  The assignment will be also discussed in the class on November 30, 2001.
  Please report all errors/inaccuracies to the instructor (czumaj@cis.njit.edu).
  
  
• 3rd Homework is available; it is due December 14, 6:00 pm
  Homework is available in the following formats:
  • postscript format and
  • pdf format.
  
  
• Final exam will take place on December 14, 2001, at 6:00pm, in room KUPF 103.

  This is a cumulative exam and it covers all material presented in the class. Material covered in the class (with references to the corresponding chapters in the textbook) is listed in a html file.

  It is an open-textbook exam, which means that students could use class notes and both textbooks: Richard L. Burden and J. Douglas Faires, ``Numerical Analysis,'' and Michael T. Heath, ``Scientific Computing. An Introductory Survey.'' Of course, every student can use her/his calculator (and it's highly recommended for students to bring one, as good as possible). However, the use of any other material (including any other books, computers, etc.) is forbidden.

  No students' cooperation is allowed during the final exam.

  The following text contains practice problems for preparations for the final exam:

  The files are in

  • postscript format and
  • pdf format.

  If you don't want to have problems with this exam, then look at this text above - take it very serious !!!
  
  

A random link to some resources on basic math.

References:

• Main textbook: Richard L. Burden and J. Douglas Faires, "Numerical Analysis," Brooks/Cole Pub., 7th edition, 2001.

• Michael T. Heath, "Scientific Computing. An Introductory Survey," McGraw-Hill, 2nd edition, 2001.

• Helpful additional reference (not used in the class): William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, "Numerical Recipes in C The Art of Scientific Computing," Cambridge University Press, 2nd edition, 1992.
  (See also the web page: http://www.nr.com/ for additional information about the book and numerical algorithms.)
  If you want to buy this great handbook then you may look at its Amazon web page