Instructor: Siva Athreya
Office: A 12.
Texts:
E-Mail: My e-mail address is athreya AT isibang DOT ac DOT in. Please send me an email1, from an account that you use regularly, so that I can put you on the class list.
WWW-page: I shall maintain a course home-page, at the
following address:
http://www.isibang.ac.in/~ athreya/cs205 . The
page should serve as an archive of handouts at the very least.
Project: Each of us will do an independent study project dealing with an application of numerical methods and submit a report. There will be a list of subjects to choose from. The project will be graded on the report's material content, amount studied and referenced, presentation and the results achieved. I shall keep you posted on this as the semester progresses.
Exams:
There shall be two exams in the semester. The exact date will be announced by the student incharge's office. The week during which they will be held are:
Midterm: March 7th-11th
Final Exam: May 9th-17th.
Homework: There will be regular homework assignments during the semester. A selection of which will be required to be turned in. You are encouraged to work together on solving the problems but write up your own individual solutions.
Quiz: There will be a short test on Tuesdays(12:10-1:10) in the class. The test will have one question and will be essentially based out of the previous week's homework.
Scoring: Midterm 1 is worth 25 % of the grade. Final exam is worth 50 % of the grade. The project is worth 15 %. The quizzes consists of 10 % of the grade.
Ground Rules: No late homework will be accepted. No make up quizzes will be given.
Following is the syllabus and a tentative schedule for the material
to bcovered in class.
Studying and Homework: The course requires at least one and a
half hour of study for each hour of class time. Homework will be
announced in class and posted on the web. It is imperative that you
try,(and write up solutions for), the homework problems before
their respective due dates. The problems that will be given are a
small selection so please do try other problems for practice from the
text. You are encouraged to work together on solving the problems. We
shall try to discuss the homework during one of the classes.
Feedback: Please feel free to drop by my office, to clear up
difficulties or to just discuss mathematics. I would appreciate
feedback from you as the course progresses. If there are
suggestions/clarifications that you have then feel free to ask me.
Month
Syllabus to be covered
January
Introduction to Matlab and Introduction to Numerical
Computing: Number representations, finite-precision arithmetic, errors
in computing. Convergence, iteration, Taylor series.
Solution of a Single Nonlinear Equation: Bisection method. Fixed
point methods. Newton's method. Convergence to a root, rates of
convergence.
February
Review of Applied Linear Algebra: Vectors and matrices. Basic operations, linear combinations. Basis, range, rank, vector norms, matrix norms. Special matrices.
Solving Systems of Equations (Direct Methods): Linear systems. Solution of triangular systems. Gaussian elimination with pivoting. LU decomposition, multiple right hand sides. Nonlinear systems. Newton's method.
March
Least Squares Fitting of Data: Fitting a line to data. Generalized least squares. QR decomposition.
Interpolation: Polynomial interpolation by Lagrange polynomials. Alternate bases: Monomials, Newton, divided differences. Piecewise polynomial interpolation. Cubic Hermite polynomials and splines.
April
Numerical Quadrature: Newton-Cotes methods: Trapezoid and
Simpson quadrature. Gaussian quadrature. Adaptive quadrature.
Ordinary Differential Equations: Euler's method. Accuracy and
stability. Trapezoid method. Runge-Kutta method. Boundary value
problems and finite differences.
http://www.isibang.ac.in/~athreya/cs205/notes/handout.html
[Computer Science II page]