Numerical Analysis, Jan-May 2023

Mailing list

You can find on google groups when you login via smail. Search for "2023_na" or "2023_na-group@smail.iitm.ac.in". Click on it and request to be added to the group.

Exams and Grading

 Evaluation Points Date Assignments 20 Every fortnight Midsem 30 March 3rd EndSem 50 May 12th

Assignments and Reading materials

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• All assignments need to be submitted before Sunday midnight.
• Students are strongly encouraged to typeset their solution via LaTeX/TeX. Typesetting using LaTeX/TeX will obtain 25% bonus on the score they get for the assignment.
• Students need to submit their assignments through the dropbox link provided.
• The name of the zipped file (this should contain the LaTeX/TeX source file, pdf, and code) for submitting your assignment should be as follows: ma14c093_5.zip (or .rar or .tar), where ma14c093 is your roll number and 5 implies that you are submitting your fifth assignment.
• Any copying on assignments will result in a zero on the assignment.
• We will be using JPlag to detect similarities among multiple sets of source code files.
• The grader will expect you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for poorly written proofs or answers. Clear exposition is a crucial ingredient of technical communication. Clarity of thought and presentation is more important in mathematics & sciences than any other field. The only way to master exposition is by repeated practicing.

Syllabus

Norms of vectors and matrices, Linear systems: direct and iterative schemes, Ill conditioning and convergence analysis; Interpolation and Error, Hermite interpolation, Piecewise polynomial (Spline) interpolation, Numerical differentiation, Newton-cotes and Gaussian quadrature; Difference equations, Numerical solution of IVPs: Single step and multi-step methods: order, consistency, stability and convergence analysis, Two point boundary value problems: Shooting and finite difference methods, Eigenvalue Location, Power Method, Jacobi Method;

Textbooks

• D. Kinciad & W. Cheney, Numerical Analysis and mathematics of Scientific Computing, Brooks/Cole, 1999.
• K. E. Atkinson, An Introduction to Numerical Analysis, John-Wiley & Sons, 2nd Edition, 1989.

Reference Books:

• R. L. Burden & J. D. Faires, Numerical Analysis, 7th Edition, Cengage Learning (India), 2008.
• B. Bradie, A Friendly Introduction to Numerical Analysis, Pearson Education (India), 2007.
• C. E. Gerald & P. O. Whealtley, Applied Numerical Analysis, Pearson Education (India), 2006.
• S. S. Sastry, Introductory Methods of Numerical Analysis, PHI. 2009.
• S. D. Conte & C. De Boor, Elementary Numerical Analysis, TATA Mcgraw-Hill, 2010.
• J. Stoer & R. Bulirsch, Introduction to Numerical Analysis by Springer (India), 2009.
• F. B. Hildebrand, Introduction to Numerical Analysis, Dover Publication, South Asia Edition, 2008.
• A. Iserles, A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.
• J. H. Mathews, Numerical Methods for Mathematics, Science and Engineering, PHI, 1994.
• V. S. Ryabenkii & S. V. Tsykkov, A theoretical Introduction to Numerical Analysis by, Chapman & Hall/CRC, 2010.