# Numerical Analysis, Jan-May 2023

### Credits 9 credits

### Instructor Sivaram Ambikasaran,

### Classroom NAC \(504\)

### Timings E slot; T: 11AM, W: 10AM, Th: 8AM, F: 5PM

### 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

Click here
- 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.