# Numerical Methods and Scientific Computing, Jul-Nov 2021

#### Credits 9 credits

### Instructor

Sivaram Ambikasaran,

### Exams and Grading

**Evaluation** |
**Points** |

Weekly Assignment |
60 |

EndSem |
40 |

Click here for accessing the course materials

### Course Logistics

- Each week there will be three pre-recorded online lectures, which can be accessed via the above link.
- There will also be assignments for a total worth of 60 points.
- There will be an endsemester worth 40 points.

### Assignments

- All assignments need to be submitted before Sunday midnight.
- There will be both written and computational part in the assignments.
- We will be relying on MATLAB/Octave for the computing part of the assignment.
- 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 MATLAB code) for submitting your assignment should be as follows: ma14m093_5.zip (or .rar or .tar), where ma14m093 is your roll number and 5 implies that you are submitting your fifth assignment.
- Only one submission per assignment. If you submit the assignment multiple times, only the first submission will be graded.
- 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.

### Short Syllabus

- Floating point representation, Conditioning and Stability
- Polynomial interpolation and approximation
- Numerical Differentiation
- Numerical Integration
- Root finding
- Numerical Solution of Ordinary differential equation
- Monte Carlo methods

### Textbooks

- Numerical Methods in Scientific Computing - Volume I, by Germund Dahlquist & Ake Bjorck
- Approximation Theory and Approximation Practice, by Nick Trefethen
- Fundamentals of Engineering Numerical Analysis, by Parviz Moin
- Interpolation and Approximation by Polynomials, by George M. Phillips
- Spectral Methods in MATLAB, by Nick Trefethen
- Exploring Monte Carlo Methods, by William L. Dunn & J. Kenneth Shultis