Office: Department of Computational & Data Sciences, SERC building, Room 205.

Office hours: Tuesday 3:00 PM-5:00 PM or by appointment.

; The book is available here.*Approximation Theory and Approximation Practice*, by Lloyd N. Trefethen*Interpolation and Approximation by Polynomials*, by George M. Phillips*Chebyshev and Fourier spectral methods*, by John P. Boyd

Evaluation | Homework | Quiz | Project |

Points | 60 | 20 | 20 |

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 mathematical 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.

- https://www.sharelatex.com/
- https://www.overleaf.com/

- http://www.tutorialspoint.com/compile_cpp11_online.php
- https://www.codechef.com/ide

There will be a short (3-5 minutes) quiz in almost every class.

This could be a work arising out a published article or from material/discussions in class. The project is due on April 12th. Below are some articles for suggestion.

- Barycentric Lagrange Interpolation: Sumit Sharma
- Fast algorithms for polynomial interpolation, integration and differentiation: Vaishnavi Gujjula
- From electrostatics to optimal node interpolation: Shifa Sindhu
- Lebesgue constants in polynomial interpolation: Hariprasad Manjunath
- On Lebesgue function for polynomial interpolation: Manisha Goyal
- Polynomial interpolation: Lagrange versus Newton: Kandappan V A
- Proof of the conjectures of Bernstein and Erdos: Abhay Gupta
- The Black Box Fast Multipole Method: Govindan Srinivasan
- Two results on polynomial interpolation in equally spaced points
- Approximation by superpositions of sigmoidal function: Biplab Kumar Pradhan
- High dimensional polynomial interpolation on sparse grids
- Bivariate Lagrange interpolation at the Padua points: Bhanu Prakash

Week |
Tuesday |
Thursday |
Homework |

Jan 9-13 | Introduction, Polynomial interpolation for a wide range of functions, Runge phenomenon | Fundamental theorem of polynomial interpolation, Started looking at Chebyshev and Legendre nodes | Homework 1: Due on Jan 18 |

Jan 16-20 | No class | Orthogonal polynomials | Homework 2: Due on Jan 25 |

Jan 23-27 | Legendre polynomials | Republic day | Homework 3: Due on Feb 1 |

Jan 30-Feb 3 | Chebyshev polynomials | Weierstrass approximation theorem | Homework 4: Due on Feb 8 |

Feb 6-10 | Best approximation | Homework 5: Due on Feb 15 | |

Feb 13-17 | Homework 6: Due on Feb 22 | ||

Feb 20-24 | |||

Feb 27-Mar 3 | Homework 7: Due on Mar 8 | ||

Mar 6-Mar 10 | Homework 8: Due on Mar 13 | ||

Mar 13-17 | Homework 9: Due on Mar 17 | ||

Mar 20-24 | Homework 10: Due on April 12 | ||

Mar 27-31 | Homework 11: Due on April 19 | ||

Apr 3-7 | Project due on Apr 12 and final report due on April 19 |