Weekly outline

  • 26 July - 1 August

  • 2 August - 8 August

  • 9 August - 15 August

    • Lecture 7: Convergence in a metric space
    • Brief lecture notes



    • Extra reading material:
      Following book uses the concept of convergence in the analysis of numerical schemes to solve PDEs. One should use a scheme that is convergent. Convergence in the field of numerical analysis is explained in Section 2.6. The necessary background is built in Chapter 1 and part of Chapter 2 before Section 2.6.

    • Chapter 1 and 2 from: Numerical Solutions of PDE: An introduction, by Morton and Mayers

    • Interesting book:
      Proofs and Refutations: The logic of mathematical discovery.
      Imre Lakatos
      Cambridge University Press.
    • Note:
      One copy of the following book has been put into the Course Reserve section of the RC, while the 5 remaining copies will soon be put in the Short Loan section:
      Introductory functional analysis with applications. New York. John Wiley and Sons
      Erwin, Kreyszig


    • Lecture 8: Convergence of a sequence of functions
    • Brief lecture notes


    • Lecture 9: Example of a Complete space
    • Brief lecture notes
  • 16 August - 22 August

  • 23 August - 29 August

  • 30 August - 5 September

    • Reference for Lebesgue Integral and Lp spaces:
      The Lebesgue- Stieltjes Integral: A Practical Introduction
      by M.Carter and B.van Brunt
      Other books on Lebesgue integrals, real analysis, measure theory and functional analysis may also cover the relevant topics.


    • Exam week


  • 6 September - 12 September

  • 13 September - 19 September

    • Lecture 19: Operator norm
    • Brief lecture notes


    • Lecture 20 & 21: Solved examples on convergence in metric and NVS.
    • These notes contain a minor correction in the alternative proof for Q.2 and the complete proof of Q.3


  • 20 September - 26 September

  • 27 September - 3 October

    • Assignment 4: Optional submission, will not be graded.



    • Lecture 25: Gram-Schmidt Orthonormalization, Orthonormal basis, Best Approximation theorem
    • Brief lecture notes



    • Lecture 26: Parseval's relation and theorem as special cases of Pythagoras theorem
    • Brief lecture notes



    • Lecture 27: Convex optimization
    • Brief lecture notes



  • 4 October - 10 October

  • 11 October - 17 October

  • 18 October - 24 October

    • Lecture 32: Rectangular system of linear equations, Non- Singular, Inconsistent and Under-determined system of linear equations.

    • Lecture 33: Rank of a matrix, Row space, Column space, Nullspace and Left nullspace with their dimensions.


    • Lecture 34: Fundamental theorem of Linear algebra, Inverses and Moore- Penrose Pseudo-inverse of a matrix.


  • 25 October - 31 October

    • Lecture 35: Least square filters - Using Calculus




    • Lecture 36: Least square filter design - Using projection



    • Lecture 37: QR decomposition


    • Linear-Phase FIR Filter Design By Least Squares
      - by Ivan Selesnick
    • I expect the Communication specialization students to help others (incl. me) understand these notes.


    • Spline project report LATEX file:
  • 1 November - 7 November

    • Diwali break

  • 8 November - 14 November

    • Lecture 38: Eigenvalues and Eigenvectors with applications to solutions of Diff. eqns.




    • Lecture 39: Diagnolization of a matrix, Eigenvalues related to invertibility and Eigenvectors related to diagnolization, Eigenfunctions of LTI systems.


    • Submitting the spline project:
      Submit single zip file. Only one file per group.
      The main directory should contain a readme.txt file explaining the contents of all files (in one line each).
      The readme.txt file should also contain the names and Id's of the students in the group.
      The main directory should contain a pdf report of your project (max 2 pages) and your matlab codes in a sub-directory.
      The main matlab file should be named spline2dclosed.m


    • Lecture 40: Similarity transformations


  • 15 November - 21 November

    • Lecture 41: Differentiability, differential and the derivative


  • 22 November - 28 November

    • Final exam question paper:


    • Solutions to exam questions:



    • Your answer sheets will be available on Thursday 2nd December 2010 in CEP 205 from 11 am to 11:30 am. Please pass this message to all your colleagues.
  • 29 November - 5 December