Computer Science II


  • Basic Information
    • Instructor : Siva Athreya .
    • Email : athreya@isibang.ac.in
    • Classes : Wednesday and Friday: 09:55-10:55 and 11:10-12:10
    • Scoring : Final Exam: 50%, Midterm Exam: 25%, Quizzes: 20%, Homework and in-class worksheets: 5%.

  • References
    • Computational Methods for Numerical Analysis with R by James P. Howard, II.
    • Using R for Numerical Analysis in Science and Engineering by Victor A. Bloomfield.
    • Numerical Methods with Matlab by G. Recktenwald.


  • Week 1 : January 8th and 10th 2020.
  • Topics Covered
    • Overview of course material.
    • R- Basics.
    • Dropbox usage and working with Rnw Files.
    • Limitations of Computations by machine, Floating point line.
    • Algorithm for finding square root of number.
    • Horner's method for evaluating polynomials
  • Classboard Photos
  • Week 1 Notes

  • Week 2 : January 14th and 16th 2020.

  • Week 3 : January 21st and 23rd 2020.
  • Topics Covered
    • Taylor's Theorem
    • Truncation Error
    • Truncation Error versus Round off Error: Finite Difference Approximation of Derivative.
  • Classboard Photos
  • Week 3 Notes

  • Week 4 : January 28th and 30th 2020.

  • Week 5 : February 4th 2020.
  • Topics Covered
    • Rate of Convergence of the Secant Method.
    • Plotting of functions in R
    • Root finding as a fixed point iteration.
  • Classboard Photos
  • Week 5 Notes

  • Week 6 : February 11th and 13th 2020.
  • Topics Covered
    • Polynomial Interpolation
      • Monomial Basis, Vandermonde Matrix
      • Lagrange Polynomials
    • Numerical Integration
      • Midpoint Rule
      • Trapezoid Rule
      • Simpson's Rule
    • Error Bounds
  • Classboard Photos
  • Week 6 Notes

  • Week 7 : February 18th and 20th 2020.
  • Topics Covered
    • Numerical Integration Error Bounds and Composite Rules:
      • Midpoint Rule
      • Trapezoid Rule
      • Simpson's Rule
    • Adaptive Simpson's Rule
  • Classboard Photos
  • Week 7 Notes

  • Week 8 : March 3rd and 5th 2020.

  • Week 9 : March 10th and 12th 2020.



  • Week 10 : March 17th and 19th 2020.

  • Week 11 : March 24th and 26th 2020.
  • Topics Covered
    • Gaussian Elimination :
      • Without Pivot.
      • With Partial Pivoting.
      • WIth Partial Scaled Pivoting.



  • Week 12 : March 31st and April 2nd 2020.
  • Topics Covered
      Review of Linear Algebra: Problems in Homework 10.
    • Review: Method of Least Squares and Normal Equations.
    • Ordinary Differential Equations: Existence, Uniqueness and 1-d Vector Fields.

  • Week 13 : April 7th and April 9th 2020.
  • Topics Covered
      Ordinary Differential Equations: Euler's Method, Midpoint Method, Runge-Kutta Method
    • Higher Dimensions.



  • Week 14 : April 14th 2020.
  • Topics Covered
      Linear Algebra Review: LU and Cholesky Decomposition.


Last Modified: April 16th, 2020. Courses Page Teaching Page