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.
First day Handout.
Tasks Day 1.
Example RNW File.
Instructions on how to complie Rnw files and how to submit Hw.
Worksheet-10-01-2020 and Homework 1,
Worksheet-Solutions.
,
Hw1-Solutions.
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.
Worksheet-14-01-2020.
Homework 2.
Topics Covered
Unavoidable Errors in Computing
Floating Point Representation
Round-Off Error
Taylor's Theorem
Classboard Photos
Week 2 Notes
Floating point Representation Notes
Week 3 : January 21st and 23rd 2020.
Worksheet-21-01-2020.
Quiz 2 Solutions.
Homework 3,
Solution.
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.
Worksheet-28-01-2020.
Quiz 3 Solutions.
Homework 4.
Topics Covered
Finding Roots.
Bisection Method
Newton-Raphson Method
Secant Method
Convergence of the Methods.
$O(\cdot)$, $\Theta (\cdot)$, $o(\cdot)$ notation.
Classboard Photos
Week 4 Notes
Newton Method-Convergence
Secant Method-Convergence
Week 5 : February 4th 2020.
Worksheet-04-02-2020:
Part I
,
Part II
Homework 5.
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.
Worksheet-11-02-2020
Homework 6.
Quiz 4 Solutions.
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.
Worksheet-18-02-2020
Homework 7.
Quiz 5 Solutions.
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.
Worksheet-05-03-2020
Homework 8.
Topics Covered
Newton's Polynomial
Piecewise Polynomial Interpolation
Cubic Splines
Notes: Newton Polynomial and Piecewise Interpolation.
Notes: Cubic Splines.
Week 9 : March 10th and 12th 2020.
Worksheet-10-03-2020
Homework 9.
Topics Covered
Cubic Splines- Implementation
Gauss-Quadrature
Notes: Cubic Splines- solving for b.
Notes: Guass Quadrature.
Week 10 : March 17th and 19th 2020.
Homework 10.
Topics Covered
Gauss-Legendre Quadrature
Notes: Gauss-Legendre Quadrature.
Notes: Gaussian Elimination.
,
Video recording of Zoom class:
Mar 17th
,
Mar 19 Part 1
,
Mar 19 Part 2
Week 11 : March 24th and 26th 2020.
Worksheet-26-03--2020.
Notes: March 24th
Topics Covered
Gaussian Elimination :
Without Pivot.
With Partial Pivoting.
WIth Partial Scaled Pivoting.
Week 12 : March 31st and April 2nd 2020.
Notes: March 31st
Video recording: March 31st
Notes: April 2nd
Video: April 2nd
Part I
,
Part II
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.
Notes: Apr7th
Video: April 7th
Part I
,
Part II
(In video, there was an Error in Rungekutta order 4 algorithm; corrected in notes.)
Worksheet: Apr9th
Homework 11
Notes: Apr9th
Video: April 7th
Part I
,
Part II
Topics Covered
Ordinary Differential Equations: Euler's Method, Midpoint Method, Runge-Kutta Method
Higher Dimensions.
Week 14 : April 14th 2020.
Worksheet A
Topics Covered
Linear Algebra Review: LU and Cholesky Decomposition.
Last Modified: April 16th, 2020.
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