TEW  Numerical Analysis
Speakers and Syllabus
Name of the Speaker with affiliation  No. of Lectures  Detailed Syllabus 
Dr. Amiya Bhowmick Assistant professor Department of Mathematics ICT, Mumbai.  6  Transcendental and Polynomial Equations Iteration methods based on second degree equation: Muller method, Chebyshev method, Multipoint iteration method. Iterative methods for polynomial equations; Descarts rule of signs, BirgeVieta method, Bairstrow method. Methods for multiple roots. NewtonRaphson method. System of non linear equations by Newton Raphson method. Methods for complex roots. Condition of convergence and Rate of convergence of all above m 
Dr. Vinayak Kulkarni Professor Department of Mathematics University of Mumbai, Mumbai. 
6  Linear System of Equations Matrix representation of linear system of equations. Direct methods: Gauss elimination method. Pivot element, Partial and complete pivoting, Forward and backward substitution method, Triangularization methodsDoolittle and Crouts method, Choleskys method. Error analysis of direct methods. Iteration methods: Jacobi iteration method, Gauss Siedal method. Convergence analysis of iterative method. Eigen value problem, Jacobis method for symmetric matrices Power method to determine largest eigenvalue and eigenvector. 
Dr. Seema Purohit Professor Emeritus, B K Birla College, Kalyan Ex Professor, Kirti College, University of Mumbai, Mumbai. 
Interpolation Interpolating polynomials, Uniqueness of interpolating polynomials. Linear, Quadratic and Hillgher order interpolation. Lagranges Interpolation. Finite difference operators: Shift operator, forward, backward and central difference operator, Average operator and relation between them. Difference table, Relation between difference and derivatives. Interpolating polynomials using finite differences GregoryNewton forward difference interpolation, GregoryNewton backward difference interpolation, Stirlings Interpolation. Results on interpolation error. 

Dr. Hanumant Salunkhe Assistant Professor Department of Technology Shivaji University, Kolhapur.  Numerical differentiation: Numerical diferentiation based on Interpolation, Numerical differentiation based on finite differences (forward, backward and central), Numerical Partial differentiation. Numerical Integration Numerical Integration based on Interpolation. NewtonCotes Methods, Trapezoidal rule, Simpson's 1/3rd rule, Simpson's 3/8th rule. Determination of error term for all above methods. Convergence of numerical integration: Necessary and sufficient condition (with proof). Composite integration methods; Trapezoidal rule, Simpson's rule 
References:
 S. S. Sastry Introductory methods of Numerical Analysis, Prentice Hall India Learning Private Limited.
Name of the tutors:

S. No.
Name
Affiliation
1
Mr.Ejaz Shaikh
V.G.VazeCollege,Mulund(E)
2
Mr.Akshay Lambore
V.G.VazeCollege,Mulund(E)
3
Ms.Farheen Maniyar
V.G.VazeCollege,Mulund(E)
4
Ms.ChhayaZagade
V.G.VazeCollege,Mulund(E)
Time Table
Timetable (with names of speakers and tutors):
Day 
Date 
Lecture 1 
Tea 
Lecturer 2 
Lecture 3 
Lunch 
Lecture 4 
Tea 
Discussion 
Snacks 


(9.30–10.30) 
(10.3510.55) 
(11.00–12.00) 
(12.00–1.00 
(1.002.20) 
(2.303.30) 
(3.353.55) 
(4.00500) 
(5.055.35) 
Mon 
24/02/2025 
AB 

AB 
VK 

VK 

AB/ES/AL 

Tue 
25/02/2025 
VK 

VK 
AB 

AB 

AB/ES/AL 

Thu 
27/02/2025 
AB 

AB 
VK 

VK 

VK/ES/AL 

Fri 
28/02/2025 
SP 

SP 
HS 

HS 

HS/FM/CZ 

Sat 
01/03/2025 
SP 

SP 
HS 

HS 

HS/FM/CZ 

Mon 
03/03/2025 
HS 

HS 
SP 

SP 

SP/FM/CZ 

Full forms for the abbreviations of speakers and tutors:
AB: Dr. Amiya Bhowmick VK:
Dr. Vinayak Kulkarni SP:
Dr. Seema Purohit
HS: Dr. Hanumant Salunkhe.
ES: Mr. Ejaz Shaikh
AL: Mr. Akshay Lambore
FM: Ms. Farheen Maniyar
CZ: Ms. Chhaya Zagade