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, Birge-Vieta method, Bairstrow method. Methods for multiple roots. Newton-Raphson 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 methods-Doolittle 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 Gregory-Newton forward difference interpolation, Gregory-Newton 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. Newton-Cotes 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
Time-table (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) |
(10.35-10.55) |
(11.00–12.00) |
(12.00–1.00 |
(1.00-2.20) |
(2.30-3.30) |
(3.35-3.55) |
(4.00-500) |
(5.05-5.35) |
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