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:

  1. 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

 

 

 

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