Number of  NPTEL Courses Completed                  6

Journals Published (National)

1. C.Duraisamy., B.Usha., "Solving Fuzzy Differential Equations by Modified Euler’s Method",  Journal of Indian Academy of Mathematics , Vol.33, No.2 pp.493-502, 2011.

2.   C.Duraisamy., B.Usha.,  "Solution of Fuzzy Differential Equations", Bulletin of Pure and Applied Mathematics, vol.5, no.2, pp.180-192, 2011.

Journals Published (International)

1. C.Duraisamy., B.Usha.,  "Another Approach to Solution of Fuzzy  Differential Equations", Applied Mathematical Sciences, vol.4, no.16, pp.777-790,2010.

2.  C.Duraisamy., B.Usha., ‘Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method of order two’, Research  Journal  of  Pure Algebra, vol.1, no.7, pp.152-160, 2011.

3.  C.Duraisamy., B.Usha., , ‘Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method of order three’, International Journal of  Advanced Scientific and Technical Research, vol.1, pp.1-13,2011.

4.  C.Duraisamy., B.Usha.,  ‘Numerical Solution of Fuzzy Differential Equations by Taylor Method’, International Journal of Mathematical Archive, vol.2, no.8, pp.1368-1375,2011.

5. C.Duraisamy., B.Usha.,  ‘Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method of order four’, European Journal of  Scientific Research, vol.67, no.2, pp.324-337,2012.

6.  C.Duraisamy., B.Usha.,  ‘A New Approach to Solution of Fuzzy Differential Equations’, International Journal of Emerging Trends in Engineering Development, vol.2, no.3, pp.281-292 ,2013.

7. Dr.B.Usha., ‘A New Approach to Solution of Fuzzy Differential Equations by Runge-Kutta Method of order two’, International Journal of Modern Trends in Engineering and Research, vol.2, no.1, pp.114-121 ,2016.

8. Dr.B.Usha.,Dr.AL.Nachammai.,Dr.M.Dhavamani., ‘ Solving Fuzzy Differential Equations by Runge-Kutta Method ’, Asian  Journal of Research in Social Sciences and Humanities , vol.6, no.9, pp.147-160 ,2016.

9. Dr.B.Usha.,Dr.AL.Nachammai.,Dr.M.Dhavamani.,"A Comparative study of the methods of solving Intuitionistic fuzzy Linear programming problem",International Journal of Advanced Research Ideas and Innovatives in Technology,

   1. vol.4, no.2, pp.290-300,2018.

10. Dr.B.Usha.,Dr.AL.Nachammai, "Numerical solution for Fuzzy differential equations", Advances in Mathematics:Scientific Journal,Vol.8,No.3, 838-842,2019.

11. Dr.AL.Nachammai, Dr.B.Usha, "On the centroids of Intuitionistic Fuzzy number and its application to IFLP problems", Advances in Mathematics:Scientific Journal, Vol.8, No.3,830-837,2019.

12. Dr. B.Usha , Dr.AL.Nachammai  , Ms.N.Suganya Baby ,"Solving Fuzzy Differential Equations using Error Analysis " ,International Journal of Research Publication and Reviews , Vol.4, No.2,1194-1200, February 2023 .

13. Dr. B.Usha , Dr.AL.Nachammai  , Ms.N.Suganya Baby ,"MODIFIED TWO-STEP SIMPSON METHOD FOR FINDING NUMERICAL SOLUTION OF FUZZY DIFFERENTIAL EQUATIONS ", International Research Journal of Modernization in Engineering Technology and Science , Vol.5, No.2,1443-1448, February 2023 .

14. Dr. Manish Kaushik , Dr. Ashutosh Mishra, Dr. V. DheenaDhayalan , Dr. B.Usha ,Pranjal Rawat , Modi BHUMIKA Kumarbhai , "THE CRITICAL ROLE OF IMPLEMENTING BLOCKCHAIN TECHNOLOGY IN ENHANCING FINANCIAL RISK MANAGEMENT IN BANKING COMPANIES"

15.  M.Venkatachalapathy , K.Abdul Razak, M.Ayyappan,V.S.Mathu Suresh, S.N.Subhathra and B.Usha , "A Simplified Approach to Solving Balanced Generalized Quadratic Fuzzy Transportation Problems" , Communications on Applied Nonlinear Analysis ,  Vol. 32, No.7, 765- 781, 2025..

16. S. Ramya , S.Sangeetha , B.Usha , N Sheeba Florance ,P. Ramesh , S Muthuperumal , "Graph-Theoretical Methods for Improving Feature Extraction in Complex Vision Tasks Using Graph Neural Networks (GNNs) " , International Conference on Next Generation Information System Engineering (NGISE), October 2025 .

17. Dr. E. PUNARSELVAM, Dr.T. RAMESHKUMAR, MIHIRKUMAR B. SUTHAR, Dr.SEETHA J, K. PRAKASH, 5SEEMA AGGARWAL, Dr. DIVYA SHARMA, Dr. B. USHA, Dr. T. VENGATESH ,"TRANSFORMING ENVIRONMENTAL SCIENCE WITH DATA-DRIVEN MODELS: THE ROLE OF MACHINE LEARNING AND DEEP LEARNING" , Testing, Psychometrics, Methodology in Applied Psychology  , Vol.32, No.S8, 2307-2317, 2025 .

18. Dr. B.Usha , "New Differentiability concepts for Fuzzy Differential Equation", International Journal of Web of Multidisciplinary Studies , Vol.3, No.2,261-276,2026.

  Paper Presented in National Conferences

1.   Usha, B & Duraisamy, C , ‘Numerical Solution of Fuzzy Differential Equations by Runge-Kutta Method’, National Conference on Scientific Computing and Applied Mathematics , Organized by Department of Mathematics, VLB Janakiammal College of Engineering, Coimbatore,2011.

2.  Usha, B & Duraisamy, C , ‘Solving Fuzzy Differential Equations by Runge-Kutta Method of order four’, National Conference on Discrete and Fuzzy Mathematics, Organized by Department of Mathematics, Karunya University, Coimbatore,2011.       

  3.  Usha, B & Duraisamy, C , ‘Solving Fuzzy Differential Equations by Runge-Kutta Method of order two’, National Conference on Advances in                     Mathematical Analysis and Applications, Organized by Department of Mathematics, KSR College of Engineering, Tiruchengode,2011.

4.  Usha, B & Duraisamy, C , ‘Another Approach to Solution of Fuzzy Differential Equations by Modified Two-Step Simpson’s Method’, National                  Conference on Fuzzy Techniques in Image Processing , Organized by Department of Mathematics, Kongu Engineering College, Perundurai,       2013.     

5.   Usha, B & N.Suganya Baby , ‘Numerical & approximate Solutions of Fuzzy Differential Equations by Taylor Method’, National Conference on                 contributions of Mathematics in Science & Technology , Organized by Department of Mathematics, Bannari Amman Institute of Technology,          Sathy,     2019.

Paper Presented in International Conferences

1. Usha, B & Duraisamy, C , ‘Another Approach to Solution of Fuzzy Differential Equations by Modified Euler’s Method’, International Conference on Communication and Computational Intelligence, Organized by Department of Computer Science, Kongu Engineering College, Perundurai. (The same paper is published in IEEE explorer),2010.

2. Usha, B & Duraisamy, C ,Suganya Baby ,N, ‘A Study on Fuzzy Differential Equations using Runge-Kutta method of order four ' International Conference on Applied Mathematics and Informatics, Organized by Department of Mathematics, Kongu Engineering College, Perundurai.

3. Usha, B , ' Solving Ordinary Differential Equation with Initial Condition' , International Conference on Recent Trends in Graph Theory and Nano Materials , Organized by Department of Mathematics, Vivekanandha Arts and Science  College for Women.

Funded Programmes Organized (Seminar/Conference/Workshop/FDP/STTP/Other)

E-Content :

 1.  MULTIVARIABLE CALCULUS AND COMPLEX ANALYSIS - MULTIVARIABLE CALCULUS AND COMPLEX ANALYSIS 

• FUNCTIONS OF TWO OR MORE VARIABLES

•  TOTAL DIFFERENTIAL

•  TAYLORS SERIES FOR FUNCTIONS OF TWO VARIABLES

•  MAXIMA AND MINIMA

•  CONSTRAINED MAXIMA AND MINIMA

  2.PROBABILITY, TRANSFORMS & PARTIAL DIFFERENTIAL EQUATIONS -  PROBABILITY ,TRANSFORMS & PARTIAL DIFFERENTIAL EQUATIONS 

• FOURIER SERIES

•  FOURIER SERIES-ODD & EVEN FUNCTION

•  HALF RANGE SERIES

•  CHANGE OF INTERVAL

•  CHANGE OF INTERVAL-ODD & EVEN FUNCTION

3. NUMERICAL METHODS FOR ENGINEERS - NUMERICAL METHODS FOR ENGINEERS    

• SOLUTION TO ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

• INTERPOLATION

• NUMERICAL DIFFERENTIATION AND INTEGRATION

• NUMERICAL SOLUTION OF FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS

• SOLUTIONS OF BOUNDARY VALUE PROBLEMS IN PDE                        

4. MATRICES AND ORDINARY DIFFERENTIAL EQUATIONS - MATRICES AND DIFFERENTIAL EQUATIONS 

• EIGEN VALUES & VECTORS

•  ORTHOGONAL MATRICES

•  DIAGONALISATION OF A MATRIX

•  REDUCTION OF QUADRATIC FORM

•  CAYLEY HAMILTON THEOREM 

5.   PROBABILITY AND STATISTICS -  PROBABILITY AND STATISTICS 

• JOINT DISTRIBUTION

•  MARGINAL & CONDITIONAL DISTRIBUTIONS

•  COVARIANCE

•  CORRELATION

•  REGRESSION

6.STATISTICS AND NUMERICAL METHODS - STATISTICS AND NUMERICAL METHODS

• SINGLE MEAN AND DIFFERENCE OF MEAN -LARGE SAMPLE TESTS

•  SINGLE MEAN AND DIFFERENCE OF MEAN-SMALL SAMPLE TESTS

•  SIGNIFICANCE OF VARIANCES

•  SIGNIFICANCE OF GOODNESS OF FIT

•  SIGNIFICANCE OF INDEPENDENCE OF ATTRIBUTES

7. MATHEMATICS-III - MATHEMATICS-III   

• PARTIAL FRACTION METHOD  

•  CALCULUS OF RESIDUE

•  SOLUTION OF DIFFERENCE EQUATION -APPLICATION OF Z-TRANSFORM

 8  APPLIED STATISTICS FOR FOOD TECHNOLOGY - APPLIED STATISTICS FOR FOOD TECHNOLOGY 

• LARGE SAMPLE TESTS

•  SMALL SAMPLE TESTS

•  TESTING THE SIGNIFICANCE OF VARIANCES

•  TESTING THE SIGNIFICANCE OF GOODNESS OF FIT

•  TESTING THE SIGNIFICANCE OF INDEPENDENCE OF ATTRIBUTES

9.TRANSFORMS AND PROBABILITY THEORY -  TRANSFORMS AND PROBABILITY THEORY

•  FOURIER TRANSFORM

•  LAPLACE TRANSFORM

•  Z-TRANSFORM

•  Z-TRANSFORM PROPERTIES

•  MARKOV PROCESS

10. PROBABILITY THEORY AND INFERENTIAL STATISTICS  -  PROBABILITY THEORY AND INFERENTIAL STATISTICS 

• JOINT DISTRIBUTION FUNCTION

•  COVARIANCE

•  REGRESSION

   11.  DISCRETE MATHEMATICAL STRUCTURES -  DISCRETE MATHEMATICAL STRUCTURES

• PROPOSITIONAL CALCULUS

•  PREDICATE CALCULUS

• SET THEORY

• FUNCTIONS

• GROUP THEORY