Dr. Vinod Mishra

Basic Details


Dr. Vinod Mishra






Phone (O)






Educational Details

Educational Qualification

B.Sc. (Himachal Pradesh University: 1989)

M.Sc. (Kurukshetra University: 1991)

Ph.D. (Gurukula Kangri Vishwavidyalaya: 1998)



1. Twenty seven years of regular teaching

Professor (2010-Present)
Associate Professor (2006-2010)
Assistant Professor (2002-2005)
Lecturer (Senior Scale) (1998-2002)
Lecturer (1992-1998)

PG (M.Sc. Maths) teaching: Wavelet Analysis; Classical Mechanics; Fluid Dynamics

UG (B.E.) teaching: Engineering & Applied Mathematics; Numerical Analysis
2. Post-doctoral research experience of one year
3. Five months of industrial exposure
4. Invited Lectures arranged (02): Prof. Oscar Joao Abdounur (2011, Brazil) & Prof. Bhudev Sharma (2015, USA)
5. Programs organized (02): National Workshop- IWCM2006 as Chairman, National Seminar- NSSA2007 as Chairman
6. Popular Program Organized (01): National Science Day Program 2014 (Seminar, Quiz, Poster Presentation) as Convener. External Speakers of the Seminar: Prof. S.L. Singh (Ex Professor of GKV Haridwar), Prof. Chandra Shakher (IIT Delhi), Prof. Deepak Grover (Ex Professor of CCSHAU Hisar), Prof. G.S. Randhawa (IIT Roorkee) and Prof. S.K. Dhameja (NITTR Chandigarh
7. Formerly Head, Department of Mathematics, SLIET Longowal

Book Authored

Book authored

Reference-cum-Text Book:
Title: Theory of Transforms with Applications

Publisher: Ane Books Pvt Ltd, New Delhi, 2017, Pages 370 (Hardcover) (Price Rs 1995/-)
Chapters: i) Fourier Series,ii) Continuous Fourier Transform, iii) Discrete and Fast Fourier Transforms, iv) Laplace Transform, v) Numerical Inverse Laplace Transform,vi) Mellin Transform, vii) Hankel Transform, viii) Legendre Transform and ix) Z Transform
Appendix   Bibliography   Index


Professional Memebership

Professional Membership

1. Indian Mathematical Society (Life Member)
2. Calcutta Mathematical Society (Life Member)
3. Indian Society for Industrial and Applied Mathematics (Life Member)
4. Indian Society for History of Mathematics (Life Member)
5. American Mathematical Society (Annual;1997)
6. Vijnana Parishad of India (Life Member)



1. Formerly ‘Fellow’, Indian Institute of Advanced Study, Shimla

2. Invited Lectures/Talks delivered  during national and international conferences on History of Mathematics/Wavelet Analysis/Numerical Laplace Transform) (finance born by host institutions): 23 including at Indian Institute of Advanced Study (Shimla), Gurukula Kangri Vishwavidyalaya (Hardwar), National University of Singapore, Graphic Era University (Dehradun), Tribhuvan University (Kathmandu), TIFR-IITB National Centre for Mathematics (Mumbai), Indian Institute of Technology Bombay, Jawaharlal Nehru University (New Delhi), Hemvanti Nanadan Bahuguna University (Pauri Campus), Bundelkhand University(Jhansi), National Institute of Technology Manipur (Imphal), Sikkim University (Gangtok), Inter University Centre for Astronomy & Astrophysics (Pune), Sri Chandrashekhrendra Saraswati Vishwa Mahavidyalaya (Kanchipuram) and Sant Longowal Institute of Engineering and Technology (Longowal)

3. Guest Lectures delivered: (a) 02 on Classical Mechanics at Chandigarh University (Punjab) for M.Sc. Students,  and (b) 03 each on Vector Calculus and Numerical Methods at NIT Uttarakhand for B.Tech. Students

4. Technical Sessions Chaired (during National and International Conferences): 11



Selected publications (UGC Approved/SCOPUS/WOS/SCI-Expanded Journals)  out of forty four are given below.

A. History of Mathematics:
1. Theorem of Square on the Diagonal in Vedic Geometry and its Application, Indian Journal of History of Science (Indian National Science Academy) 31 (1996), 155-166.
2. First Degree Indeterminate Analysis in Ancient India and its Application by Virasena, Indian Journal of History of Science (Indian National Science Academy) 32 (1997), 127-133.

3. Computing Square Root of N: A Modern Generalization of Ancient Technique, Indian Journal of History of Science (Indian National Science Academy)  46 (2011), 49-61.


B. Wavelet Analysis:

4. Wavelet-Galerkin Solutions of Ordinary Differential Equations, International Journal of Mathematical Analysis 5 (2011), 407-424.
5. Haar Wavelet Approximation Solutions for the Generalized Lane Emden Equations Arising in Astrophysics, Computer Physics Communications  (Elsevier) 184 (2013), 2169-2177.
6. Haar Wavelet Approach for Solving Nonlinear Differential and Integral Equations, Neural, Parallel and Scientific Computations 22 (2014), 421-430.
7. Haar Wavelet Solutions of Nonlinear Oscillator Equations, Applied Mathematical Modelling  (Elsevier) 38 (2014), 4958-4971.
8. Haar Wavelet Based Numerical Investigation of Coupled Viscous Burgers Equation, International Journal of Computer Mathematics  (Taylor & Francis) 92 (2015), 1643-1659.

C. Numerical Inverse Laplace Transform:
9. Newton-Raphson based Modified Laplace Adomian Decomposition Method for Solving Quadratic Ricatti Differential Equations, Matec Web of Conferences 57, 05001 (2016), 1-4.

10.Modified Laplace Adomian Decomposition Method for Solving Nonlinear Volterra Integral and Integro-differential Equations based on Newton-Raphson Formula, European Journal of Pure and Applied Mathematics 11 (2018), 202-214.  
11. Numerical Inversion of Laplace Transform based on Bernstein Operational Matrix, Mathematical Methods in Applied Sciences (John Wiley & Sons) 41 (2018), 9231-9243.
12. Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations, Symmetry-Basel (MDPI) 11 (2019), No 530, 1-20.

13. Solutions of Volterra Integral and Integro-Differential Equations using Modified Adomian Decomposition Method, Journal of Applied Mathematics, Statistics and Informatics (DeGruyter) 15 (2019), 5-18.

14. Solving Linear Fractional Order Differential Equations by Chebyshev Polynomials based Numerical Inverse Laplace Transform, Mathematics in Engineering, Science and Aerospace 10 (2019), 781-791.

15.Numerical Inverse Laplace Transform based on Bernoulli Polynomials Operational Matrix for Solving Nonlinear Differential Equations, Results in Physics (Elsevier) 16 (2020), No 102836, 1-7.

16. Laplace Transform Inversion using Bernstein Operational Matrix of Integration and its Application to Differential and Integral Equations, Proceedings (Indian Academy of Sciences)-Mathematical Sciences (Springer) 130 (2020), No. 60, 1-29.


Complete list of publications and citations are available at:


Video Link of Invited Lecture in a Conference (CHDM 2015) Delivered at  IIT Bombay: https://www.youtube.com/watch?v=B3MoRe49Xr8


Full Conference Proceedings live at: https://old.shaale.com/live/ciib



Research Areas of Interest:
I. Wavelet Analysis (Using Galerkin and Collocation Techniques) (Ph.D. Thesis supervised: Sabina and Harpreet Kaur).
II. Numerical Inverse Laplace Transform (Using Bernstein, Laquerre, Chebyshev and Bernoulli Polynomials)
(Ph.D. Thesis superved: Dimple Rani)

III. Magic Squares and Fibonacci Like Sequences (PhD guidance continue: 02)
IV. History of Mathematics (Ancient, medieval & Pre-modern)