Dr. Vinod Mishra





Educational Qualification

B.Sc.(1989), M.Sc.(1991), Ph.D. (1998)


1. Twenty five years of regular teaching of UG & PG classes. PG teaching: Wavelet Analysis, Classical Mechanics & Fluid Dynamics
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.
Speakers of Seminar: Prof. S.L. Singh (Former Professor of GKU Haridwar & UGC
Emeritus Fellow); Prof. Chandra Shakher (IIT Delhi), Prof. Deepak Grover (Former
Professor of CCSHAU Hisar), Prof. G.S. Randhawa (IIT Roorkee) and Prof. S.K.
Dhameja (NITTTR Chandigarh)
7. Formerly Head, Department of Mathematics, SLIET, Longowal
8. Ph.D thesis examiner: Baraktullah University, Bhopal
9. Faculty Selection Committee attended: NIT Hamirpur
10. Indian Institute of Advanced Study Society, Shimla (Member, Ex officio, 1999-2000)

Book authored

Reference Books:
1. Theory of Transforms with Applications, Ane Books Pvt Ltd, New Delhi, 2017, Pages 370 (Hardcover) (published) (Price Rs 1995/-)
Chapters: i) Fourier Series, ii) Continuous Four 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

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 (18) at national and international conferences on History of Mathematics/Wavelet Analysis/Numerical Laplace Transform Including at Indian Institute of Advanced Study Shimla, Gurukula Kangri University Haridwar, National University of Singapore, Graphic Era University Dehradun, Tribhuvan University Kathmandu, Indian Institute of Technology Bombay, Hemvanti Nanadan Bahuguna University Pauri Campus, Bundelkhand University Jhansi, National Institute of Technology Manipur and Sikkim University Gangtok

3. Guest Lectures delivered (02) on Classical Mechanics: Chandigarh University (Mohali)

4. Technical Sessions Chaired during National and International Conferences: 09


A. Wavelet Analysis of Numerical Problems

1. Wavelet Solutions of Parabolic Equations, Matematika 26 (2010), 61-69.
2. Wavelet Solutions and Stability Analysis of Parabolic Equations, Journal of Indonesian Mathematical Society 16 (2010), 69-87.
3. Wavelet-Galerkin Solutions of Ordinary Differential Equations, International Journal of Mathematical Analysis 5 (2011), 407-424.
4. Wavelet-Galerkin Finite Difference Solutions of ODEs, Advanced Modeling and Optimization 13 (2011), 539-549.
5. Wavelets and the Evaluation of Filter Coefficients, International Journal of Mathematical Archive 2 (2011), 1776-1793.
6. Haar Wavelet Approach to Fluid Flow Between Parallel Plates, International Journal of Fluids Engineering 4 (2011), 403-410.
7. Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems, American Journal of Computational Mathematics 1 (2011), 176-182.
8. Haar Wavelet Solutions of Certain Differential, Integral and Integro-differential Equations, International Journal of Applied Mathematics and Mechanics 8 (2012), 69-82.
9. Wavelet-Galerkin Solutions of One and Two Dimensional Partial Differential Equations, Journal of Emerging Trends in Computing and Information Sciences 3 (2012), 1373-1378.
10. Haar Wavelet Quasilinearization Approach for Solving Lane Emden Equations, International Journal of Mathematics and Computer Applications Research 2 (2012), 47-60.
11. Haar Wavelet Approximation Solutions for the Generalized Lane Emden Equations Arising in Astrophysics, Computer Physics Communications (Elsevier) 184 (2013), 2169-2177.
12. A Collocation Approach with Haar Wavelets to Solve Volterra Population Model for Population Growth of a Species, Mathematical Sciences International Research Journal 2 (2013), 2676-2680.
13. Haar Wavelet Solutions of Nonlinear Oscillator Equations, Applied Mathematical Modelling (Elsevier) 38 (2014), 4958-4971.
14. Haar Wavelet Approach for Solving Nonlinear Differential and Integral Equations, Neural, Parallel and Scientific Computations 22 (2014), 421-430.
15. Haar Wavelet Based Numerical Investigation of Coupled Viscous Burgers Equation, International Journal of Computer Mathematics (Taylor & Francis) 92 (2015), 1643-1659.

B. Numerical Inversion of Laplace Transforms

16. Review of Numerical Inversion of Laplace Transforms using Fourier Analysis, Fast Fourier Transform and Orthogonal Polynomials, Mathematics in Engineering, Science and Aerospace 5 (2014), 239-261.
17.Chebyshev Polynomial based Numerical Inverse Laplace Transform Solutions of Linear Volterra Integral and Integro-differential Equations, American Research Journal of Mathematics 1 (2015), 22-32.
18. Numerical Inverse Laplace Transform using Chebyshev Polynomial, WASET 9 (2015), 577-581.
19.Approximate Solution of Boundary Value Problem with Bernstein Polynomial Laplace Decomposition Method, International Journal of Pure and Applied Mathematics 114 (2017), 823-833.
20. Dimple Rani and Vinod Mishra, 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.

C. Foundations of Mathematics: History and Education

21. Capillary Ascent of a Liquid, Indian Journal of Theoretical Physics 43 (1995), 309-315.
22. Height and Distance Problems in Ancient Mathematics, Ganita Bharati 18 (1996), 25-30.
23. Theorem of Square on the Diagonal and its Application, Indian Journal of History of Science 31 (1996), 155-166.
24. First Degree Indeterminate Analysis in Ancient India and its Application by Virasena, Indian Journal of History of Science 32 (1997), 127-133.
25. Values of p from Antiquity to Ramanujan, Sugakushi kenkyu, No. 157, 1998, 12-25.
26. Incircumscribing Triangles & Cyclic Quadrilaterals in Ancient & Medieval Indian Geometry, Sugakushi kenkyu, No. 161, 1999, 1-11
27. Geometry in Rituals, Journal of Natural & Physical Sciences 15 (2001), 159-177.
28. Geometry Relating to Circles and Spheres, Studies in History of Medicine and Science 18 (2002),
No. 1, 47-106.
29. Combinatorics and the (So-called) Binomial Theorem, Studies in History of Medicine and Science 18 (2002), No.2, 59-121
30. Similarity of Plane Figures and Geometric & Group Theoretic Study of Cyclic Quadrilateral of First Kind, Journal of Natural & Physical Sciences 18 (2004), 69-102.
31. Invention of Logarithms, Studies in History of Medicine and Science 20 (2005), 61-93.
32. ComputingāˆšN: A Modern Generalization of Ancient Technique, Indian Journal of History of Science 46 (2011), 49-61.
33. Mathematical Heritage of India: Some Remedial issues: Mathematics History in Teaching, Philosophy of Mathematical Education Journal, No. 26, 2011, 1-12.
34. Progress in the Theory of Quadratic Indeterminate Analysis, American Research Journal of Mathematics 1(4) 2015, 13-26.
35. Linear Indeterminate Analysis: Theory and Applications, American Research Journal of Mathematics 1(1)2015, 16-33.
36. Progressive Series: Development and Applications, American Research Journal of Mathematics 1(3)(2015), 34-53.
D. Proceedings of Conferences
37. Newton-Raphson based Modified Laplace Adomian Decompositon Method for Solving Quadratic Ricatti Differential Equations, Matec Web of Conferences
05001 (2016), 1-4. ISSN 2261-236X
38. A Study of Homotopy Perturbation Method and its Modifications, Proceedings of NEAETMA, 2016, 325-327. ISBN 97893-82376-90-3
39. Numerical Solution of a Laminar Viscous Flow Boundary Layer Equation using Uniform Haar Wavelet Quasi-linearization Method, Proceedings of WASET 79 (2013), 1410-1415.
ISSN 2010 3778
40. Indian Mathematics: A Brief Historic Evolution, Gurukula Kangri Vijnana Patrika Aryabhata 1 (1998), 171-192.
41. Did Vedic Savants Know Irrational Numbers, Gurukula Kangri Vijnana Patrika Aryabhata 1 (1998), 193-204.


Research Areas of Interest:
I. Wavelet Analysis (Using Galerkin and Collocation Techniques)
II. Numerical Inverse Laplace Transform (Using Bernstein, Laquerre, Chevishev Polynomials)
III. History of Mathematics (Arithmetic, Algebra, Geometry, Trigonometry, Calculus, Number Theory, Indeterminate Analysis, Magic Squares, Combinatorics & Fibonacci Sequence, Transcendental Equations, Linear Systems, Cryptography)

Thesis supervised: Ph.D. (02) & M.Phil (02)
M.Sc. Project: 02