Dr. Vinod Mishra
B.Sc.(1989), M.Sc.(1991), Ph.D. (1998)
1. Twenty six 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. External Speakers of the Seminar: Prof. S.L. Singh, Prof. Chandra Shakher, Prof. Deepak Grover, Prof. G.S. Randhawa and Prof. S.K. Dhameja
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, Nov.1999- Nov.2000)
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 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
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 (22) (finance born by host institutions) at national and international conferences on History of Mathematics/Wavelet Analysis/Numerical Laplace Transform: 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, 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: 02 on Classical Mechanics at Chandigarh University (Punjab) for M.Sc. Students and 03 each on Vector Calculus & Numerical Methods at NIT Uttarakhand for B.Tech. Students
4. Technical Sessions Chaired during National and International Conferences: 10
Selected Publications in Research Journals out of Forty Eight:
A. History of Mathematics:
1. Vinod Mishra and S.L. Singh, Theorem of Square on the Diagonal in Vedic Geometry and its Application, Indian Journal of History of Science 31 (1996), 155-166.
2. Vinod Mishra and S.L. Singh, First Degree Indeterminate Analysis in Ancient India and its Application by Virasena, Indian Journal of History of Science 32 (1997), 127-133.
3. Vinod Mishra and S.L. Singh, Values of π from Antiquity to Ramanujan, Sugakushi kenkyu (Japan), No. 157, 1998, 12-25.
4. Vinod Mishra and S.L. Singh, Incircumscribing Triangles & Cyclic Quadrilaterals in Ancient & Medieval Indian Geometry, Sugakushi kenkyu (Japan), No. 161, 1999, 1-11.
5. Vinod Mishra and S.L. Singh, Geometry in Rituals, Journal of Natural & Physical Sciences 15 (2001), 159-177.
6. Vinod Mishra, Geometry Relating to Circles and Spheres, Studies in History of Medicine and Science 18 (2002), No. 1, 47-106.
7.Vinod Mishra, Combinatorics and the (So-called) Binomial Theorem, Studies in History of Medicine and Science 18 (2002), No.2, 59-121.
8. Vinod Mishra and S.L. Singh, Similarity of Plane Figures and Geometric & Group Theoretic Study of Cyclic Quadrilateral of First Kind, Journal of Natural & Physical Sciences 18 (2004), 69-102.
B. Wavelet Analysis:
1. Vinod Mishra and Sabina, Wavelet-Galerkin Solutions of Ordinary Differential Equations, International Journal of Mathematical Analysis 5 (2011), 407-424.
2. Harpreet Kaur, R.C. Mittal and Vinod Mishra, Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems, American Journal of Computational Mathematics 1 (2011), 176-182.
3. Vinod Mishra, Harpreet Kaur and R.C. Mittal, Haar Wavelet Solutions of Certain Differential, Integral and Integro-differential Equations, International Journal of Applied Mathematics and Mechanics 8 (2012), 69-82.
4.Sabina and Vinod Mishra, Wavelet-Galerkin Solutions of One and Two Dimensional Partial Differential Equations, Journal of Emerging Trends in Computing and Information Sciences 3(2012), 1373-1378.
5. Harpreet Kaur, R.C. Mittal and Vinod Mishra, Haar Wavelet Approximation Solutions for the Generalized Lane Emden Equations Arising in Astrophysics, Computer Physics Communications 184 (2013), 2169-2177.
6. Vinod Mishra and Harpreet Kaur, Haar Wavelet Approach for Solving Nonlinear Differential and Integral Equations, Neural, Parallel and Scientific Computations 22 (2014), 421-430.
7. Harpreet Kaur, R.C. Mittal and Vinod Mishra, Haar Wavelet Solutions of Nonlinear Oscillator Equations, Applied Mathematical Modelling 38 (2014), 4958-4971.
8. R.C. Mittal, Harpreet Kaur and Vinod Mishra, Haar Wavelet Based Numerical Investigation of Coupled Viscous Burgers Equation, International Journal of Computer Mathematics 92 (2015), 1643-1659.
C. Numerical Inverse Laplace Transform:
1. Vinod Mishra, 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.
2. Dimple Rani and Vinod Mishra, Bernstein Polynomial Laplace Decomposition Method, International Journal of Pure and Applied Mathematics 114 (2017), 823-833.
3. 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
4. Dimple Rani, Vinod Mishra and Carlo Cattani, Numerical Inversion of Laplace Transform based on Bernstein Operational Matrix, Mathematical Methods in Applied Sciences, 41 (2018), doi/10.1002/mma.5188
5. Dimple Rani, Vinod Mishra and Carlo Cattani, Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations, Symmetry 11 (2019), No 530
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, Chevishev Polynomials)
(Ph.D. Thesis Supervision Continue: Dimple Rani).
III. History of Mathematics and Scientific Applications (Cryptography, Indeterminate Analysis of First and Second Degree, Matrix Analysis of Magic Squares and Fibonacci Like Sequences & Polynomials)(PhD Guidance Continue: 02).
Note: NET-JRF qualified MSc Maths students with scientific temperaments may contact me for research Guidance..
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