Dr. Anil Kumar is a professor of applied sciences (mathematics) at Echelon Institute of Technology in Faridabad, India. He has over 17 years of teaching experience and specializes in areas like fluid mechanics, biomathematics, and mathematical modeling. He is involved in teaching undergraduate and postgraduate students. He has also guided 4 PhD scholars and published over 40 research papers in international and national journals as well as conferences.

1. Dr. Anil Kumar
Professor
Applied Sciences ( Mathematics)
Echelon Institute of Technology (EIT)
Faridabad, Haryana 121101, India
Contact No.: +919911362559,
Email: dranilkumar73@rediffmail.com
1

2. 2
Work and responsibilities at EIT…
I mainly engaged in ..
Teaching, Research and Administration
Teaching
B. Tech.
Theory classes in I, II and
III semester. Practical
classes for Numerical
Methods
M.B.A.
Theory classes in I and II
semester.
MCA Theory Class I Sem
Research
Fluid Mechanics,
Biomathematics,
 Mathematical
Modeling
Administration
Class coordinator
(B.Tech and M.B.A.)
 Exam Cell
coordinator

3. LIFE MEMBERSHIP OF PROFESSIONAL BODIES
 Life member, Operation Research Society of India
 Life member, Indian Mathematical Society of India .
 Life Member, Indian Society Biomechanics, India.
 Life member, National Academy of Mathematics, Ghorakhpur
India.
 Life member, Indian society of Mathematics and Mathematical
Sciences, India.
3

4. INTERNATIONAL VISIT
 Sponsored by Department of Science and
Technology New Delhi, IEEE Symposium on
Business Engineering & Industrial Application, 22-
25 Sept. 2013 Kuching (Malaysia).
4

5. Class Board/University Year of Passing Subjects Division (% Marks)
High school U.P. Board 1987 Science group First Div. [61.5%].
Intermediate
(Bio Group)
U.P. Board 1989 Phys,Chem,
Biology, Hindi,
English
First Div. [64.6%].
Intermediate
(Maths group)
U.P. Board 1991 Mathematics First Div. [65.2%].
B.Sc Dr. B.R. Ambedkar University,
Agra (U.P.)
1994 Phys., Chem. &
Maths.
Second Div. [54.4%]
M.Sc Dr. B.R. Ambedkar University,
Agra (U.P.)
1996 Mathematics First Div. [63.6%]
M.Phil. Dr. B.R. Ambedkar University,
Agra (U.P.)
1999 Mathematics First Div. [73.4%]
Ph.D Dr. B.R. Ambedkar University,
Agra (U.P.)
2003 Mathematics Awarded
Academic Qualifications

6. Presently working as Professor in Applied Sciences ( Mathematics) Echelon
Institute of Technology from 01/08/2017 – Till date
Worked as Professor in Applied Sciences (Mathematics) Chandigarh
Engineering College , Landran Mohali Panjab from 15/03/2016 –
03/08/2017.
Worked as visiting Professor in Mathematics, Gautam Budha University,
Greater Noida from 21/07/2015 -14/03/2016.
Worked as Professor in Mathematics, International Maritime Institute,
Greater Noida UP India 14 August 2014-15/05/2015.
Worked as Professor (Mathematics, HOD and Dean Diploma Engineering)
World Institute of Technology, Sohna (Affiliated to MD University
Rohtak), from 21 May 2013- 12 August 2014.
Worked as Professor (Mathematics) in the Department of Applied
Mathematics Greater Noida Institute of Technology, Greater Noida
(Affiliated to , 2 August 2010- 5 March 2013.
Teaching Experience (17 years):

7. TEACHING EXPERIENCE (17 YEARS) CONTT... :
 Worked as Associate Professor (Mathematics) in the Department of Applied
Mathematics Dronacharya College of Engineering, Greater Noida (Affiliated to
U.P. Technical University Lucknow), from 16 August 2007- 10 July 2010.
 Worked as Sr. Lecturer (Mathematics) in the Department of Mathematics Dr.
K.N. Modi Institute of Engineering & Technology, Modinagar, affiliated to U.P.
Technical University Lucknow, from 2 February 2004- 15 August 2007
 Worked as Lecturer in SSDSS/ACET Iglas Aligarh affiliated Dr. B.R.
Ambedkar University Agra /U.P. Technical University Lucknow from 1 October
2001 to 2 Feb 2004 for teaching B.Sc. / B. Tech. Classes.
 Worked as Lectureship as Guest faculty in the DDIVE, Khandari Campus, Dr.
B.R. Ambedkar University Agra from 2 August 1999 to 2 December 2000.
7

8. Ph.D Scholar’s Guided (04):
Mr. Sajjan Lal: 2010(Thesis Awarded)
Thesis Title: Computational Study of Conducting Fluid Flows through Channels
University: Dr B R Ambedkar University, Agra.
Ms Pawan Preet Kaur : 2014 (Thesis Awarded)
Thesis Title: Computational study of MHD (Magneto-Hydro Dynamic) flow problem
through Channel,
University: Sai Nath University Ranchi.
Mr Sanjeev Kumar Sharma : 2013-14 (registered)
Thesis Title: Modeling of Dynamical and Mechanical characteristics of Blood Flow
through Artery.
University: Mewar University, Rajasthan.
Ms Aarti Ratra: Mathematical modeling of some blood flow problems through
arteries, 2013-14(registered)
University: Pacific University, Udaipur Rajsthan

9.  Engineering Mathematics-I : Savera Publishing House, New Delhi, according to
syllabus, GB Technical University Lucknow, Dr Anil Kumar and Dr. C.L. Varshney,
revised edition 2009. ISBN : 978-81-921345-5-0
 A Text Book of Engineering Mathematics-II: Savera Publishing House, New Delhi,
according to syllabus, GB Technical University Lucknow, Dr Anil Kumar, Dr. C.L.
Varshney and Mr Sajjan Lal, 2011. ISBN 9788190808163
 Engineering Mathematics III: Savera Publishing House, New Delhi, according to
syllabus, GB Technical University Lucknow, Dr Anil Kumar Gupta and Mr V P
Singh, 2011.
 ISBN-9788192134567.
 Business Research Methods: Dr Anil Kumar Gupta Published by Vayu Education of
India, (2009). ISBN-10 9380097336/ISBN-13 9789380097336.
 Business Statistics: Published by Savera Publishing House, New Delhi, 2009/
revised 2015. ISBN : 978-93-81771-36-5
9
BOOKS PUBLISHED (09)…

10. PBLISHED BOOKS
 Statistics for Management: Dr Anil Kumar Gupta, Published by Vayu
Education of India, according to syllabus, affiliated to UP Technical
University, Lucknow. 2009 , ISBN-10 9380097697ISBN-
13/9789380097695.
 Remedial Mathematics: J S Singh, Dr Anil Kumar Gupta and Veeresh
Varshney, Published by Kedar Nath and Ram Nath Publication, Meerut.
2012
 Research Methodology: Dr Anil Kumar Gupta, Published by Vayu
Education of India, according to syllabus, affiliated to UP Technical
University Lucknow, 2008, revised edition 2011. ISBN-10 8190804030/
ISBN-13 9788190804035.
 Computer Based Numerical and Statistical Techniques: Dr Anil Kumar
Gupta Published by Vayu Education of India, according to syllabus UP
Technical University Lucknow, (2008). ISBN-10 9380097093/ ISBN-13
9789380097091.
10

11. PUBLICATIONS
Research papers published in International/National journals: (40)
Research papers presented in International/National conferences: (37)

12. LIST OF SCI / SCOPUS JOURNAL (NATIONAL AND INTERNATIONAL)
 Anil Kumar and G C Sharma :Performance and Analysis of Flow between Annular
Space Surrounded by a Rotating Coaxial cylinder with Co-axial Cylindrical Porous
Medium, vol. 5(3) pp 1-6, 2017, International Journal of Scientific Research in Computer
Science and Engineering, ISSN: 2320-7639
 Anil Kumar Gupta(2012): Performance Model and Analysis of Blood Flow in Small
Vessels with Magnetic Effects, International Journal of Engineering, IJE Transactions
A: Basics Pp 190 -196, Vol. 25, No. 2, Iran Impact Factor 1.0986 ISSN 1728-1431.
 Anil Kumar Gupta: Performance and analysis of blood flow through carotid artery,
International Journal of Engineering and Business Management, ISSN: 1847-9790,
2011, Vol. 3, No. 4, 1-6, ISSN: 1847-9790, Croatia. Cited 6
12

13. LIST OF SCI / SCOPUS JOURNAL (NATIONAL AND INTERNATIONAL)
 Anil Kumar, R. K. Saket, C L Varshney and Sajjan Lal : Finite difference technique
for reliable MHD steady flow through channels permeable boundaries, International
Journal of Biomedical Engineering and Technology (IJBET) UK, Vol. 4(2) pp 101-
110, 2010. inderscience.metapress.com/index/E37643H539307558.pdf, cited 02
ISSN online: 1752-6426 ISSN print: 1752-6418 InderSciecnce Publication UK
 Anil Kumar, CL Varshney and Sajjan Lal: MHD free convective fluctuating flow through a
porous effect with variable permeability Parameter, International Journal of
Engineering, Iran, Volume 23 - 3&4 - Transactions A: Basics, ISSN 1025-2495
November 2010, pp. 313-322 2010. Impact factor 1.0986, published by Materials and
Energy Research Center .
 Anil Kumar Gupta: Finite Element Galerkin’s scheme for flow in blood vessels with
magnetic effects, International Journal of Applied Systemic Studies, Inderscience
publishing, 2009 ISSN 1751-0589 (Print)/ 1751-0597 (Online) Vol. 2 (3) pp- 284-293
UK. Cited 07 inderscience.metapress.com/index/un5p33h704977375.pdf
13

14. LIST OF SCI / SCOPUS JOURNAL (NATIONAL AND INTERNATIONAL)
 R. K. Saket and Anil Kumar: Reliability of convective diffusion
process in porous blood vessels, International Journal of Chemical
Product and Process Modeling, Vol.(3) Article (25) ISSN: 1934-
2659, Canada 2008, http://www.bepress.com/cppm/vol3/iss1/25//
Impact factor 1.30 cited 01
 Anil Kumar, CL Varshney and GC Sharma: Computational technique
for flow in blood vessels with porous effects, International Journal
of Applied Mathematics and Mechanics
DOI: 10.1007/BF02438366 (English Edition) (Springer
Publishing) China, 26(1) 63-72, 2005. Cited 17 (Impact factor
0.992). SSN: 0253-4827 (print version) ISSN: 1573-2754 (electronic
version)
14

15. LIST OF SCI / SCOPUS JOURNAL (NATIONAL AND INTERNATIONAL
 Anil Kumar, GC Sharma and Madhu Jain: Performance modeling
and analysis of blood flow in elastic arteries, International Journal
of Mathematical and Computer Modeling, USA, (Elsevier) 2004
39(13) 1491-1499, ISSN: 0895-7177, Impact Factor: 1.420, Cited
(21)
 Anil Kumar, G.C. Sharma and Madhu Jain: Finite element Galerkin’s
approach for a computational study of arterial flow, International
Journal of Applied Mathematics and
Mechanics DOI: 10.1007/BF02438319 (English Edition) China,
22(9) 1012-1018, 2001 (Springer Publishing),ISSN 0253-
4827,http://www.springer.com/math ( Impact factor 0.922) cited
11
15

16. LIST OF SCI / SCOPUS JOURNAL (NATIONAL AND INTERNATIONAL CONTT..
 Anil Kumar, GC Sharma and Madhu Jain: Performance modeling and analysis of
blood flow in elastic arteries, International Journal of Mathematical and Computer
Modeling, USA, (Elsevier) 2004 39(13) 1491-1499, ISSN: 0895-7177, Impact
Factor: 1.420, Cited (23)
 Anil Kumar, G.C. Sharma and Madhu Jain: Finite element Galerkin’s approach for a
computational study of arterial flow, International Journal of Applied Mathematics
and Mechanics DOI: 10.1007/BF02438319 (English Edition) China, 22(9) 1012-
1018, 2001 (Springer Publishing),ISSN 0253-4827,http://www.springer.com/math
( Impact factor 0.922) cited 11
 Anil Kumar and G C Sharma :Performance and Analysis of Flow between Annular
Space Surrounded by a Rotating Coaxial cylinder with Co-axial Cylindrical Porous
Medium, vol. 5(3) pp 1-6, 2017, International Journal of Scientific Research in
Computer Science and Engineering, ISSN: 2320-7639
16

17. INVITED TALK
 Invited talk : Computational study of blood flow through stenosed artery
with magnetic effects, Advances in Computer Sciences, Communication
and Information Technologies Jawaharlal Nehru University, New Delhi, on
28th July 2012.
 Special session Chair Person Session Title: IEEE conference , Modeling
of Blood Flow in Elastic artery and their Applications, 09th INDIA Com; 2015
International Conference as INDIACom-2015,11-13 march 2015, Bharati
Vidyapeeth, New Delhi (INDIA)
 Invited Speaker and Session Chair on “Finite Element Method of Non-
Newtonian Behaviour of Blood on Pulsatile Flows in Stenosed Arteries
with magnetic effects”, International Conference on Sciences ,
Engineering and Technology Innovations, 3-4 June 9, 2016 , Sponsored by
PTU Jalandhar and INSA New Delhi organized by CT Institute of Technology
Jalandhar Punjab.
 Invited talk on “Use of Statistical tool for practical in Real life “ TEQIP II
sponsored STC on “Advances of Statistics in Sciences and Engineering”
Departments of Mathematics, Physics and Chemistry, National Institute of
Technology, during September 19-25, 2016 Jalandhar, Punjab
17

18. 18

19. DIFFERENTIAL EQUATION
19

20. Definition:
A differential equation is an equation containing an unknown function
and its derivatives.
32  x
dx
dy
032
2
 ay
dx
dy
dx
yd
36
4
3
3






 y
dx
dy
dx
yd
Examples:.
y is dependent variable and x is independent variable,
and these are ordinary differential equations
1.
2.
3.
ORDINARY DIFFERENTIAL EQUATIONS

21. PARTIAL DIFFERENTIAL EQUATION
Examples:
02
2
2
2






y
u
x
u
04
4
4
4






t
u
x
u
t
u
t
u
x
u








2
2
2
2
u is dependent variable and x and y are independent variables,
and is partial differential equation.
u is dependent variable and x and t are independent variables
1.
2.
3.

22. ORDER OF DIFFERENTIAL EQUATION
The order of the differential equation is order of the
highest derivative in the differential equation.
Differential Equation ORDER
32  x
dx
dy
0932
2
 y
dx
dy
dx
yd
36
4
3
3






 y
dx
dy
dx
yd
1
2
3

23. DEGREE OF DIFFERENTIAL EQUATION
Differential Equation Degree
032
2
 ay
dx
dy
dx
yd
36
4
3
3






 y
dx
dy
dx
yd
03
53
2
2












dx
dy
dx
yd
1
1
3
The degree of a differential equation is power of the highest
order derivative term in the differential equation.

24. LINEAR DIFFERENTIAL EQUATION
A differential equation is linear, if dependent variable and its
derivatives are of degree one, coefficients of a term does not depend
upon dependent variable.
Example:
36
4
3
3






 y
dx
dy
dx
yd
is non - linear because in 2nd term is not of degree one.
.0932
2
 y
dx
dy
dx
ydExample:
is linear.
1.
2.

25. Example:
3
2
2
2
x
dx
dy
y
dx
yd
x 
is non - linear because in 2nd term coefficient depends on y.
3.
Example:
is non - linear because
y
dx
dy
sin

!3
sin
3
y
yy is non – linear
4.

26. It is Ordinary/partial Differential equation of order… and of degree…, it is
linear / non linear, with independent variable…, and dependent variable….

27. 1ST – ORDER DIFFERENTIAL EQUATION
2. Differential form:
  01  ydxdyx
.
.0),,( 
dx
dy
yxf),( yxf
dx
dy

3. General form:
or
1. Derivative form:
     xgyxa
dx
dy
xa  01

28. FIRST ORDER ORDINARY DIFFERENTIAL
EQUATION

29. SECOND ORDER ORDINARY DIFFERENTIAL
EQUATION

30. NTH – ORDER LINEAR DIFFERENTIAL
EQUATION
1. nth – order linear differential equation with constant coefficients.
 xgya
dx
dy
a
dx
yd
a
dx
yd
a
dx
yd
a n
n
nn
n
n  

 012
2
21
1
1 ....
2. nth – order linear differential equation with variable coefficients
           xgyxa
dx
dy
xa
dx
yd
xa
dx
yd
xa
dx
dy
xa n
n
nn 

 012
2
2
1
1 ......

31. Solution of Differential Equation

32. y=3x+c , is solution of the 1st order differential
equation , c is arbitrary constant.
As is solution of the differential equation for every
value of c, hence it is known as general solution.
3
dx
dy
Examples
Examples
        sin cosy x y x C
           2 3
1 1 26 e 3 e ex x x
y x y x C y x C x C
Observe that the set of solutions to the above 1st order equation has one
parameter, while the solutions to the above 2nd order equation depend on two
parameters.

33. FAMILIES OF SOLUTIONS
9 ' 4 0yy x 
       1 19 ' 4 9 ( ) '( ) 4yy x dx C y x y x dx xdx C
2 2
1
This yields where .
4 9 18
Cy x
C C  
Example
Solution
The solution is a family of ellipses.
        
2
2 2 2 2
1 1 1
9
9 2 2 9 4 2
2
y
ydy x C x C y x C
Observe that given any point (x0,y0),
there is a unique solution curve of the
above equation which curve goes
through the given point.

34. ORIGIN OF DIFFERENTIAL EQUATIONS
SOLUTION
1.Geometric Origin
21 cxcy 
02
2

dx
yd
1. For the family of straight lines
the differential equation is
.
2. For the family of curves
2
2
x
cey  the differential equation is
xy
dx
dy

A.
B.
xx
ececy 3
2
2
1


the differential equation is 062
2
 y
dx
dy
dx
yd 34

35. PHYSICAL ORIGIN
1. Free falling stone
g
dt
sd
2
2
where s is distance or height and g is acceleration due to gravity.
2. Spring vertical displacement
ky
dt
yd
m 2
2
where y is displacement, m is mass and k is spring constant
3. LCR – circuit, Kirchoff ’s Second Law
Eq
cdt
dq
R
dt
qd
L 
1
2
2 q is charge on capacitor,
L is inductance,
c is capacitance.
R is resistance and
E is voltage

36. PHYSICAL ORIGIN
1.Newton’s Low of Cooling
 sTT
dt
dT
 
where
dt
dT
is rate of cooling of the liquid,
sTT 
is temperature difference between the liquid ‘T’
and its surrounding Ts
dy
y
dt

2. Growth and Decay
y is the quantity present at any time

37. Future plan (after joining the University)
Teaching
Theory & practical classes
UG and/or PG level students
Research and Ph.D/Masters Student guidance
Encourage and guide the student for the
High quality research at university and other collaborative
National/international research centres !
Project writing
For availing the funds (from UGC, AICTE etc)
to establish/up-grade the Research laboratory at
university !

38. Thank you
