BRIEF REPORT OF THE
SCIENCE ACADEMIES LECTURE WORKSHOP ON
MATHEMATICAL MODELLING USING
DIFFERENTIAL EQUATIONS
MARCH 6-7, 2014
Submitted By
DEPARTMENT OF MATHEMATICS
MAHARANI’S SCIENCE COLLEGE FOR WOMEN
Palace Road, Bangalore
A Brief Report on the ‘Science Academies’ Lecture Workshop
on Mathematical Modelling Using Differential Equations’
I. A Brief Report
The 2-day lecture workshop on ‘Mathematical Modelling Using
Differential Equations’, sponsored by the Science Academies’ (for M.Sc.
students) was successfully organised by the Co-ordinator Dr. Vanishree, R.
K., under the guidance of the Convener Prof. Pradeep, G. Siddheshwar,
F.N.A.Sc., F.I.M.A., at Maharani’s Science College for Women, Bangalore,
during March 6-7, 2014.
Day I
06-03-2014, Thursday
Registration
The registration of the candidates to participate in the Science
Academies’ Lecture Workshop on Mathematical Modelling Using
Differential Equations was done at 9.30a.m on 06-03-2014 at the portico of
the main building of our college. A total of 108 (including 59 students from
our college) candidates registered for the participation in the lecture
workshop. Duly filled in registration forms sent from the Principal/ Head of
the respective colleges were received from the participants and the
registration materials (workshop file, note pad, pen and badges) including a
detailed schedule of the workshop were provided to the participants.
Inaugural Function
The inaugural function of the workshop took place at 10.30a.m. on the
first day. Following the welcome address and introduction of the chief
guests, a brief introduction to the workshop was given by the convener of the
workshop in which he also explained the various activities of the three
Academies’ of our country (Indian Academy of Sciences- Bangalore, Indian
National Science Academy- New Delhi and The National Academy of
Sciences, India- Allahabad). The chief Guest of the function Prof.
Vasudevamurthy, A. S., in his key note address stressed upon the importance
of Mathematics in various fields and the opportunities that are available for
the students of Mathematics. He also highlighted the Summer-programmes
of the Academies’ for post-graduate students as well as teachers. The
principal of our college gave her presidential remarks.
After a high tea, lecture sessions started (each lecture sessions were
for two and half hours, including the discussions).
Lecture I: Prof. Vasudeva Murthy, A. S.
CAM-TIFR, Bangalore.
Title: On the Newtonian three body problem
The lecture focussed on understanding the evolution of celestial
bodies under the influence of gravitation. Keppler’s laws and Newton’s law
of universal gravitation were discussed in brief. The complexity of the threebody problem as against the two-body problem was demonstrated.
Numerical methods of solutions for ODE using Euler and Implicit Euler
methods were explained.
The students were allowed to discuss for about 30 minutes. The
students were inspired by the speaker and clarified their doubts about the
numerical methods of solution for the differential equations.
After the lecture there was a lunch break for about 45 minutes.
Lecture II: Prof. Nandakumaran, A. K. F.N.A.Sc.
I.I.Sc., Bangalore
Title: Why do we need analysis and linear algebra for ODE?
As the title indicates, this lecture concentrated on the basics of
calculus which links to analysis. The speaker managed to grab the attention
of the students to many important things including method of solution to
some basic ODEs by separation of variables and the need of analysis in
understanding the solution. The emphasis was on the analysis and linear
algebraic aspects of the methods involved in solving the differential
equations. Some of the problems were given as exercises to the students.
Motivated by the lecture students discussed with the speaker for 30
minutes.
With this the first day’s sessions were concluded.
Day II
07-03-2014, Friday
Lecture III: Prof. Govindan Rangarajan F.N.A.Sc., F.I.A.S.
I.I.Sc., Bangalore
Title: Chaos and Synchronization
The theory of chaos was introduced to the students by various
examples. The conditions that are responsible for chaos, like, exponential
divergence and compactness of the region were discussed. The dependency
of the chaotic system on initial conditions was stressed upon. The differential
equations that represent the chaotic systems were modelled. Theory of
fractals was introduced. Weather predictions were analysed, why the short
term (for 24hrs-48hrs) weather analysis can be believed and why it fails
when the prediction is for long term.
The importance of synchronization in the case of body pressure was
explained in this session. It was told that in the case of synchronization,
irrespective of the initial condition, the systems behave in identical manner
at large times.
This session witnessed a long discussion. The students posed many
questions about the weather analysis, satellites, the type of research and the
opportunities in this area.
This session was followed by lunch break for about 45 minutes.
Lecture IV: Prof. Pradeep, G. Siddheshwar F.I.M.A.,F.N.A.Sc.
Bangalore University, Bangalore.
Title: ODEs and PDEs-What they convey about what they
represent?
Second order partial differential equations were considered and the
various terms involved in the equation were discussed in detail. In the
classification of the differential equations, which are the equations that are
time evolutionary and which are equations that represent the equilibrium
state, were discussed.
The importance of non-dimensionalizing the equations was discussed.
Some of the second order partial differential equations like, heat equation,
wave equation and Laplace equations were non-dimensionalized for
demonstration. The speed of propagation of these equations was also
explained.
The students were allowed to discuss for about 30 minutes. They
discussed about the physical interpretations of gradient, divergence, curl and
conservative force fields.
This session was followed by Valedictory function
Valedictory Function
The workshop was concluded by the valedictory function. The chief
guest of the function, Prof. B. L. Bhagyalakshmi, Director, DCE, Karnataka,
addressed the students and urged them to choose teaching as their profession
after their master’s degree. She also stressed upon the importance of
research, especially in the field of mathematics. Convener of the workshop
Prof. Pradeep, G. Siddheshwar also addressed the gathering and gave some
important insights into the subject as well as life.
Students were asked to give their feedback. Several students came
forward and expressed their opinions. We were happy to listen to them and
felt that the purpose of organising the lecture workshop has been
accomplished. Some important points of the feedbacks are mentioned below.
1. The students understood the various opportunities available in the
field of Mathematical modelling.
2. They felt that the titles of the lectures were apt and could get the
insight of many things in the area of differential equations.
3. They had opportunities to discuss with the leading mathematicians
in the field of mathematical modelling.
4. Many students requested the co-ordinator to organise more such
events and provide opportunities to participate.
5. Many are inspired to wish to take up research in this area.
The Principal of our college thanked the academies for their support
and the department for organising the lecture workshop. Finally, Dr.
Vanishree, R. K., co-ordinator of the workshop proposed vote of thanks. She
thanked the Science academies’ of our country (Indian Academy of Science
– Bangalore, Indian National Science Academy – New Delhi and the
National Academy of Sciences, India – Allahabad) for the financial support,
The eminent speakers for their enlightening lectures, The enthusiastic
participants of the workshop from various colleges as well as our college,
Principal and management staff for their support and encouragement and the
colleagues in the department for their whole hearted support.
II. Time table of the Workshop
The workshop was conducted as per the time schedule given in the
Programme schedule. (Please see Annexure-I)
III. Statement of Expenditure
The complete statement of expenditure is given in the prescribed
format. (Please see Annexure-II)
IV. Photographs
Please see Annexure-III
V. The Number of participants who attended the workshop including
the names of colleges and institutions
Along with the students of our college, students from Central college,
Govt. Science college, Christ university, Vijaya college, Mount Carmel
college and M.E.S. college attended the workshop.
The complete list of the registered participants of the lecture workshop
is given. (Please see Annexure-IV)
Coordinator
Principal
Annexure - I
Maharani’s Science College for Women,
Palace Road, Bangalore
Science Academies’ Lecture Workshop on
‘Mathematical Modelling Using Differential Equations’
Program Schedule
06-03-2014
9.30 a.m.
: Registration
10:00 a.m. - 11:00 a.m. : Inauguration
Tea break :
11.00a.m. – 11.15 a.m
Session and Time
Speaker
Session I
11.15-12.30 pm
Prof. A. S. Vasudeva Murthy
Session II
Topic
On the Newtonian threebody problem
Topic Continues
12.30-1.45 pm
Lunch break
Session III
1.45- 2.30pm
Prof. A. K. Nandakumaran
2.30-3.45 pm
Tea break
Why do we need
analysis
and
linear
algebra for ODE?
3.45-4.00pm
Session IV
Topic Continues
4.00-5.15pm
07-03-2014
Session I
Prof. G. Rangarajan
10.00- 11.15 am
Tea break
Chaos
Synchronization
and
11.15- 11.30am
Session II
Topic Continues
11.30-12.45 pm
Lunch break
12.45- 1.30pm
Session III
1.30-2.45 pm
Prof. P. G. Siddheshwar
Session IV
2.45-4.00 pm
Tea break
4.00-4.15pm
Valedictory Function
4.15- 4.45 pm
Venue: Conference Hall
ODEs and PDEs-What
they convey about what
they represent?
Topic Continues