This course provides introduction of mathematical modeling and analysis in biological sciences. It is designed for students in both applied mathematics and bio-medical / biological sciences. The major content of this course is chosen from population dynamics. This course covers the fundamentals of deterministic models in both discrete and continuous time domain. This course includes both linear and non-linear models with sufficient amount of theoretical background. The relevant concepts and solution methods of various difference and differential equations are provided. We have also focused on graphical solution for clear analysis of nature of models.
Important For Certification/Credit Transfer:
Weekly Assignments and Discussion Forum can be accessed ONLY by enrolling here
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Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.
INTENDED AUDIENCE: UG/PG students of technical universities/colleges
CORE/ELECTIVE: Core
UG/PG: UG and PG
PREREQUISITES: Basic Calculus
INDUSTRY SUPPORT: NIL
2156 students have enrolled already!!
ABOUT THE INSTRUCTOR:
Dr. Ameeya Kumar Nayak is Associate Professor in Department of Mathematics at IIT Roorkee and actively involved in teaching and research in the direction of numerical modeling of fluid flow problems for last ten years. His research interests are in the fundamental understanding of species transport in macro and micro-scale confinements with applications in biomedical devices and micro electro mechanical systems. He has authored and co-authored more than 32 peer-reviewed journal papers, which includes publications in Springer,ASME, American Chemical Society and Elsevier journals. He is also active in writing book chapter with reputed international publication house.
COURSE LAYOUT:
Week 1 : Overview of mathematical modeling, types of mathematical models and methods to solve the same; Discrete time linear models – Fibonacci rabbit model, cell-growth model, prey-predator model; Analytical solution methods and stability analysis of system of linear difference equations; Graphical solution – cobweb diagrams; Discrete time age structured model – Leslie Model; Jury’s stability test; Numerical methods to find eigen values – power method and LR method.
Week 2 : Discrete time non-linear models- different cell division models, prey-predator model; Stability of non-linear discrete time models; Logistic difference equation; Bifurcation diagrams.
Week 3 : Introduction to continuous time models – limitations & advantage of discrete time model, need of continuous time models; Ordinary differential equation (ODE) – order, degree, solution and geometrical significance; Solution of first order first degree ODE – method of separation of variables, homogeneous equation, Bernoulli equation; Continuous time models – model for growth of micro-organisms, chemostat; Stability and linearization methods for system of ODE’s.
Week 4 : Continuous time single species model – Allee effect; Qualitative solution of differential equations using phase diagrams; Continuous time models – Lotka Volterra competition model, prey-predator models.
SUGGESTED READING MATERIALS:
1.J.N. Kapur, Mathematical Models in Biology and Medicine, East-West Press Private limited.
2.Leah, Edelstein, Keshet, Mathematical Models in Biology, SIAM publications.
3.J.D. Murray, Mathematical Biology Vol. I, II, 3rd edition, Springer publications.
CERTIFICATION EXAM :
The exam is optional for a fee.
Date of Exams : October 28 (Sunday)
Time of Exams : Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm
Exam for this course will be available in both morning & afternoon sessions.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.
CERTIFICATION:
Final score will be calculated as : 25% assignment score + 75% final exam score
25% assignment score is calculated as 25% of average of Best 3 out of 4 assignments.
E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc.
