Mathematical Modelling: Analysis and Applications

COURSE DURATION : 4 weeks

Ameeya Kumar Nayak

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What you will learn

  • Modelling

  • Mathematics

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.

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Introduction to Mathematical Modeling
Preview 25:14
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Discrete Time Linear Models in Population Dynamics - I
Preview 55:14
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Discrete Time Linear Models in Population Dynamics - II
Preview 27:36
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Discrete Time Linear Age Structured Models
Preview 25:45
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Numerical Methods to Compute Eigen Values
Preview 25:41

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Discrete Time Non-Linear Models in Population Dynamics - II
Preview 27:36
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Analysis on Logistic Difference Equation
Preview 24:08
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Classifications of Bifurcation
Preview 22:58
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Discrete Time Non - Linear Models in Population Dynamics - II
Preview 27:22
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Discrete Time Prey - Predator Model
Preview 19:01

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Introduction to Continuous Time Models
Preview 30:22
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Solution of First Order First Degree Differential Equations
Preview 27:02
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Continuous Time Models in Population Dynamics - I
Preview 27:26
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Continuous Time Models in Population Dynamics - II
Preview 31:19
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Stability and Linearization of System of Ordinary Differential Equations
Preview 39:59

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Continuous Time Single Species Models
Preview 24:15
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Qualitative Solution of Differential Equations - Phase Diagrams - I
Preview 54:59
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Qualitative Solution of Differential Equations - Phase Diagrams - II
Preview 32:47
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Continuous Time Lotka - Volterra Competition Model
Preview 30:40
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Continuous Time Prey - Predator Model
Preview 33:49
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Meet Your Instructor

Instructor
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0 Students
2 Courses
About 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.

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Free

  • Course Duration
    10 h 13 m 13 s
  • Course Level
    Intermediate
  • Student Enrolled
    4
  • Language
    English
This Course Includes
  • 10 h 13 m 13 s Video Lectures
  • 0 Quizzes
  • 0 Assignments
  • 0 Downloadable Resources
  • Full Lifetime Access
  • Certificate of Completion