Modeling and Differential Equations

  Shall be declared soon

Participants will be familiar with techniques and tools of solving first order ODE and Linear ODE of higher order and will be able to use them for the relevant applications in allied disciplines

Participants will have good understanding of process of Mathematical Modeling, and are expected to be able to construct Mathematical models for some real world problems

 9000/-

MM-001:- Differential Equations and Modeling

1: Models of problems in Science and Engineering leading to ordinary differential equations (ODE), Solutions of first order first degree ODE and Applications

2: Models leading to higher order linear ODE, Solutions of homogeneous and non-homogeneous ODE. Applications of ODE.

3: Legendre and Bessel’s equations: Legendre polynomials and Bessel’s functions, Systems of ODE: Solutions using eigen values and eigen vectors; Phase- plane Analysis

MM-002:- Partial Differential Equations

1: Surfaces and curves in space, Partial differential equations (PDE)

2: First order PDEs: Models leading to PDEs, General solution of Linear PDE, Nonlinear PDE

3:Second order PDEs of Mathematical Physics: Wave equation, Heat equation, Laplace Equation

MM-003:-Modeling & Simulations

1: Needs and Techniques of mathematical modeling

2: Models in population dynamics:

3: Modeling of Physical systems

4: Compartment Models: Models for exponential decay and Radioactivity, Radiocarbon Dating, Lake Pollution models, Drug assimilation into the blood, Simple Traffic Models: Automobile velocities and Velocity field, Traffic flow and Traffic density, Flow, density and velocity relationship, Conservation of number of cars, Steady-State Car-following models