Course Details

Subject {L-T-P / C} : BM6231 : Computational Methods in Biomedical Engineering { 3-0-0 / 3}

Subject Nature : Theory

Coordinator : Dr. Ravi Kant Avvari

Syllabus

Module I
Introduction to computation, mathematical modelling – analytical and numerical method, mathematical tools, application in biomedical engineering.
Module II
Systems of linear and non-linear equations, Cramer's rule, Gauss elimination, Gauss Jordan, LU decomposition, Gauss-Seidel method, iterative solution techniques. Eigen values and eigen vectors, power iteration methods. Algebraic Equations – bisection method, Newton-Raphson and secant method.
Module III
System of ODE and nonlinear ODE, partial differential equations (PDE), classification of PDE – elliptic equations, parabolic equations (transient diffusion equation), hyperbolic equations (wave equation), numerical differentiation and integration, Taylor’s series, Picard’s method, Euler’s method, Runge Kutta and Milne’s method, trapezoidal method, Simpson's method, quadrature method, explicit and implicit schemes, finite difference method, finite volume method, concept of finite element method, solution of Laplace’s and Poisson’s equations, solution of heat transfer equation.
Module IV
Problems in biomechanics and biomaterials, inverse problems in the field of biomedical imaging.

Course Objectives

Course Outcomes

At the end of the course the student will be able to: <br />CO1: Apply suitable methods for mathematical modelling <br />CO2: Solve linear and non-linear equations using iterative methods <br />CO3: Apply various numerical methods for solving an equation <br />CO4: Develop a computational solution to the ODE/PDE <br />CO5: Develop solution for problems in biomedical engineering

Essential Reading

Supplementary Reading