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.

To become familiar with concept of computation in biomedical engineering

To learn various method of solving linear and non-linear equations

To learn various method of solving ODE and PDE

To review computational problems in biomedical engineering

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

Gupta S.K., Numerical Methods for Engineers, New Age International

Chapra S.C. and Canale R.P., Numerical Methods for Engineers, McGraw Hill , 2006

Joe D Hoffman, Numerical Methods for Engineers and Scientists, Marcel Dekker , 2001

T. Veerarajan and T. Ramachandran, Numerical methods with programs in C, Tata McGraw-Hill , 2006