MA2L304
Undergraduate (ITEP)
· Generally offered: Spring
Numerical Methods
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Errors in numerical computations, floating-point arithmetic, Solution of nonlinear equations: Bisection, Newton-Raphson, Secant, Fixed-point iteration methods, rate of convergence.
Unit II: Interpolation: Lagrange, Newton divided difference, finite difference operators, Newton forward and backward interpolation, Cubic spline interpolation. Numerical differentiation and integration: Trapezoidal, Simpson’s rules, Gaussian quadrature.
Unit III: Solution of systems of linear equations: Gauss elimination, pivoting, LU decomposition, Jacobi and Gauss-Seidel iterative methods. Eigenvalue problems: Power method.
Unit IV: Numerical solution of ordinary differential equations: Euler, Modified Euler, Runge-Kutta methods of order 2 and 4, Multistep methods. Introduction to numerical solution of PDEs.
Full syllabus document →
Unit II: Interpolation: Lagrange, Newton divided difference, finite difference operators, Newton forward and backward interpolation, Cubic spline interpolation. Numerical differentiation and integration: Trapezoidal, Simpson’s rules, Gaussian quadrature.
Unit III: Solution of systems of linear equations: Gauss elimination, pivoting, LU decomposition, Jacobi and Gauss-Seidel iterative methods. Eigenvalue problems: Power method.
Unit IV: Numerical solution of ordinary differential equations: Euler, Modified Euler, Runge-Kutta methods of order 2 and 4, Multistep methods. Introduction to numerical solution of PDEs.