Solution of Nonlinear Equations
Errors in numerical calculations; Sources and propagation of errors; Taylor's theorem; Solving nonlinear equations using trial-and-error, half-interval, Newton, fixed point iteration methods.
Numerical Method Chapters
B.Sc. CSIT - Third Semester
Interpolation and Regression
Interpolation vs extrapolation; Lagrange interpolation; Newton interpolation—divided, forward and backward differences; Cubic spline; Polynomial regression.
Numerical Differentiation and Integration
Differentiating continuous and tabulated functions; Newton’s difference-based differentiation; Max/min from tables; Numerical integration methods.
Solving System of Linear Equations
Gaussian elimination; Pivoting; Gauss–Jordan method; Matrix inverse using Gauss–Jordan; LU decomposition.
Solution of Ordinary Differential Equations
Initial value problems; Taylor series method; Picard’s method; Euler method and improvements; Runge–Kutta methods.
Solution of Partial Differential Equations
Classification of PDEs; Difference equations; Laplace and Poisson equations; Engineering applications.