# Numerical Method - Syllabus

Embark on a profound academic exploration as you delve into the Numerical Method course () within the distinguished Tribhuvan university's CSIT department. Aligned with the 2065 Syllabus, this course (CSC-204) seamlessly merges theoretical frameworks with practical sessions, ensuring a comprehensive understanding of the subject. Rigorous assessment based on a 60+20+20 marks system, coupled with a challenging passing threshold of , propels students to strive for excellence, fostering a deeper grasp of the course content.

This 3 credit-hour journey unfolds as a holistic learning experience, bridging theory and application. Beyond theoretical comprehension, students actively engage in practical sessions, acquiring valuable skills for real-world scenarios. Immerse yourself in this well-structured course, where each element, from the course description to interactive sessions, is meticulously crafted to shape a well-rounded and insightful academic experience.

**Course Synopsis: **This course contains the concept of numerical techniques of solving the differential equations and algebraic equations.

**Goal:**To be familiar with the theory of numerical analysis for solving algebraic equations,ordinary and partial differential equations related to engineering problems

#### Units

Review of calculus and Taylor's theorem, Errors in numerical calculations, Trial and error method, Half- interval method, and convergence, Newton's method, secant method and their convergence, Fixed point iteration and its convergence, Newton's method for polynomials and Horner's method

Interpolation and Approximation

Lagrang's polynomials, Newton's interpolation using difference and divided differences, Cubic spline interpolation, Least squares method for linear and nonlinear data

Numerical Differentiation and Integration

Newton's differentiation formulas, Maxima and minima of tabulated function, Newton-Cote's quadrature formulas, Trapeziodal rule, Simpson's rule, 2D algorithm, Gaussian integration algorithm, Romberg integration formulas

Solution of Linear Algebraic Equations

Review of the existence of solutions and properties of matrices, Gaussian elimination method , pivoting, ill-conditioning, Gauss-Jordan method, Inverse of matrix using Gauss elimination method, Method of factorization, Dolittle algorithm, Cholesky's factorization, Iterative solutions, Eigen values and eigen vectors problems, Solving eigen value problems using power method.

Solution of Ordinary Differential Equations

Review of differential equations, Initial value problem, Taylor series method, Picard's method, Euler's method and its accuracy, Heun's method, Runge-Kutta methods, Solution of the higher order equations, Boundary value problems: Shooting method and its algorithm

Solution of Partial Differential Equations

Review of partial differential equations, Deriving difference equations, Laplacian equation and Poisson's equation, engineering examples