# Numerical Methods - Syllabus

Embark on a profound academic exploration as you delve into the Numerical Methods course (NM) within the distinguished Tribhuvan university's BCA department. Aligned with the BCA Curriculum, this course (CACS252) 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 Description**

This course covers solution of nonlinear equations, interpolation and approximation, numerical differentiation and integration and solution of linear algebraic equation, ordinary differential equations and partial difrential equations. it provides knowledge for numerical analysis.

**Course Objectives **

The general objectives of this subject are to make students familiar with the

theory of numerical analysis for solving algebraic and transcendental equations,

solution of ordinary and partial differential equations, numerical di fferentiation

and integration.

#### Units

Introduction, Types of Equation, Errors in Computing, The Bisection Method; The Method of False Position, Newton- Raphson Method, Solution of System of Nonlinear Equation, Fixed Point Iteration and Convergence

Interpolation and Approximation

Introduction, Errors in Polynomial Interpolation, Lagrange's Polynomials, Newton's Interpolation using Difference and Divided Differences, Cubic Spline Interpolation, Least Squares Method for Linear and Non-linear Data.

Numerical Differentiation and Integration

Introduction to Numerical Differentiation, Newton's Differentiation Formulas, Numerical Integration (Trapezoidal Rule, Simpson's 1/3 rule, 3/8 rule); Romberg Integration; Numerical Double Integration.

Solution of Linear Algebraic Equations

Review of the existence of solutions and properties of matrices. Consistency of a Linear System of Equations, Gaussian Elimination Method, Gauss-Jordan Method, Inverse of matrix using Gauss Elimination Method, Method of factorization, Iterative Methods(Jacobi & Gauss-Seidel Iteration),Power Method.

Solution of Ordinary Differential Equations

Introduction to Differential Equations, Initial Value Problem, Taylor Series Method, Picard's Method, Euler's Method and Its Accuracy, Heun's method, Runge-Kutta Methods, Solutions of Higher Order Equations, Boundary Value Problems, Shooting Method and Its Algorithm.

Solution of Partial Differential Equations

Introduction to Partial Differential Equations, Deriving Differences Equations, Laplacian Equation and Poisson's Equation.

#### Lab works

**Laboratory Works **

Laboratory works will consist of program development and testing of Non-linear Equations, Interpolation, Numerical Differentiation and Integration, Linear Algebraic Equations, Ordinary and Partial Differential Equations using C or C+ I Builder.