Unit 1 Introduction to Numerical Analysis

9 lecture hours

• Analytic & Numerical solution
• Sources of error (Inherent error
• Truncation error
• Round off error
• Absolute error/ Relative error)
• Significant digits
• Loss of significant digit
• Solution to transcendental equations: Initial Approximation (Bisection method)
• Methods based on first degree approximation (Secant Method
• Regula - Falsi Method
• Newton - Raphson Method and its modifications)
• Rate of Convergence

Unit 2 System of linear algebraic equations and Eigenvalue problems

• Direct Methods (Cramer’s rule
• Gauss – Elimination method [Pivoting]
• Gauss – 14 30 Program Name: Engineering Level: Master of Engineering Branch: Textile Engineering Course / Subject Code : Course / Subject Name : Computational Methods for Textiles ME01025071 Jordan Elimination method
• LU Decomposition
• Cholesky factorisation)
• Iteration Methods (Jacobi Iteration method
• Gauss – Seidel method)
• Eigenvalues and Eigenvectors (Jacobi& Given’s method for symmetric matrices
• Power method
• Inverse power method
• Shift of Origin)

Unit 3 Interpolation

8 lecture hours

• Arbitrary points (Lagrange Interpolation
• Newton’s Divided Difference)
• Equispaced points (Finite Differences
• Newton Forward Difference
• Newton Backward Difference)

Unit 4 Ordinary differential equations

• Euler Method
• Taylor Series Method
• Explicit Runge Kutta Method (second
• higher order). 7 15

Unit 5 Fundamentals of computer programming

7 lecture hours

• Flow charts
• Pseudo Code Concepts: Structured Programming
• Object Oriented Programming Programming in C++: Classes and Objects
• Constructor sand Destructors
• Operator Overloading
• Virtual Functions