## COURSE OBJECTIVES

The course of numerical computing is meant for solving mathematical problems using only simple arithmetic operations. The approach involves formulation of mathematical models physical situations that can be solved with arithmetic operations. It requires development, analysis and use of algorithms. Numerical computations invariably involve a large number of arithmetic calculations and, therefore, require fast and efficient computing devices. The microelectronic revolution and the subsequent development of high, low cost personal computers have had a profound impact on the application of numerical computing methods to solve scientific problems.

### COURSE LEARNING OUTCOMES (CLO)

CLO: 1. Understand the role of approximations and errors in the implementation and development of numerical methods.
CLO: 2. Gain sufficient information to successfully approach an engineering problem.
CLO: 3. Solve problems involving linear algebraic equations and appreciate the application of these equations in many fields of engineering.
CLO: 4. Approach engineering problems dealing with optimization

### COURSE CONTENTS

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• Introduction to MATLAB
• Introduction to Numerical Computing
• Error Analysis
• Solution of Non Linear Equations (Bisection Method)
• Solution of Non Linear Equations (Regula-Falsi Method)
• Solution of Non Linear Equations (Method of Iteration)
• Solution of Non Linear Equations (Newton Raphson Method)
• Solution of Non Linear Equations (Secant Method)
• Solution of Linear System of Equations (Gaussian Elimination Method)
• Solution of Linear System of Equations(Gauss–Jordon Elimination Method)
• Solution of Linear System of Equations(Jacobi Method)
• Solution of Linear System of Equations(Gauss–Seidel Iteration Method)
• Operators
• Interpolation(Introduction and Difference Operators)
• Interpolation Newton’s Forward difference Formula
• Sterling Central Difference Interpolation
• Newton’s Backward Difference Interpolation Formula
• Lagrange’s Interpolation formula
• Divided Differences
• Lagrange’s Interpolation formula, Divided Differences (Examples )
• Numerical Integration Simpson’s 1/3rd Rule
• Numerical Integration Simpson’s 3/8th Rule
• Numerical Integration Trapezoidal Rule
• Numerical Integration Weddle’s Rule