## COURSE OBJECTIVES

An ability to define linear equation and identify system of linear equations and non-linear equations, describe linear transformation and matrix of linear transformation, classification eigen value and eigen vectors problems.

## COURSE LEARNING OUTCOMES (CLO)

CLO-1: Demonstrate competence with the ideas in linear algebra to work with linear systems and vector spaces. (C3)
CLO-2: Analyze the linear systems of engineering sciences using the concepts of linear algebra. (C4)
CLO-3: Apply various techniques for solving nonlinear equations and system of equations.(C3)
CLO-4: Select the numerical methods for solving problems involving integration and differential equations. (C4)

## COURSE CONTENTS

1. Linear Algebra
• System of Linear Equations and Matrices – Four Lectures
• Introduction to System of Linear Equations
• Matrix Form of a System of Linear Equations
• Gaussian Elimination Method
• Gauss-Jordan Method
• Consistent and Inconsistent Systems
• Homogeneous System of Equations
• Matrix Algebra – Three Lectures
• Definitions
• An Algorithm for finding the Inverse of a matrix
• Characterization of Invertible Matrices
• LU Factorization
• Applications of Linear Systems – Three Lectures
• Traffic Flow Problems
• Electric Circuit Problems
• Economic Models
• Linear Transformations – Three Lectures
• Introduction
• Matrix Transformations
• Domain and Range of Linear Transformations
• Geometric Interpretation of Linear Transformations
• Matrix of Linear Transformations
• Eigenvalues and Eigenvectors – Three Lectures
• Definition of Eigenvalues and Eigenvectors
• Computations of Eigenvalues
• Properties of Eigenvalues
• Diagonalization
• Applications of Eigenvalues

2. Numerical Analysis

• Solutions of Algebraic Equations – Four Lectures
• The Bisection Method
• Fixed Point Iterative Method
• Newton- Raphson Method
• Interpolation – Four Lectures
• Definition and Motivation
• The Taylor’s Interpolation Polynomials
• The Lagrange Interpolation Polynomials
• Numerical Differentiation and Integration – Four Lectures
• Numerical Differentiation
• Trapezoidal rule
• Simpson’s rule
• Numerical ODE’s – Four Lectures
• Elementary Theory of Initial Value Problems
• Euler’s Method
• Higher Order Taylor’s Methods
• Runge Kutta Methods