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 their competence with the ideas in linear algebra to work with linear systems and vector spaces. (C3)
CLO-2: Apply the knowledge of linear algebra to model and solve linear systems that appear in engineering sciences. (C3)
CLO-3: Apply various techniques for solving nonlinear equations and system of equations. (C3)
CLO-4: Identify and describe 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