[vc_row el_class=”inner-body-content” css=”.vc_custom_1667299738274{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes” css=”.vc_custom_1667299718243{margin-top: 0px !important;}”][vc_column_text]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.[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” use_theme_fonts=”yes”][vc_column_text]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)[/vc_column_text][vc_custom_heading text=”COURSE CONTENTS” use_theme_fonts=”yes”][vc_column_text css=”.vc_custom_1667299671607{margin-bottom: 0px !important;}”]

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

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