Linear Algebra and Numerical Analysis (MTME2063)

Pre-requisite(s)

None

Recommended Book(s)

  • Linear Algebra And Its Applications By David C. Lay, 4th Edition
  • Numerical Analysis By Richard L. Burden, J. Douglas Faires

Reference Book(s)

  • Advanced Engineering Mathematics, By Erwin Kreyszig, 8th Edition  
  • Elementary Linear Algebra With Applications, H. Antone, Chris Rorres
  • T. J. Akai, Applied Numerical Methods For Engineers

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)

  1. CLO-1: Demonstrate their competence with the ideas in linear algebra to work with linear systems and vector spaces. (C3)
  2. CLO-2: Apply the knowledge of linear algebra to model and solve linear systems that appear in engineering sciences. (C3)
  3. CLO-3: Apply various techniques for solving nonlinear equations and system of equations. (C3)
  4. CLO-4: Identify and describe the numerical methods for solving problems involving integration and differential equations. (C4)

Course Contents

Linear Algebra

 1.       System of Linear Equations and Matrices

  • 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

 2.      Matrix Algebra

  • Definitions
  • An Algorithm for finding the Inverse of a matrix 
  • Characterization of Invertible Matrices
  • LU Factorization

 3.      Applications of Linear Systems

  • Traffic Flow Problems
  • Electric Circuit Problems
  • Economic Models

 4.      Linear Transformations

  • Introduction
  • Matrix Transformations
  • Domain and Range of Linear Transformations
  • Geometric Interpretation of Linear Transformations
  • Matrix of Linear Transformations

 5.      Eigenvalues and Eigenvectors

  • Definition of Eigenvalues and Eigenvectors
  • Computations of Eigenvalues
  • Properties of Eigenvalues
  • Diagonalization
  • Applications of Eigenvalues

 

Numerical Analysis

 6.      Solutions of Algebraic Equations

  • The Bisection Method
  • Fixed Point Iterative Method
  • Newton- Raphson Method

 7.      Interpolation

  • Definition and Motivation
  • TheTaylor’s Interpolation Polynomials
  • The Lagrange Interpolation Polynomials

  8.      Numerical Differentiation and Integration

  • Numerical Differentiation
  • Trapezoidal rule
  • Simpson’s rule

 9.      Numerical ODE’s

  • Elementary Theory of Initial Value Problems
  • Euler’s Method
  • Higher Order Taylor’s Methods
  • Runge Kutta Methods

Mapping of CLOs to Program Learning Outcomes

CLOs/PLOs

CLO:1

CLO:2

CLO:3

CLO:4

PLO:1 (Engineering Knowledge)

 

 

 

PLO:2 (Problem Analysis)

 

 

 

 

PLO:3 (Design Development of Solutions)

 

 

 

 

PLO:4 (Investigation)

 

 

 

 

PLO:5 (Modern Tool Usage)

 

 

 

 

PLO:6 (Engineer & Society)

 

 

 

 

PLO:7 (Environment and Sustainability)

 

 

 

 

PLO:8 (Ethics)

 

 

 

 

PLO:9 (Individual & Team Work)

 

 

 

 

PLO:10 (Communication)

 

 

 

 

PLO:11 (Project Management)

 

 

 

 

PLO:12 (Life Long Learning)

 

 

 

 

Mapping of CLOs to Assessment Modules

Assessment Modules \ CLOs

CLO:1

CLO:2

CLO:3

CLO:4

Assignments (18%)

 

 

 

 

Quizzes (17%)

 

 

 

 

Midterm Exam (20%)

 

 

 

 

Final Exam (45%)