# Linear Algebra and Numerical Analysis (MTME2063)

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%)