# CV2019 Matrix Algebra and Computational Methods

[Lectures: 26 hrs; Tutorials: 13 hrs; Pre-requisites: None; Academic Unit: 3.0]

Learning Objective

To equip students with fundamentals in linear algebra and numerical methods required for the upper years of studies.

Course Content

Introduction to matrix algebra; Linear system of equations; Gauss elimination and solution types for Ax=b; Linear independence; Rank of matrix and solution type; Matrix inverse; Gauss-Jordan elimination; Determinant of matrix; Cramer’s rule; Inverse of matrix; Matrix norm and Matrix conditioning; Eigenvalues and Eigenvectors; Mathematical Modelling and Numerical Methods; Roots of Equations; Numerical Interpolation; Numerical Integration and Differentiation; Numerical Solution of Ordinary Differential Equations.

Course Outline

 S/N Topic 1 Introduction to matrix algebra, linear system of equations, Gauss elimination and solution types for Ax=b 2 Pivoting, Linear independence, Rank of matrix, Rank and solution type 3 Matrix inverse, Gauss-Jordan elimination, Determinant of matrix 4 Cramer’s rule, Inverse by formula, Matrix norm and Matrix conditioning 5 Eigenvalues and Eigenvectors I, Eigenvalues and Eigenvectors II 6 Eigenvalues and Eigenvectors III, Further Examples 7 Revision – Matrix Algebra, Mathematical Modelling and Numerical Methods 8 Roots of Equations I, Roots of Equations II 9 Roots of Equations III, Interpolation I 10 Interpolation II, Numerical Integration and Differentiation I 11 Numerical Integration and Differentiation II, Numerical Integration and Differentiation III 12 Numerical Solution of Ordinary Differential Equations I, Numerical Solution of Ordinary Differential Equations II 13 Numerical Solution of Ordinary Differential Equations III, Revision – Numerical methods

Learning Outcome

At the end of the course, students will be able to understand the basic concepts of matrix algebra, solving linear equations, and numerical methods. In addition, students will be able to apply these basic concepts in solving practical engineering problems.

Textbooks/References

1. Howard Anton and Chris Rorres, “Elementary Linear Algebra with Applications, 9th Edition”, 9th Edition, John Wiley & Sons, 2005.
2. Chapra, S. C. and Canale R. P. “Numerical Methods for Engineers”, 5th Edition, McGraw-Hill, 2006.
3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 9th Edition, John Wiley & Sons, 2006.​