BSc in Mechanical Engineering

Course Information Package

Course Unit CodeAMAT181
Course Unit DetailsBSc Automotive Engineering (Required Courses) - BSc Mechanical Engineering (Required Courses) - BSc Civil Engineering (Required Courses) - BSc Electrical Engineering (Required Courses) - BSc Computer Engineering (Required Courses) - BSc Computer Science (Required Courses) -
Number of ECTS credits allocated5
Learning Outcomes of the course unitBy the end of the course, the students should be able to:
  1. Explain the notion of a matrix, including its transpose, identify the properties of special types of matrices and perform different matrix operations.
  2. Generate determinants of any order using minors, compute 2x2, 3x3 determinants directly and find the inverse of a matrix by employing its determinant and the transpose of the matrix of cofactors.
  3. Use Cramer’s Rule for solving square linear systems with the aid of determinants, employ Gaussian Elimination for solving systems of linear equations, perform elementary row matrix reduction to echelon form and back substitution to obtain the solution of the system, apply Gaussian Elimination to find the inverse of a square matrix using augmentation, execute Gauss-Jordan elimination and implement a readily available inverse of the matrix of coefficients to solve a square linear system.
  4. Explain the notion of multiplicity of roots of the characteristic equation, employ these concepts to various applications and compute eigenvalues and corresponding eigenvectors of square matrices.
  5. Defend the notion of vectors in two, three and higher dimensions, perform operations with vectors including dot/Cartesian and vector products, outline the concept of an orthogonal basis of the Euclidean space as well as the geometric structure of linearly independent vectors, show vector linear transformations in concrete geometric examples and exploit the properties of vector spaces and subspaces.
  6. Define linear transformations, perform elementary transformations available, rank and determinants and apply these concepts to real-life examples identifying their geometric implications.
  7. Employ the computer programming language Matlab to solve different matrix operations and systems of linear equations, to compute eigenvalues and eigenvectors, to execute elementary vector manipulation, to exhibit linear transformations and to construct plots.
Mode of DeliveryFace-to-face
Recommended optional program componentsNONE
Course Contents

Vectors and Linear spaces. Vector concept, operations with vectors, generalization to higher dimensions, Euclidean space, basis, orthogonal basis: linear dependence, Cartesian products, vector products, vector transformations, Gram-Schmidt orthogonalization, vector spaces and subspaces. Geometric examples.

Matrices and Determinants. Matrix concept, operations with matrices, Special matrices, definition of a determinant and its properties, determinant of a product, inverse matrix, properties and computation.

Linear Transformations. Definition of linear transformations, properties, elementary transformations, rank and determinants.

Simultaneous Linear Equations. Cramer’s rule, Gaussian elimination, Gauss-Jordan elimination, homogeneous linear equations, geometric interpretation.

Quadratic forms and Eigenvalue Problem. Quadratic forms, definitions, Normal form, eigenvalue problem, characteristic equation, eigenvalues and eigenvectors, singular value decomposition.

MATLAB Applications. Basic matrix algebra, the determinant of a matrix of n-order, solving simultaneous equations with n unknowns with a number of techniques, finding eigenvalues and eigenvectors. Elementary vector manipulation, finding linear dependence. Linear Transformations, plotting transforms on the x-y plane.

Recommended and/or required reading:
  • Gareth W., Linear Algebra with Applications, Jones and Barlett Pubs, 2000
  • Anton H., Elementary Linear Algebra with Applications, John Wiley, 2000.
  • Anton H., Contemporary Linear Algebra MATLAB Technology Resource Manual, John Wiley, 2002.
Planned learning activities and teaching methods

The taught part of course is delivered to the students by means of lectures, conducted with the aid of computer presentations. Lecture notes and presentations are available through the web for students to use in combination with the textbooks.

Computer Laboratories are utilized for special Matlab sessions, students learn how to use Matlab effectively, develop the functional units taught in lectures and gain greater insight into the underline mathematics.

Several examples and exercises are solved in class to practice the theory and methodology taught. Students work on their own during class hours on examples and practice problems. Extra assignments are given to students to tackle at home, including exercises using MATLAB.
Assessment methods and criteria
Final Exam60%
Language of instructionEnglish
Work placement(s)NO