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Module code: EE112
Credits: 5
Semester: 2
International: Yes
Overview Overview

Indicative Syllabus
• Introduction, motivation and scope
• The Laplace Transform
• Basic Laplace Transform
• Inverse Laplace Transform
• Solving first-order ODEs using the Laplace Transform.
• Vector algebra
• Vectors in coordinate independent form and in 2-Space, 3-Space and n-Space.
• Addition, multiplication of vectors by a scalar.
• Basic properties of vectors, subtraction and scalar (dot) and vector (cross) product of vectors.
• Rules of Vector algebra.
• Unit vectors i,j,k.
• Inner (Dot) product in n-space and Vector (Cross) product in 3space.
• Orthogonality of vectors.
• Applications of inner and vector products.
• Vector equation of a line in 3-space, Equation of plane in 3-space.
• Triple scalar product, Triple vector product.
• Time derivative of a vector function.
• Vector equation of a curve in parametric form in 2 and 3 space.
• Arc length, unit tangent, unit principal normal vectors. Curvature.
• Matrix algebra
• Overview of Matrix algebra and its usefulness in solving systems of linear equations.
• Matrix addition, subtraction and multiplication.
• Matrix properties – transpose, symmetric, rank
• Solving linear systems of equations using Gaussian and Gauss-Jordan elimination.
• Special matrices such as the identity matrix, the zero matrix, and orthogonal matrices.
• Solving linear systems using the inverse of a matrix. Properties of the inverse matrix.
• Calculating the inverse matrix using row operations.
• Definition of the determinant and discussion of its properties.
• Calculating the inverse matrix using the method of cofactors.
• Solving linear systems using the inverse matrix and Cramer’s rule.
• Eigenvalues and eigenvectors.
• Diagonalization of matrices. Cayley-Hamilton theorem.
• Linear Independence, basis and dimension, with connection to row operations and determinant.

Open Learning Outcomes
Open Teaching & Learning methods
Open Assessment
Open Autumn Supplementals/Resits
Open Pre-Requisites
Open Co-Requisites
Open Timetable
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