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## ENGINEERING MATHEMATICS 2

Module code: EE112
Credits: 5
Semester: 2
Department: THEORETICAL PHYSICS
International:  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. Learning Outcomes Teaching & Learning methods Assessment Repeat options Timetable 