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ENGINEERING MATHEMATICS 2

Module code: EE112
Credits: 5
Semester: 2
Department: THEORETICAL PHYSICS
International:
Coordinator: Prof. Peter Coles (THEORETICAL PHYSICS)
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.

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