
Federal University OyeEkiti Institutional Repository >
FACULTY OF ENGINEERING >
Mechanical Engineering >
Mechanical Engineering Course Outline >
Please use this identifier to cite or link to this item:
http://repository.fuoye.edu.ng/handle/123456789/475

Title:  Engineering MathematicsIII 
Authors:  FUOYE 
Keywords:  Matrices and Determinants Laplace’s development Eigenvectors 
Issue Date:  23Mar2015 
Abstract:  Matrices and Determinants: Matrices, some special matrices, matrix
operations. Determinants and some useful theorems.
• Laplace’s development. Solution of system of linear equations by
determinants. Linear dependence and independence, rank of a matrix.
General system of linear equations, existence and properties of solution,
Gaussian elimination. Matrix inverse by elementary matrices, adjoint, and
partitioning methods. Characteristic polynomial, characteristic equation,
eigenvalues and eigenvectors. Diagonalization of matrices, application to
system of first order linear differential equations.
• Multiple Integrals: Iterated integrals, multiple integrals over elementary
regions. Change of variables, Jacobians. Differentiation of integrals involving
a parameter, Leibniz’s rule.
• Vector Algebra: Vector field, gradient and directional derivative, divergence,
curl. Line and surface integrals, Stoke’s theorem. Volume integrals,
divergence theorem. Orthogonal transformations, scale factors, basis
vectors. Cylindrical and spherical polar coordinate systems, gradient,
divergence and curl in these systems.
• Fourier Series: periodic functions, trigonometric series. Fourier coefficients,
Parsevals theorem, Functions of arbitrary period, even and odd functions.
Half range expansion. Complex form of Fourier series. Integral Transform:
Derivation of transforms and inverses (Fourier and Laplace). Applications of
these transforms in boundary and initial value problems. Z transforms.
• Partial Differential Equations: Elementary properties of Gamma, Beta, Error,
Bessel functions and Legendre polynomials. Basic concepts of partial
differential equations. Classification of 2nd order linear partial differential
equation into basic types. The principle of superposition. The wave, diffusion
and Poisson’s equations. Boundary and initialvalue problems. D’Alembert’s
solution for wave equation. Method of separation of variables. Biharmonic
equation. 
Description:  Matrices and Determinants: Matrices, some special matrices, matrix
operations. Determinants and some useful theorems.
• Laplace’s development. Solution of system of linear equations by
determinants. Linear dependence and independence, rank of a matrix.
General system of linear equations, existence and properties of solution,
Gaussian elimination. Matrix inverse by elementary matrices, adjoint, and
partitioning methods. Characteristic polynomial, characteristic equation,
eigenvalues and eigenvectors. Diagonalization of matrices, application to
system of first order linear differential equations.
• Multiple Integrals: Iterated integrals, multiple integrals over elementary
regions. Change of variables, Jacobians. Differentiation of integrals involving
a parameter, Leibniz’s rule.
• Vector Algebra: Vector field, gradient and directional derivative, divergence,
curl. Line and surface integrals, Stoke’s theorem. Volume integrals,
divergence theorem. Orthogonal transformations, scale factors, basis
vectors. Cylindrical and spherical polar coordinate systems, gradient,
divergence and curl in these systems.
• Fourier Series: periodic functions, trigonometric series. Fourier coefficients,
Parsevals theorem, Functions of arbitrary period, even and odd functions.
Half range expansion. Complex form of Fourier series. Integral Transform:
Derivation of transforms and inverses (Fourier and Laplace). Applications of
these transforms in boundary and initial value problems. Z transforms.
• Partial Differential Equations: Elementary properties of Gamma, Beta, Error,
Bessel functions and Legendre polynomials. Basic concepts of partial
differential equations. Classification of 2nd order linear partial differential
equation into basic types. The principle of superposition. The wave, diffusion
and Poisson’s equations. Boundary and initialvalue problems. D’Alembert’s
solution for wave equation. Method of separation of variables. Biharmonic
equation. 
URI:  http://repository.fuoye.edu.ng/handle/123456789/475 
Appears in Collections:  Mechanical Engineering Course Outline

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
