1st Edition
Advanced Engineering Mathematics with Modeling Applications
Foundations of mathematical modeling
Engineering analysis
Conservation laws and mathematical modeling
Problem formulation
Nondimensionalization
Scaling
Linear algebra
Introduction
Three-dimensional space
Vector spaces
Linear independence
Basis and dimension
Inner products
Norms
Gram-Schmidt orthonormalization
Orthogonal expansions
Linear operators
Adjoint operators
Positive definite operators
Energy inner products
Ordinary differential equations
Linear differential equations
General theory for second-order differential equations
Differential equations with constant coefficients
Differential equations with variable coefficients
Singular points of second-order equations
Bessel functions
Differential equations whose solutions are expressible in terms of Bessel functions
Legendre functions
Variational methods
Introduction
The general variational problem
Variational solutions of operator equations
Finite-element method
Galerkin’s method
Eigenvalue problems
Eigenvalue and eigenvector problems
Eigenvalues of adjoint operators
Eigenvalues of positive definite operators
Eigenvalue problems for operators in finite-dimensional vector spaces
Second-order differential operators
Eigenvector expansions
Fourth-order differential operators
Differential operators with eigenvalues in boundary conditions
Eigenvalue problems involving Bessel functions
Eigenvalue problems in other infinite-dimensional vector spaces
Solvability conditions
Asymptotic approximations to solutions of eigenvalue problems
Rayleigh’s quotient
Rayleigh-Ritz method
Green’s functions
Partial differential equations
Homogeneous partial differential equations
Second-order steady-state problems, Laplace’s equation
Time-dependent problems: Initial value problems
Nonhomogeneous partial differential equations
Problems in cylindrical coordinates
Problems in spherical coordinates
Index
Biography
S. Graham Kelly
