Advanced engineering mathematics, SI / Peter V. O'neil

Includes Index.

Table of Contents. – Ch.1 Ordinary differential equations - - First –order differential equations - - Exact equations - - Homogeneous, Bernoulli, and Riccati equations - - Numerical methods - - Singular solutions - - Some Applications of separable equations. – Ch. 2 Second order differential equations - - The Linear second order equation problems - - method of variation of parameters - - Method of Undetermined coefficients - - The Euler differential equation - - Series Solutions. Ch. 3 the Laplace transform - - Solution of initial value problems - - Implulses and the dirac delta function - - The Heaviside function and shifting theorems - - Heaviside’s Formula - - Systems of linear differential equations. – Ch. 4 Sturm-Liouville problems and Eigenfunction expansions - - Eigenvalues, Eigenfunctions and sturm-liouville problems - - Eigenfunction expansions - - Properties of coefficients - - Fourier series. – Ch.5 The Heat equation - - diffusion problems in bounded medium - - Insulated ends - - One radiating end - - Nonhomogeneous Boundary conditions - - The heat equation on the real line - - Derivation of the heat equation - - A Reformulation of the solution on the line. – Ch. 6 The wave equation - - Wave motion on a bounded interval - - Wave motion in an unbounded medium - - d’Alembert’s solution and characteristics - - The wave equation with a forcing term and higher dimensions. – Ch. 7 Laplace’s equation - -The dirrichlet problems for a Rectangle, Disk - - The Poisson integral formula - - A Dirichlet problem in 3 Dimensions - - The Neumann problem. – Ch. 8 Special functions and applications - - Legendre Polynomials - - Bessel functions - - Some applications of Bessel functions. – Ch. 9 Transform methods of solution - - Laplace transform methods - - Fourier transform methods - - Fourier sine and cosine transform methods. – Ch. 10 Matrices and linear Algebra - - Vectors and the vector space Rn - - Vectors in the plane and 3-space - - The Dot product - - The Cross product - - n-Vectors and the algebraic structure of Rn - - Orthogonal sets and orthogonalization. – Ch. 11 Matrices, Determinants, and Linear systems - - Row operations and reduced matrices - - Solution of homogeneous linear systems - - Matrix inverses - - Determinants - - Cramer’s rule - - The Matrix tree theorem - - A determinant formula for a matrix inverse. – Ch. 12 Eigenvalues, Diagonalization, and special matrices - - Eigenvalues and Eigenvectors - - Diagonalization - - Symmetric matrices. – Ch. 13 Systems differential equations - - Systems of Linear differential equations - - Linear systems. – Ch. 14 Nonlinear systems and qualitative analysis - - Linearization. – Ch. 15 Vector analysis - - Vector differential calculus - - vector functions of one variable. – Ch. 16 Vector Integral calculus - - line integrals - - Green’s theorem - - Surface integrals - - Gauss’s divergence theorem - - Stokes’s theorem. – Ch. 17 Fourier analysis - - Fourier series - - Sine and cosine series. – Ch. 18 Fourier transforms. – Ch. 19 Complex functions - - Complex numbers and functions - - Geometry and Arithmetic of complex numbers - - Complex functions - - The exponential and trigonometric functions - - The Complex logarithm. – Ch. 20 Integration - - The Integral of a complex function - - Cauchy’s Theorem. – Ch. 21 Series representations of functions - - Power series - - The Laurent Expansion. – Ch. 22 Singularities and the residue theorem - - Classification of singularities - - Evaluation of real integrals. – Ch. 23 Conformal mappings - - Bilinear transformations.