(BQ) Part 1 book "Advanced engineering mathematics" has contents: Linear second order equations, first order differential equations, the laplace transform, series solutions, approximation of solutions, vectors and vector spaces, matrices and linear systems,. and other contents. | This page intentionally left blank Guide to Notation L[ f ] Laplace transform of f L[ f ](s) Laplace transform of f evaluated at s L−1 [F] inverse Laplace transform of F H (t) Heaviside function f ∗g often denotes a convolution with respect to an integral transform, such as the Laplace transform or the Fourier transform δ(t) delta function vector with components a, b, c ai + bj + ck standard form of a vector in 3-space V norm (magnitude, length) of a vector V F · G dot product of vectors F and G F × G cross product of F and G n-space, consisting of n-vectors Rn [ai j ] matrix whose i, j-element is ai j . If the matrix is denoted A, this i, j element may also be denoted Ai j Onm n × m zero matrix n × n identity matrix In transpose of A At reduced (row echelon) form of A AR rank(A) rank of a matrix A . [A. .B] augmented matrix inverse of the matrix A A−1 |A| or det(A) determinant of A pA (λ) characteristic polynomial of A often denotes the fundamental matrix of a system X = AX T often denotes a tangent vector N often denotes a normal vector n often denotes a unit normal vector κ curvature ∇ del operator ∇ϕ or grad ϕ gradient of ϕ Du ϕ(P) directional derivative of ϕ in the direction of u at P f d x + g dy + h dz line integral C F · dR another notation for C f d x + g dy + h dz with F = f i + gj + hk C C1 C2 · · · Cn join of curves C1 , C2 , · · · , Cn f (x, y, z) ds line integral of f over C with respect to arc length C 1 Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. October 14, 2010 15:48 THM/NEIL Page-1 27410_00_IFC_p01-02 2 Guide to Notation ∂(
