Advanced Topics in Applied Mathematics: For Engineering and by Sudhakar Nair

By Sudhakar Nair

This publication is perfect for engineering, actual technology, and utilized arithmetic scholars and execs who are looking to increase their mathematical wisdom. complex subject matters in utilized arithmetic covers 4 crucial utilized arithmetic subject matters: Green's features, fundamental equations, Fourier transforms, and Laplace transforms. additionally incorporated is an invaluable dialogue of themes resembling the Wiener-Hopf process, Finite Hilbert transforms, Cagniard-De Hoop strategy, and the right kind orthogonal decomposition. This publication displays Sudhakar Nair's lengthy lecture room adventure and contains quite a few examples of differential and indispensable equations from engineering and physics to demonstrate the answer strategies. The textual content contains workout units on the finish of every bankruptcy and a recommendations handbook, that's to be had for teachers.

Show description

Read or Download Advanced Topics in Applied Mathematics: For Engineering and the Physical Sciences PDF

Similar applied books

Tietz's Applied Laboratory Medicine, Second Edition

Utilizing a problem-based procedure, Tietz's utilized Laboratory drugs, moment variation offers fascinating situations to demonstrate the present use and interpretation of the main in most cases to be had scientific laboratory assessments. The instances current precise descriptions of the indicators, analysis, and remedy of illness.

Principles of Applied Clinical Chemistry Chemical Background and Medical Applications: Volume 1: Maintenance of Fluid and Electrolyte Balance

"Clinical Chemistry encompasses the research of the basic princi­ ples of chemistry as utilized to an figuring out of the functioning of the human organism in well-being and illness. " 1 From its very definition, scientific chemistry is an utilized technology. Its scope contains the subsequent: I. reviews designed to explain the chemical mechanisms wherein the human more often than not capabilities.

CRC Concise Encyclopedia of Mathematics, Second Edition

Upon book, the 1st variation of the CRC Concise Encyclopedia of arithmetic acquired overwhelming accolades for its exceptional scope, clarity, and software. It quickly took its position one of the best promoting books within the background of Chapman & Hall/CRC, and its reputation maintains unabated. but additionally unabated has been the commitment of writer Eric Weisstein to gathering, cataloging, and referencing mathematical proof, formulation, and definitions.

Extra info for Advanced Topics in Applied Mathematics: For Engineering and the Physical Sciences

Example text

The angle φ gives a rigidbody rotation. 204) which solves the Laplace equation on a unit circle. In this form, it is easy to see that g is indeed zero when r = 1. Conformal mapping can be used to map domains onto a unit circle and the Green’s function, Eq. 204), can be used to solve the Poisson equation. In particular, the Schwartz-Christoffel transform maps polygons onto the upper half plane. 205) (x, y) ∈ ∂ . 206) with the boundary condition u = h, Let g satisfy ∇ 2 g = δ(x − ξ , y − η), g=0 on (x, y) ∈ ∂ .

In Chapters 3 and 4, using the Fourier and Laplace transform methods, additional Green’s functions are developed. These include the Green’s functions of heat conduction and wave propagation problems. There is an extensive literature concerning the use of Green’s functions in quantum mechanics, and the famous Feynman diagrams deal with perturbation expansions of Green’s functions. , and Stegun, I. (1965). Handbook of Mathematical Functions (National Bureau of Standards), Dover. , and Litkouhi, B.

159) where i , j , and k are the cartesian unit vectors, we can write the Sturm-Liouville equation as ∇ · (p∇u) + qu = f . 161) Let be the outward normal to the boundary surface ∂ . The inner product is now defined as the volume integral u, v = uvd . 162) As before, let the Green’s function, g(x, ξ ), satisfy Lg = δ(x − ξ ). 164) Then provided g satisfies the homogeneous boundary conditions on ∂ . We now have u(x) = g(x, ξ )f (ξ )d . 165) Formally, this shows the Green’s function representation of the solution of any self-adjoint partial differential equation in an n-dimensional domain.

Download PDF sample

Rated 4.67 of 5 – based on 10 votes