Complex Analysis with Applications to Flows and Fields: 1st Edition (Hardback) book cover

Complex Analysis with Applications to Flows and Fields

1st Edition

By Luis Manuel Braga da Costa Campos

CRC Press

1,029 pages | 235 B/W Illus.

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Hardback: 9781420071184
pub: 2010-09-03
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Description

Complex Analysis with Applications to Flows and Fields presents the theory of functions of a complex variable, from the complex plane to the calculus of residues to power series to conformal mapping. The book explores numerous physical and engineering applications concerning potential flows, the gravity field, electro- and magnetostatics, steady heat conduction, and other problems. It provides the mathematical results to sufficiently justify the solution of these problems, eliminating the need to consult external references.

The book is conveniently divided into four parts. In each part, the mathematical theory appears in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. Each chapter begins with an introduction or summary and concludes with related topics. The last chapter in each section offers a collection of many detailed examples.

This self-contained book gives the necessary mathematical background and physical principles to build models for technological and scientific purposes. It shows how to formulate problems, justify the solutions, and interpret the results.

Table of Contents

Complex Domain: Circuits and Stability

Complex numbers and quaternions

Stability of an equilibrium position

Addition, product, and inverses

Impedance of associations of circuits

Functions power and root

Electron in an electromagnetic field

Multivalued functions, branch-points, and branch-cuts

Motion of a pendulum and a ship

Stereographic projection of a sphere

Examples

Integrals and Residues: Flows and Gravity

Differentiation and holomorphic functions

Potential flow and multipoles

Primitive and contour integrals

Pressure and corner flows

Loop integrals and poles

Images on plane walls

Improper integrals and principal value

Mass and the gravity field

Cauchy conditions and infinitesimals

Examples

Power Series: Electricity and Magnetism

Convergence of and operations on series

Multiple reflections in a lens

Analytic series of ascending powers

Electrostatics, charges, and dielectrics

Singular series of ascending–descending powers

Magnetostatics, currents, and permeability

Classification of singularities and functions

Forces and moments on bodies

Combined test of convergence

Examples

Conformal Mapping: Heat and Aerodynamics

Analytic continuation and rational functions

Steady heat conduction

Conformal and critical points

Wing sections and planforms

Linear and homographic transformations

Channels, condensers, and wakes

Mapping of domains and boundaries

Hodograph for free jets

Essential singularities, roots, and periods

Examples

Bibliography

Index

About the Author

Luis Manuel Braga da Costa Campos is the director of the Center for Aeronautical and Space Science and Technology at Lisbon Technical University in Portugal.

About the Series

Mathematics and Physics for Science and Technology

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied