Complex Analysis With Applications to Flows and Fields

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.

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.

Complex Domain: Circuits and StabilityComplex numbers and quaternionsStability of an equilibrium positionAddition, product, and inversesImpedance of associations of circuitsFunctions power and rootElectron in an electromagnetic fieldMultivalued functions, branch-points, and branch-cutsMotion of a pendulum and a shipStereographic projection of a sphereExamples
Integrals and Residues: Flows and GravityDifferentiation and holomorphic functionsPotential flow and multipolesPrimitive and contour integralsPressure and corner flowsLoop integrals and polesImages on plane wallsImproper integrals and principal valueMass and the gravity fieldCauchy conditions and infinitesimalsExamples
Power Series: Electricity and MagnetismConvergence of and operations on seriesMultiple reflections in a lensAnalytic series of ascending powersElectrostatics, charges, and dielectricsSingular series of ascending–descending powersMagnetostatics, currents, and permeabilityClassification of singularities and functionsForces and moments on bodiesCombined test of convergenceExamples
Conformal Mapping: Heat and AerodynamicsAnalytic continuation and rational functionsSteady heat conductionConformal and critical pointsWing sections and planformsLinear and homographic transformationsChannels, condensers, and wakesMapping of domains and boundariesHodograph for free jetsEssential singularities, roots, and periodsExamples
Bibliography
Index