1st Edition

Complex Analysis with Applications to Flows and Fields

    1030 Pages 235 B/W Illustrations
    by CRC Press

    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.

    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

    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

    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

    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




    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.