Building on the author’s previous book in the series, Complex Analysis with Applications to Flows and Fields (CRC Press, 2010), Transcendental Representations with Applications to Solids and Fluids focuses on four infinite representations: series expansions, series of fractions for meromorphic functions, infinite products for functions with infinitely many zeros, and continued fractions as alternative representations. This book also continues the application of complex functions to more classes of fields, including incompressible rotational flows, compressible irrotational flows, unsteady flows, rotating flows, surface tension and capillarity, deflection of membranes under load, torsion of rods by torques, plane elasticity, and plane viscous flows. The two books together offer a complete treatment of complex analysis, showing how the elementary transcendental functions and other complex functions are applied to fluid and solid media and force fields mainly in two dimensions.

The mathematical developments appear in odd-numbered chapters while the physical and engineering applications can be found in even-numbered chapters. The last chapter presents a set of detailed examples. Each chapter begins with an introduction and concludes with related topics.

Written by one of the foremost authorities in aeronautical/aerospace engineering, 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.

Contents

Sequences of Fractions or Products

Power Series, Singularities, and Functions

Series of Fractions for Meromorphic Functions (Mittag-Leffler 1876, 1884)

Meromorphic Function as a Ratio of Two Integral Functions

Factorization with Infinite Number of Zeros

Infinite Products for Circular Functions

Recurrence Formulas and Continued Fractions (Wallis 1656; Euler 173>Optimal and Doubly Bounded Sharpening Approximations

Transformation of Series and Products into Fractions (Euler 1785)

Continued Fraction for the Ratio of Two Series (Lambert 1770)

Conclusion

Compressible and Rotational Flows

Source, Sink, and Vortex in a Compressible Flow

Potential Vortex with Rotational Core (Rankine; Hallock and Burnham 1997)

Minimum Energy (Thomson 1849) and Intrinsic Equations of Motion

Laplace/Poisson Equations in Complex Conjugate Coordinates

Second Forces/Moment and Circle Theorems

Cylinder in a Unidirectional Shear Flow

Monopole Interactions and Equilibrium Positions

Cylinder in a Stream with Two Trailing Monopoles (Föppl 1913)

Reciprocity Theorem (Green 1828) and Path Function (Routh 1881)

Conclusion

Exponential and Logarithmic Functions

Derivation Property, Series, and Rational Limit

Continued Fractions and Computation of the Number e

Transformation of Sums t...