ABSTRACT

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 he

part |2 pages

Part 1 Complex Domain: Circuits and Stability

chapter 1|10 pages

Complex Numbers and Quaternions

chapter 2|10 pages

Stability of an Equilibrium Position

chapter 3|10 pages

Addition, Product, and Inverses

chapter 4|10 pages

Impedance of Associations of Circuits

chapter 5|10 pages

Power, Root, and Logarithm

chapter 6|12 pages

Electron in an Electromagnetic Field

chapter 8|10 pages

Motion of a Pendulum and a Ship

chapter 10|18 pages

Examples 10.1 to 10.20

part |2 pages

Part 2 Integrals and Residues: Flows and Gravity

chapter 11|12 pages

Differentiation and Holomorphic Functions

chapter 12|16 pages

Potential Flow and Multipoles

chapter 13|12 pages

Primitive and Contour Integrals

chapter 14|24 pages

Pressure and Corner Flows

chapter 15|14 pages

Loop Integrals and Poles

chapter 16|24 pages

Images on Plane Walls

chapter 17|18 pages

Improper Integrals and Principal Value

chapter 18|18 pages

Mass and the Gravity Field

chapter 19|12 pages

Cauchy Conditions and Infinitesimals

chapter 20|22 pages

Examples 20.1 to 20.20

part |2 pages

Part 3 Power Series: Electricity and Magnetism

chapter 21|20 pages

Convergence of and Operations on Series

chapter 22|18 pages

Multiple Reflections in a Lens

chapter 23|18 pages

Analytic Series of Ascending Powers

chapter 24|22 pages

Electrostatics, Charges, and Dielectrics

chapter 26|24 pages

Magnetostatics, Currents, and Permeability

chapter 28|54 pages

Forces and Moments on Bodies

chapter 29|22 pages

Combined Test of Convergence

chapter 30|26 pages

Examples 30.1 to 30.20

part |2 pages

Part 4 Conformal Mapping: Heat and Aerodynamics

chapter 31|24 pages

Analytic Continuation and Rational Functions

chapter 32|28 pages

Steady Heat Conduction

chapter 33|20 pages

Conformal and Critical Points

chapter 34|54 pages

Wing Sections and Planforms

chapter 35|20 pages

Linear and Homographic Transformations

chapter 36|66 pages

Channels, Condensers, and Wakes

chapter 37|42 pages

Mapping of Domains and Boundaries

chapter 38|56 pages

Hodograph for Free Jets

chapter 39|44 pages

Essential Singularities, Roots, and Periods

chapter 40|56 pages

Examples 40.1 to 40.20