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Complex analysis with applications to flows and fields
1 online resource (1029 pages) : 309 illustrations
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.
Part Part 1 Complex Domain: Circuits and Stability -- chapter 1 Complex Numbers and Quaternions -- chapter 2 Stability of an Equilibrium Position -- chapter 3 Addition, Product, and Inverses -- chapter 4 Impedance of Associations of Circuits -- chapter 5 Power, Root, and Logarithm -- chapter 6 Electron in an Electromagnetic Field -- chapter 7 Multivalued Functions, Branch-Points, and Branch-Cuts -- chapter 8 Motion of a Pendulum and a Ship -- chapter 9 Stereographic Projection and Genus of a Surface -- chapter 10 Examples 10.1 to 10.20 -- part Part 2 Integrals and Residues: Flows and Gravity -- chapter 11 Di?erentiation and Holomorphic Functions -- chapter 12 Potential Flow and Multipoles -- chapter 13 Primitive and Contour Integrals -- chapter 14 Pressure and Corner Flows -- chapter 15 Loop Integrals and Poles -- chapter 16 Images on Plane Walls -- chapter 17 Improper Integrals and Principal Value -- chapter 18 Mass and the Gravity Field -- chapter 19 Cauchy Conditions and Inαnitesimals -- chapter 20 Examples 20.1 to 20.20 -- part Part 3 Power Series: Electricity and Magnetism -- chapter 21 Convergence of and Operations on Series -- chapter 22 Multiple Reβections in a Lens -- chapter 23 Analytic Series of Ascending Powers -- chapter 24 Electrostatics, Charges, and Dielectrics -- chapter 25 Singular Series of Ascending-Descending Powers -- chapter 26 Magnetostatics, Currents, and Permeability -- chapter 27 Classiαcation of Singularities and Functions -- chapter 28 Forces and Moments on Bodies -- chapter 29 Combined Test of Convergence -- chapter 30 Examples 30.1 to 30.20 -- part Part 4 Conformal Mapping: Heat and Aerodynamics -- chapter 31 Analytic Continuation and Rational Functions -- chapter 32 Steady Heat Conduction -- chapter 33 Conformal and Critical Points -- chapter 34 Wing Sections and Planforms -- chapter 35 Linear and Homographic Transformations -- chapter 36 Channels, Condensers, and Wakes -- chapter 37 Mapping of Domains and Boundaries -- chapter 38 Hodograph for Free Jets -- chapter 39 Essential Singularities, Roots, and Periods -- chapter 40 Examples 40.1 to 40.20.