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E-raamat: Complex Analysis for Practical Engineering

  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Mar-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319130637
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Complex Analysis for Practical EngineeringSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 02-Mar-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319130637
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Maximizing reader insights into the fundamentals of complex analysis, and providing complete instructions on how to construct and use mathematical tools to solve engineering problems in potential theory,  this  book covers complex analysis in the context of  potential flow problems. The basic concepts and  methodologies covered are easily extended  to other problems of potential theory.

Featuring case studies and problems that aid readers understanding of  the key topics and of  their application  to practical engineering problems, this book is suitable as a guide for engineering practitioners.

The complex analysis problems discussed in this book will prove useful in solving practical problems in a variety of engineering disciplines, including flow dynamics, electrostatics, heat conduction and gravity fields.

 
1 Potential Theory in Practical Engineering
1(18)
1.1 Potential Flow
2(7)
1.1.1 Continuity Equation
2(2)
1.1.2 Irrotationality
4(1)
1.1.3 Discharge and Circulation
5(1)
1.1.4 Laplace's Equation
6(1)
1.1.5 Flow in Porous Media
7(2)
1.2 Physical Processes in Potential Theory
9(2)
1.2.1 Fickian Diffusion
9(1)
1.2.2 Heat Conduction
9(1)
1.2.3 Gravitational Fields
10(1)
1.2.4 Electrostatic Fields
11(1)
1.3 Velocity Potential
11(8)
1.3.1 Uniform Flow
11(1)
1.3.2 Sources and Sinks
12(1)
1.3.3 Equipotential Lines
13(1)
1.3.4 Principle of Superposition
14(5)
2 Complex Potential and Differentiation
19(62)
2.1 Complex Numbers
20(12)
2.1.1 Definition
20(1)
2.1.2 Algebraic Properties
21(1)
2.1.3 Complex Plane
22(2)
2.1.4 Polar Form of Complex Numbers
24(2)
2.1.5 Exponential Form of Complex Numbers
26(2)
2.1.6 Roots
28(4)
2.2 Functions of a Complex Variable
32(3)
2.2.1 Definition
32(1)
2.2.2 Elementary Functions
33(2)
2.3 Complex Differentiation
35(13)
2.3.1 Limit and Continuity
35(2)
2.3.2 Differentiability
37(2)
2.3.3 Analytic Functions
39(1)
2.3.4 L'Hospital's Rule
40(2)
2.3.5 Cauchy---Riemann Equations in Cartesian Form
42(4)
2.3.6 Cauchy---Riemann Equations in Polar Form
46(2)
2.4 Harmonic Functions
48(5)
2.4.1 Analyticity of Elementary Functions
48(1)
2.4.2 Laplace's Equation in Cartesian Form
49(1)
2.4.3 Laplace's Equation in Polar Form
50(1)
2.4.4 Harmonic Conjugate
51(2)
2.5 Stream Function and Complex Potential
53(12)
2.5.1 Definition
53(1)
2.5.2 Uniform Flow
54(1)
2.5.3 Sources and Sinks
55(1)
2.5.4 Streamlines
56(2)
2.5.5 Complex Velocity
58(7)
2.6 Further Topics in Complex Potential
65(16)
2.6.1 Orthogonal Families
65(3)
2.6.2 Streamlines as Impermeable Boundaries
68(2)
2.6.3 Discharge and Stream Function
70(3)
2.6.4 Circulation and Velocity Potential
73(2)
2.6.5 Dipoles
75(1)
2.6.6 Vortices
76(5)
3 Transformation and Conformal Mapping
81(48)
3.1 Analytic Function and Mapping
82(9)
3.1.1 Analyticity and Conformality
82(6)
3.1.2 General Transformations
88(3)
3.2 Mapping by Elementary Functions
91(8)
3.2.1 Linear Function
91(2)
3.2.2 Power Function
93(2)
3.2.3 Bilinear Function
95(1)
3.2.4 Exponential Function
96(1)
3.2.5 Logarithmic Function
97(2)
3.3 Applications of Conformal Mapping
99(11)
3.3.1 Composition
99(4)
3.3.2 Joukowski Transformation
103(7)
3.4 Mobius Transformation
110(11)
3.4.1 Extended Complex Plane
110(3)
3.4.2 Fixed Points
113(1)
3.4.3 Cross Ratio
114(7)
3.5 Schwarz---Christoffel Transformation
121(8)
3.5.1 The Real Axis and a Polygon
121(3)
3.5.2 Transformation in Integral Form
124(1)
3.5.3 Parametric Equations for Flow Profiles
125(4)
4 Boundary Value Problems and Integration
129(48)
4.1 Boundary Value Problems
130(4)
4.1.1 Domain and Boundary
130(2)
4.1.2 Boundary Conditions in Engineering Problems
132(1)
4.1.3 Boundary Conditions in Complex Analysis
133(1)
4.2 Complex Integration
134(16)
4.2.1 Contours
135(1)
4.2.2 Contour Integrals
136(2)
4.2.3 Definite Integrals
138(4)
4.2.4 Cauchy's Integral Theorem
142(4)
4.2.5 Cauchy's Integral Formula
146(4)
4.3 Complex Variable Boundary Element Method
150(9)
4.3.1 Mathematical Preliminaries of the CVBEM
150(1)
4.3.2 Discretization
151(4)
4.3.3 Cauchy's Integral Formula in Discretized Form
155(1)
4.3.4 Nodal Equation
156(3)
4.4 Formulations of the CVBEM
159(9)
4.4.1 Known-Variable Equivalence
160(3)
4.4.2 Unknown-Variable Equivalence
163(3)
4.4.3 Dual-Variable Equivalence
166(2)
4.5 Moduli of Functions
168(9)
4.5.1 Mean Value Properties
169(1)
4.5.2 Maximum Modulus Theorem
169(8)
5 Singularity and Series
177(66)
5.1 Sequences and Series
178(3)
5.1.1 Convergence of Sequences
178(1)
5.1.2 Convergence of Series
179(1)
5.1.3 Power Series
180(1)
5.2 Taylor Series
181(6)
5.2.1 Taylor's Theorem
181(3)
5.2.2 Special Taylor Series
184(1)
5.2.3 Uniqueness of Taylor Series Expansions
185(2)
5.3 Laurent Series
187(7)
5.3.1 Laurent's Theorem
188(5)
5.3.2 Uniqueness of Laurent Series Expansions
193(1)
5.4 Singularities and Zeros
194(8)
5.4.1 Classification of Singularities
194(3)
5.4.2 Zeros of Analytic Functions
197(2)
5.4.3 Poles and Zeros
199(3)
5.5 Residue Theory
202(19)
5.5.1 Residues
202(2)
5.5.2 Residues at Poles
204(3)
5.5.3 Residue Theorem
207(2)
5.5.4 Residue Integration of Real Integrals
209(12)
5.6 Applications of Laurent Series
221(10)
5.6.1 Flow Through a Distorted Circle
221(3)
5.6.2 Flow Around a Source-Sink Pair
224(7)
5.7 Implicit Singularity Programming
231(12)
5.7.1 Flow Through a Finite Conductivity Fracture
231(1)
5.7.2 Singular Solution of Fractures
232(2)
5.7.3 Procedure and Formulation
234(6)
5.7.4 Flow Over a Thin Shield
240(3)
6 Further Applications in Practical Engineering
243(38)
6.1 Explicit Singularity Programming
244(13)
6.1.1 Singular Solution of Sources and Sinks
244(1)
6.1.2 Procedure and Formulation
245(1)
6.1.3 Branch Cuts Across a Boundary
246(7)
6.1.4 Logarithmic Singularity on a Boundary
253(4)
6.2 Generalized Singularity Programming
257(6)
6.2.1 Commingled Singularities
258(1)
6.2.2 Multiple Fractures
259(4)
6.3 Streamline Tracking
263(18)
6.3.1 Velocity Vector Method
263(2)
6.3.2 Stream Function Method
265(2)
6.3.3 Evaluation of Complex Velocities
267(1)
6.3.4 Streamlines Through Fractures
268(1)
6.3.5 Tracer Transport
269(2)
6.3.6 Streamline Simulation
271(10)
Appendix A Vector Operator 281(4)
Appendix B Relevant Theorems 285(4)
Appendix C Conservative Field 289(2)
Appendix D Coefficients in Singularity Programming 291(6)
Appendix E Example Computation of the CVBEM 297(6)
References 303(2)
Index 305
Kozo Sato, Ph.D., is a professor of Graduate School of Engineering and Director of Frontier Research Centre for Energy and Resources at the University of Tokyo. His areas of expertise include mathematical modelling of fluid flow through heterogeneous media, reservoir characterization through tracer and pressure-transient analyses, and thermodynamics of underground fluid systems, with research interests in petroleum development and CCS (carbon dioxide capture and storage). Sato holds a BS degree from the University of Tokyo, and MS and Ph.D. degrees from Stanford University, all in petroleum engineering.
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