Applied Complex Variables for Scientists and EngineersCambridge University Press, 7 de fev. de 2002 - 392 páginas This is an introduction to complex variable methods for scientists and engineers. It begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. One feature that will appeal to scientists is the high proportion of the book devoted to applications of the material to physical problems. These include detailed treatments of potential theory, hydrodynamics, electrostatics, gravitation and the uses of the Laplace transform for partial differential equations. The text contains some 300 stimulating exercises of high quality, with solutions given to many of them. It will be highly suitable for students wishing to learn the elements of complex analysis in an applied context. |
Conteúdo
II | 1 |
III | 5 |
IV | 7 |
V | 13 |
VI | 16 |
VII | 17 |
VIII | 22 |
IX | 26 |
LVI | 160 |
LVII | 164 |
LVIII | 169 |
LIX | 177 |
LXII | 179 |
LXIII | 180 |
LXIV | 183 |
LXV | 184 |
X | 27 |
XI | 29 |
XII | 33 |
XIII | 40 |
XV | 42 |
XVI | 44 |
XVII | 47 |
XVIII | 48 |
XX | 50 |
XXI | 52 |
XXII | 54 |
XXIII | 55 |
XXIV | 60 |
XXV | 61 |
XXVI | 63 |
XXVII | 65 |
XXVIII | 69 |
XXIX | 73 |
XXX | 74 |
XXXI | 81 |
XXXIV | 82 |
XXXV | 84 |
XXXVI | 85 |
XXXVII | 90 |
XXXVIII | 92 |
XXXIX | 94 |
XL | 96 |
XLI | 99 |
XLII | 102 |
XLIII | 105 |
XLIV | 109 |
XLV | 112 |
XLVI | 118 |
XLVII | 119 |
XLVIII | 120 |
XLIX | 127 |
L | 136 |
LI | 138 |
LII | 142 |
LIV | 147 |
LXVI | 186 |
LXVII | 190 |
LXVIII | 196 |
LXIX | 205 |
LXX | 208 |
LXXI | 211 |
LXXII | 212 |
LXXIII | 221 |
LXXIV | 227 |
LXXV | 232 |
LXXVII | 234 |
LXXVIII | 236 |
LXXIX | 239 |
LXXX | 243 |
LXXXI | 244 |
LXXXII | 248 |
LXXXIII | 251 |
LXXXIV | 258 |
LXXXVI | 262 |
LXXXVII | 263 |
LXXXVIII | 272 |
LXXXIX | 273 |
XCI | 280 |
XCII | 285 |
XCIII | 287 |
XCIV | 291 |
XCV | 298 |
XCVII | 303 |
XCVIII | 308 |
XCIX | 326 |
C | 332 |
CI | 335 |
CII | 338 |
CIII | 341 |
CIV | 350 |
CV | 358 |
CVI | 368 |
CVII | 377 |
389 | |
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Termos e frases comuns
analytic function angle bilinear transformation boundary condition branch cut branch point C₁ C₂ Cauchy integral formula Cauchy-Riemann relations closed contour complex function complex numbers complex plane complex potential complex variable Consider constant contour integral convergence corresponding cosh deduce defined denote derivative differential domain equation Evaluate Example f(zo Figure Find finite flow field Fourier function f(z given harmonic function imaginary inequality infinite inside integrand inverse Laplace transform Laurent series mapping modulus multi-valued function obtain potential flow power series problem radius real axis real numbers region residue respectively Riemann sphere satisfies semi-infinite Show sin² sinh Solution steady state temperature streamlines Suppose f(z symmetric points Taylor series theorem unit circle upper half-plane vector velocity vertical w₁ w₂ x-axis z-plane z₁ and z2 zero ду дф дх
Referências a este livro
Mathematical Methods for Engineers and Scientists 1: Complex Analysis ... Kwong-Tin Tang Visualização parcial - 2006 |