000			05161 a2200277 4500
008			2012
020			_a9781449628703
040			_aGAMADERO _bspa _cGAMADERO
041			_aeng
050	0	0	_aQA331.7 _bM37 _c2012
100			_aMathews John
245			_aComplex analysis / _bfor mathematics and engineering
250			_a6a Edición
260			_bJONES AND BARTLETT LEARNING _aUSA _c2012
300			_a645 _bIlustración _c19 X 23.5 cm
505			_aContents Preface ix Chapter 1 Complex Numbers 1 1.1 The Origin of Complex Numbers 1 1.2 The Algebra of Complex Numbers 5 1.3 The Geometry of Complex Numbers 12 1.4 The Geometry of Complex Numbers, Continued 18 1.5 The Algebra of Complex Numbers, Revisited 24 1.6 The Topology of Complex Numbers 30 Chapter 2 Complex Functions 38 2.1 Functions of a Complex Variable 38 2.2 Transformations and Linear Mappings 41 2.3 The Mappings w = zn and w = z1/n 47 2.4 Limits and Continuity 53 2.5 Branches of Functions 60 2.6 The Reciprocal Transformation w = 1/z (Prerequisite for Section 9.2) 64 Chapter 3 Analytic and Harmonic Functions 71 3.1 Differentiable Functions 71 3.2 The Cauchy-Riemann Equations 76 3.3 Analytic Functions and Harmonic Functions 84 Chapter 4 Sequences, Series, and Julia and Mandelbrot Sets 95 4.1 Definitions and Basic Theorems for Sequences and Series 95 4.2 Power Series Functions 109 4.3 Julia and Mandelbrot Sets 116 Page vi Chapter 5 Elementary Functions 125 5.1 The Complex Exponential Function 125 5.2 Branches of the Complex Logarithm Function 132 5.3 Complex Exponents 138 5.4 Trigonometric and Hyperbolic Functions 143 5.5 Inverse Trigonometric and Hyperbolic Functions 152 Chapter 6 Complex Integration 157 6.1 Complex Integrals 157 6.2 Contours and Contour Integrals 160 6.3 The Cauchy-Goursat Theorem 175 6.4 The Fundamental Theorems of Integration 189 6.5 Integral Representations for Analytic Functions 195 6.6 The Theorems of Morera and Liouville and Some Applications 201 Chapter 7 Taylor and Laurent Series 208 7.1 Uniform Convergence 208 7.2 Taylor Series Representations 214 7.3 Laurent Series Representations 223 7.4 Singularities, Zeros, and Poles 232 7.5 Applications of Taylor and Laurent Series 239 Chapter 8 Residue Theory 244 8.1 The Residue Theorem 244 8.2 Calculation of Residues 246 8.3 Trigonometric Integrals 252 8.4 Improper Integrals of Rational Functions 256 8.5 Improper Integrals Involving Trigonometric Functions 260 8.6 Indented Contour Integrals 264 8.7 Integrands with Branch Points 270 8.8 The Argument Principle and Rouché's Theorem 274 Chapter 9 Conformal Mapping 281 9.1 Basic Properties of Conformal Mappings 281 9.2 Bilinear Transformations 287 9.3 Mappings Involving Elementary Functions 294 9.4 Mapping by Trigonometric Functions 303 Page vii Chapter 10 Applications of Harmonic Functions 310 10.1 Preliminaries 310 10.2 Invariance of Laplace's Equation and the Dirichlet Problem 312 10.3 Poisson's Integral Formula for the Upper Half Plane 323 10.4 Two-Dimensional Mathematical Models 327 10.5 Steady State Temperatures 329 10.6 Two-Dimensional Electrostatics 342 10.7 Two-Dimensional Fluid Flow 349 10.8 The Joukowski Airfoil 360 10.9 The Schwarz-Christoffel Transformation 369 10.10 Image of a Fluid Flow 380 10.11 Sources and Sinks 384 Chapter 11 Fourier Series and the Laplace Transform 397 11.1 Fourier Series 397 11.2 The Dirichlet Problem for the Unit Disk 406 11.3 Vibrations in Mechanical Systems 412 11.4 The Fourier Transform 418 11.5 The Laplace Transform 422 11.6 Laplace Transforms of Derivatives and Integrals 430 11.7 Shifting Theorems and the Step Function 433 11.8 Multiplication and Division by t 438 11.9 Inverting the Laplace Transform 441 11.10 Convolution 448 Appendix A Undergraduate Student Research Projects 456 Bibliography 458 Answers to Selected Problems 466 Index 477
520			_aDirigida a estudiantes de pregrado de matemáticas, física o ingeniería, la sexta edición de Análisis Complejo para Matemáticas e Ingeniería ofrece una presentación completa y práctica de esta interesante área de las matemáticas. Los autores logran un equilibrio entre los aspectos puros y aplicados de la materia, presentando los conceptos con un estilo claro y apropiado para estudiantes de penúltimo y último año de carrera. Gracias a su presentación completa y accesible, y a sus numerosas aplicaciones, la sexta edición de este clásico permite a los estudiantes resolver con facilidad incluso las demostraciones más complejas. Los nuevos ejercicios ayudan a los estudiantes a evaluar su comprensión del material y a evaluar su progreso en el curso. También se encuentran disponibles en línea ejercicios adicionales de Mathematica y Maple, así como una guía de estudio para estudiantes.
526			_aIngeniería en Tecnologías de la Información y Comunicación
650		0	_aProgramación _9729
700			_bRussell W. Howell
942			_cLIB _2ddc _e 6a Edición
945			_a1 _badmin _c1270 _dMaría Elena Olvera Picina
999			_c5573 _d5573