This book presents an economical and unified treatment of a wealth of topics related to the Fourier integral. Its outstanding feature is the organization of the material and the simplicity and clarity of presentation. The author develops the theoretical concepts with rigor unusual in engineering texts, but avoids the mathematical elaboration that is of no interest to applied scientists.

TABLE OF CONTENTS

Preface

PART ONE

Chapter 1. Introduction
1.1 Fourier Analysis
1.2 The Laplace Transform
1.3 Linear Systems
1.4 Singularuty Functions
1.5 The Fourier Transform in Probability Theory

Chapter 2. Basic Theorems and Examples
2.1 The Fourier Integral
2.2 Special Forms of the Fourier Integral
2.3 Simple Theorems
2.4 Examples
2.5 The Convolution Theorem
2.6 On the Proof of the Fourier-integral Theorem

Chapter 3. Singularity Functions and Line Spectra
3.1 Basic Examples
3.2 Fourier Series
3.3 Poisson's Sum Formula
3.4 Periodic Frequency Spectra
3.5 Sampling Theorem

Chapter 4. Numerical Techniques and Uncertainty Principle
4.1 Evaluation of the Fourier Transform
4.2 Evaluation of the Inversion Integral
4.3 Approximate Evaluation of the Convolution Integral
4.4 Duration of a Signal and Uncertainty Principle
Problems
Solutions

PART TWO

Chapter 5. Linear Systems
5.1 Definitions
5.2 The System Function
5.3 Evaluation of the Step Response

Chapter 6. Low-pass Filters
6.1 Definitions
6.2 Amplitude Distortion
6.3 Casual Systems with Linear Phase
6.4 Phase Distortion
6.5 Summary

Chapter 7. Bandpass Filters
7.1 Symmetrical Systems
7.2 Modulated Input
7.3 Unsymmetrical Systems
7.4 Modulated Input
7.5 Group, Phase, and Signal-front Delay
7.6 Group, Phase, and Signal-front Velocity
7.7 The Principle of Stationary Phase

Chapter 8. Spectrum Analysers
8.1 Simultaneous Spectral Analysis
8.2 Sequential Spectral Analysis
8.3 Periodic Signals
Problems
Solutions

PART THREE

Chapter 9. The Laplace Transform
9.1 The Unilateral Laplace Transform
9.2 Relationship between the Fourier Integral of a Casual Function and The Unilateral Laplace Transform
9.3 The Inversion Formula
9.4 Evaluation of f(t)
9.5 Initial-value Theorem
9.6 The Bilateral Laplace Transform

Chapter 10. Integral Theorems
10.1 Integral Theorems
10.2 Relationship between R(w) and X(w)
10.3 Minimum-phase-shift Functions
10.4 Energy of a Signal
10.5 Causality Conditions
Problems
Solutions

PART FOUR

Chapter 11. Positive Funtions and Limit Therorems
11.1 The Density Function
11.2 Repeated Convolution
11.3 The Central-limit Therorem
11.4 Error Correction

Chapter 12. Generalized Harmonic Analysis, Correlation, and Power Spectra
12.1 Introdution
12.2 Finite Energy Signals
12.3 Finite Power Signals
12.4 Functions with Arbitrary Power Spectra
12.5 Generalized Harmonic Analysis
Problems
Solutions

APPENDIXES

Appendix I. The Impulse Function as Distribuition
I1. Definitions
I2. Generalized Limits
I3. Physical Concepts as Distributions

Appendix II. Analytic Functions
II1. Definitions
II2. Integration
II3. Calculus of Residues
II4. Saddle Point Method of Integration
II5. Positive Real Functions

Index

This reputable translation covers trigonometric Fourier series, orthogonal systems, double Fourier series, Bessel functions, the Eigenfunction method and its applications to mathematical physics, operations on Fourier series and much more. Over 100 problems at ends of chapters. Answers in back of book. 1962 ed.

This handbook is unusual in that it combines in a single volume formulas and tables from both elementary and advanced mathematics. For example, topics treated range from those in algebra, geometry, trigonometry, analytic geometry and calculus to Fourier series, Laplace and Fourier transforms, Bessel and Legendre functions and many other advanced special functions. Such topics are needed by both students and research workers in the fields of engineering, physics, mathematics and other sciences.

Este livro apresenta uma abordagem clássica da teoria das funções de variável complexa e destina-se a ser usado como texto de apoio para as aulas de Análise Complexa e Equações Diferenciais ou outras unidades curriculares dos cursos de Engenharia que recorram à análise complexa.

Na primeira parte do livro são apresentados os fundamentos da álgebra dos números complexos, com especial ênfase na interpretação geométrica das suas propriedades. A parte principal do livro inclui os resultados clássicos do cálculo diferencial e integral com funções de variável complexa; é dada especial atenção ao teorema de Cauchy e suas consequências, aos desenvolvimentos em séries de potências e ao prolongamento analítico de funções de variável complexa.

A parte final do livro é dedicada à transformação conforme e à sua aplicação na resolução do problema de valores na fronteira para a equação de Laplace em duas dimensões; inclui uma tabela de transformações conformes de uso frequente.

Os numerosos exercícios propostos no final de cada capítulo permitem uma melhor consolidação dos conhecimentos adquiridos durante a leitura do texto.

António Horácio Simões de Abreu nasceu em Vouzela em 1923, filho de um casal de professores do ensino primário. Completou o curso liceal no Liceu Pedro Nunes onde, tendo tido a mais alta classificação a nível nacional, não recebeu o prémio correspondente do então Presidente Carmona por não ser filiado na Mocidade Portuguesa.

Concluiu o curso de Engenharia Electrotécnica, tendo sido o aluno mais classificado em Matemática pelos professores Mira Fernandes e Ferreira de Macedo. Recebeu o prémio “Mira Fernandes”. Foi assistente de Ferreira de Macedo no IST, no decurso do 4º ano do seu curso. Tal como aconteceu com Ferreira de Macedo, foi afastado de funções docentes do IST que só retomaria no final dos anos sessenta. Foi ainda professor da Escola Náutica Infante D. Henrique.

Casou em Lisboa, na cadeia de Caxias. António Simões de Abreu foi militante muito activo contra o regime salazarista vigente antes do 25 de Abril de 1974. No próprio dia em que concluía, em 1946, em Tancos, o 2º ciclo de oficiais milicianos, foi preso em regime agravado na cadeia de Penamacor. Seguiram-se ao longo da vida seis prisões pela PIDE/ DGS. Aderiu ao PCP em 1942, nas Juventudes Comunistas, tendo integrado desde finais de 1946 até 1948 a Comissão Central do MUD-Juvenil, entre outros com Areosa Feio, Júlio Pomar, Mário Soares, Octávio Pato, Óscar dos Reis, Rui Grácio e Salgado Zenha. Em 1958 trabalhou com Arlindo Vicente, e teve papel destacado no entendimento da sua candidatura com a de Humberto Delgado. No final de uma vida politicamente muito activa participou, pouco antes do 25 de Abril, no Congresso dos Engenheiros e, no início da revolução, no movimento sindical docente que teve então um amplo desenvolvimento. Recebeu a Ordem da Liberdade dias antes de falecer em 2005.
PREFÁCIO

I ÁLGEBRA DOS COMPLEXOS

1 ÁLGEBRA DOS COMPLEXOS

1.1 O conjunto C dos números complexos, suporte de um espaço vectorial real, com dimensão 2
1.1.1 Introdução
1.1.2 Dimensão
1.1.3 Norma no espaço vectorial C
1.2 O conjunto C como suporte de um corpo, extensão do corpo real R
1.2.1 Introdução
1.2.2 O corpo C como extensão do corpo R
1.2.3 O corpo C, como extensão do corpo R, não pode ser ordenado
1.3 Representação geométrica. Forma trigonométrica. Radiciação
1.3.1 Introdução
1.3.2 Forma trigonométrica
1.4 As operações do espaço vectorial e do corpo C no plano de Argand
1.5 Complexos conjugados. Propriedades e aplicações
1.5.1 Definição
1.5.2 Propriedades
1.5.3 Aplicações
1.6 Exercícios

II ANÁLISE COMPLEXA

2 DIFERENCIAÇÃO

2.1 Topologia do espaço C. Conjuntos particulares
2.1.1 Introdução
2.1.2 Sucessões e séries
2.1.3 Funções de R em C. Linhas de Jordan. Regiões simples e multiplamente conexas
2.2 Funções de variável complexa. Limite. Continuidade
2.2.1 Generalidades. Significado geométrico
2.2.2 Limite. Continuidade
2.3 Derivada num ponto. Diferenciabilidade e analiticidade. Significado geométrico
2.3.1 Derivada e diferencial
2.3.2 Significado geométrico local
2.3.3 Analiticidade. Transformação conforme
2.3.4 Derivadas de ordem superior à primeira
2.3.5 Equações de Cauchy-Riemann. Funções harmónicas em R^2
2.4 Séries de potências. Funções transcendentes elementares
2.4.1 Séries de potências
2.4.2 A função exponencial
2.4.3 As funções hiperbólicas e circulares
2.5 Inversão de algumas funções elementares. Expressões multívocas. Pontos de ramificação e linhas de ramificação. Superfícies de Riemann
2.5.1 Alguns exemplos
2.5.2 Superfícies de Riemann
2.6 Pontos singulares
2.7 Exercícios

3 INTEGRAÇÃO

3.1 Definição e cálculo do integral
3.1.1 Introdução
3.1.2 Definição do integral. Propriedades
3.1.3 Cálculo do integral, por redução a integrais de Riemann
3.2 Teorema de Cauchy. Algumas consequências importantes
3.2.1 Teorema de Cauchy-Goursat
3.2.2 Algumas consequências imediatas
3.3 Fórmulas integrais de Cauchy. Consequências.
3.3.1 Fórmulas integrais de Cauchy
3.3.2 Consequências importantes das fórmulas integrais de Cauchy
3.4 Aplicação do Teorema dos Resíduos ao cálculo de certos integrais reais
3.4.1 Integral entre mais infinito e menos infinito de f(x)dx
3.4.2 Integral entre zero e dois pi de g(cos theta, sen theta) d theta
3.4.3 Lema de Jordan
3.4.4 Integrais que contêm ramos extraídos de expressões multívocas
3.5 Exercícios

4 DESENVOLVIMENTOS EM SÉRIE. PROLONGAMENTO ANALÍTICO

4.1 Desenvolvimento de Taylor
4.1.1 Teorema de Taylor
4.1.2 Alguns desenvolvimentos taylorianos
4.2 Desenvolvimento de Laurent
4.2.1 Teorema de Laurent
4.2.2 Zeros e singularidades. O ponto infinito
4.3 Prolongamento analítico
4.4 Exercícios

5 TRANSFORMAÇÃO CONFORME

5.1 Generalidades
5.1.1 Teorema da Aplicação de Riemann
5.1.2 Transformação de Schwarz-Christoffel
5.1.3 Transformação de fronteiras na forma paramétrica
5.1.4 Transformação de um semi-plano num círculo de raio 1
5.2 Algumas transformações elementares
5.2.1 Translacção
5.2.2 Homotetia em relação à origem
5.2.3 Rotação em torno da origem
5.2.4 Transformação w = az
5.2.5 Transformação de semelhança
5.2.6 Inversão
5.3 A transformação de Möbius
5.4 O problema fundamental. Aplicações à Física
5.4.1 Introdução
5.4.2 Os problemas de Dirichlet e de Neumann no plano
5.4.3 Aplicação da teoria da transformação conforme à resolução do problema de Dirichlet
5.5 Tabela de transformações conformes de uso frequente
5.6 Exercícios

REFERÊNCIAS BIBLIOGRÁFICAS

"Fundamentals of Electric Circuits, 2e" is intended for use in the introductory circuit analysis or circuit theory course taught in electrical engineering departments. The main objective of this book is to present circuit analysis in a clear, easy-to-understand manner, with many practical applications to interest the student. Each chapter opens with either historical sketches or career information on a sub-discipline of electrical engineering. This is followed by an introduction that includes chapter objectives. Each chapter closes with a summary of the key points and formulas. The authors present principles in an appealing and lucid step-by-step manner, carefully explaining each step. Important formulas are highlighted to help students sort out what is essential and what is not. Many pedagogical aids reinforce the concepts learned in the text so that students get comfortable with the various methods of analysis presented in the text.

This textbook has been revised to include new exercises ranging from simple problems to challenging issues that involve several components. Brief design studies offer students the opportunity to develop engineering judgement and creativity.

Book Description
The fourth edition retains the basic objectives of the first three editions which is to present a comprehensive and rigorous treatment of engineering thermodynamics from the classical viewpoint. It includes thorough development of the second law, featuring the entropy production concept, and energy analysis. Known for its emphasis on design, the authors have updated design applications to include economic considerations. Environmental topics and applications have been expanded and updated.

Book Info
Contents include energy and the first law of thermodynamics, the second law of thermodynamics, vapor power systems, gas power systems, ideal gas mixtures and psychrometrics, chemical and phase equilibrium, and more. Previous edition: c1996. DLC: Thermodynamics.

From the Back Cover
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• New Thermodynamics in the News items tie reports from the popular press, such as fuel cells, to concepts covered in the text.
• A strong problem-solving methodology encourages readers to develop an orderly approach to problem solving, think systematically, and reduce typical errors.
• End-of-chapter materials builds problem-solving skills in three modes: Conceptual (Exercises: Things Engineers Think About); Skill building (Problems: Developing Engineering Skills); and Exploration (Design and Open-Ended Problems: Exploring Engineering Practice).
• Online study guide, including key concepts summaries and additional homework problems with answers and selected solutions, offer tools to test your understanding of chapter material.
• Design/Open-Ended Problems provide brief design experiences that provide opportunities to think creatively, apply constraints, and consider alternatives.
• Thorough development of the second law, featuring the entropy production concept and energy analysis, provide a state-of-the-art introduction to second law analysis.
• IT: Interactive Thermodynamics software (purchased separately) features property data calculation, systems modeling, and “what if’ calculation capabilities, so you can explore more realistic thermodynamic system behavior.
• ThermoNet tutorials for basic engineering concepts feature animations, pop-up quizzes, and additional worked examples. Available through the book’s website.

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Effective pedagogy, everyday examples, an outstanding collection of practical problems—these are just a few reasons why Munson, Young, and Okiishi's Fundamentals of Fluid Mechanics is the best-selling fluid mechanics text on the market. In each new edition, the authors have refined their primary goal of helping you develop the skills and confidence you need to master the art of solving fluid mechanics problems.

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* 80 short Fluids Mechanics Phenomena videos, which illustrate various aspects of real-world fluid mechanics.
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* 30 extended laboratory problems that involve actual experimental data for simple experiments. The data for these problems is provided in Excel format.
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Student Solution Manual and Study Guide

A Student Solution Manual and Study Guide is available for purchase, including essential points of the text, "Cautions" to alert you to common mistakes, 109 additional example problems with solutions, and complete solutions for the Review Problems.

This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical concepts and methods useful in the description of situations involving systems which consist of very many particulars. It attempts, in particular, to introduce the reader to the disciplines of thermodynamics, statistical mechanics, and kinetic theory from a unified and modern point of view. The presentation emphasizes the essential unity of the subject matter and develops physical insight by stressing the microscopic content of the theory.

The third edition of "Fundamentals of Thermal-Fluid Sciences" presents a balanced coverage of thermodynamics, fluid mechanics, and heat transfer packaged in a manner suitable for use in introductory thermal sciences courses. By emphasizing the physics and underlying physical phenomena involved, the text gives students practical examples that allow development of an understanding of the theoretical underpinnings of thermal sciences. All the popular features of the previous edition are retained in this edition while new ones are added. This book features learning objectives. Each chapter now begins with an overview of the material to be covered and chapter-specific learning objectives to introduce the material and to set goals. It includes an early introduction to the first law of thermodynamics (Chapter 2) establishing a general understanding of energy, mechanisms of energy transfer, and the concept of energy balance, thermo-economics, and conversion efficiency.It features separate coverage of closed system and control volume energy analyses. The energy analysis of closed systems is now presented in a separate chapter (Chapter 5), and the conservation of mass is covered together with conservation of energy in another chapter (Chapter 6). It offers a new chapter on fluid kinematics. The all new Chapter 11 covers topics related to fluid kinematics, such as the Lagrangian and Eulerian descriptions of fluid flows, flow patterns, and flow visualization. It features updated steam and refrigerant-134a tables. The steam and refrigerant-134a tables are updated using the most current property data from EES. Students will now get the same result when solving problems whether they use properties from EES or property tables in the appendices. Media Resources and Limited Academic Version of EES with selected text solutions are packaged with the text on the Student DVD.A website offers online resources for instructors including PowerPoint[registered] lecture slides, and complete solutions to homework problems.