I – Introdução
II – Integrais Duplos
III – Integrais Triplos
IV – Integral ao Longo de Uma Linha
V – Integrais de Superfície

This text is intended for a one-term course in introductory differential equations and is designed for students in pure and applied mathematics who have had a course in calculus. The text presents a balance of mathematical rigour and intuitive thinking. The illustrations aim to enhance the conceptual material and allow students to visualize the mathematics. The treatment of chaotic dynamical systems introduces students to the basic ideas surrounding chaotic motion. Problem sets, which contain computer applications, are carefully graduated from the routine to the more challenging and extension exercises asking students to expand on the material are included to pique student interest. Brief historical notes place topics in their proper historical and cultural context.

Part 1 Introduction to Differential Equations: Prologue; Basic Definitions and Concepts; Solutions, Initial Value Problems, and Existence of solutions. Part 2 First Order Differential Equations: First Order Linear Equations; Separable Equations; Growth and Decay Phenomena; Mixing Phenomena; Cooling and Heating Phenomena; More Applications; The Direction Field and Newton's Method; Higher order Numerical Methods. Part 3 Second Order Linear Equations: Introduction to Second Order Linear Equations; Fundamental Solutions of the Homogeneous Equation; Reduction of Order; Homogeneous Equations with Constant Coefficients - Real Roots; Homogeneous Equations with Constant Coefficients - Complex Roots; The Nonhomogeneous Equation; Solving Nonhomogeneous Equations - Method of Undetermined Coefficients; Solving Nonhomogeneous Equations - Method of Variation of Parameters; Mechanical Systems and Simple Harmonic Motion; Unforced Undamped Vibrations; Forced Vibrations; Introduction to Higher Order Equations (optional). Part 4 Series Solutions: Introduction - A Review of Power Series; Power Series Solutions About an Ordinary Point - Part I; Power Series Solutions About an Ordinary Point - Part II; Series Solutions about Singular Points - The Method of Frobenius; Bessel's Functions. Part 5 The Laplace Transform: Definition of the Laplace Transform; Properties of the Laplace Transform; The Inverse Laplace Transform; Initial-Value Problems; Step Functions and Delayed Functions; Differential Equations with Discontinuous Forcing Functions; Impulse Forcing Functions; The Convolution Integral. Part 6 System of Differential Equations: Introduction to Linear Systems - The Method of Elimination; Review of Matrices; Basic Theory of First Order Linear Systems; Homogeneous Linear Systems with Real Eigenvalues; Homogeneous Linear Systems with Complex Eigenvalues; Nonhomogeneous Linear Systems; Nonhomogeneous Linear Systems - The Laplace Transform (optional); Applications of Linear Systems; Numerical Solution of Systems of Differential Equations. Part 7 Difference Equations: Introduction to Difference Equations; Homogeneous Equations; Nonhomogeneous Equations; Applications; The Logistic Equation and the Path to Chaos; Iterative Systems - Julia Sets and the Mandelbrot Set (optional). Part 8 Nonlinear Differential Equations and Chaos: Phase Plane Analysis of Autonomous Systems; Equilibrium Points and Stability for Linear Systems; Stability - Almost Linear Systems; Chaos, Poincare Sections and Strange Attractors. Part 9 Partial Differential Equations: Fourier Series; Fourier Sine and Cosine Series; Introduction to Partial Differential Equations; The Vibrating String - Separation of Variables; Interpretation of the Vibrating String as Superposition; The Heat Equation and Separation of Variables; Laplace's Equation Inside a Circle. Appendix: Complex Numbers and Complex-Valued Functions. Answers to Problems.

For junior/senior-level electricity and magnetism courses. This book is known for its clear, concise and accessible coverage of standard topics in a logical and pedagogically sound order. The Third Edition features a clear, accessible treatment of the fundamentals of electromagnetic theory, providing a sound platform for the exploration of related applications (ac circuits, antennas, transmission lines, plasmas, optics, etc.). Its lean and focused approach employs numerous examples and problems.

This best-selling text by John Taylor, now released in its second edition, introduces the study of uncertainties to lower division science students. Assuming no prior knowledge, the author introduces error analysis through the use of familiar examples ranging from carpentry to well-known historic experiments. Pertinent worked examples, simple exercises throughout the text, and numerous chapter-ending problems combine to make the book ideal for use in physics, chemistry, and engineering lab courses. The first edition of this book has been translated into six languages.

There is good reason for the tradition that students of science and engineering start college physics with the study of mechanics: mechanics is the cornerstone of pure and applied science. The concept of energy, for example, is essential for the study of the evolution of the universe, the properties of elementary particles, and the mechanisms of biochemical reactions. The concept of energy is also essential to the design of a cardiac pacemaker and to the analysis of the limits of growth of industrial society. However, there are difficulties in presenting an introductory course in mechanics which is both exciting and intellectually rewarding. Mechanics is a mature science and a satisfying discussion of its principies is easily lost in a superficial treatment. At the other extreme, attempts to "enrich" the subject by emphasizing advanced topics can produce a false sophistication which emphasizes technique rather than understanding. This text was developed from a first-year course which we taught for a number of years at the Massachusetts Institute of Technology and, earlier, at Harvard University. We have tried to present mechanics in an engaging form which offers a strong base for future work in pure and applied science. Our approach departs from tradition more in depth and style than in the choice of topics; nevertheless, it reflects a view of mechanics held by twentieth-century physicists.

The 8th edition of "Introduction to Operations Research" remains the classic operations research text, while incorporating a wealth of state-of-the-art, user-friendly software and more coverage of modern OR topics. The hallmark features of this edition include solid coverage of fundamentals and state-of-the-practice operations research software used in conjunction with examples from the text. This edition will also feature the latest developments in OR, such as metaheuristics, simulation, and spreadsheet modeling.

Provides comprehensive coverage of all the fundamentals of quantum physics. Full mathematical treatments are given. Uses examples from different areas of physics to demonstrate how theories work in practice. Text derived from lectures delivered at Massachusetts Institute of Technology.

Since the publication of the first edition over 50 years ago, Introduction to Solid State Physics has been the standard solid state physics text for physics students. The author's goal from the beginning has been to write a book that is accessible to undergraduates and consistently teachable. The emphasis in the book has always been on physics rather than formal mathematics. With each new edition, the author has attempted to add important new developments in the field without sacrificing the book's accessibility and teachability.

* A very important chapter on nanophysics has been written by an active worker in the field. This field is the liveliest addition to solid state science during the past ten years
* The text uses the simplifications made possible by the wide availability of computer technology. Searches using keywords on a search engine (such as Google) easily generate many fresh and useful references

PREFÁCIO

Este livro destina-se a servir de texto de apoio às disciplinas 
que, nos primeiros anos dos cursos superiores de engenharia, apre- 
sentam a introdução à teoria das redes eléctricas e fazem o estudo 
de circuitos electrónicos básicos. A matéria tratada corresponde ao 
primeiro semestre da sequência de disciplinas que, nestes cursos, se 
ocupa do estudo dos circuitos e sistemas electrónicos.
A rápida evolução da tecnologia, particularmente no domínio 
da electrónica e dos computadores, tem levado à criação de novas 
disciplinas, o que motivou nos actuais planos de estudo dos cursos 
de engenharia a antecipação do ensino dos circuitos e sistemas 
electrónicos para os primeiros anos. O ensino da teoria dos circui- 
tos é feito em disciplinas que ensinam também circuitos electrónicos 
simples. O presente texto tem por objectivo constituir elemento de 
estudo de tais disciplinas.
O principal critério adoptado na elaboração deste livro foi a 
busca de um elevado grau de concisão, sem prejuízo do rigor e da 
coerência lógica. Entende-se que o que valoriza o programa de 
uma disciplina, ou um livro de texto que lhe sirva de apoio, não é a 
inclusão de um conjunto muito completo e variado de tópicos. É, 
antes, uma selecção muito cuidada dos assuntos tratados e da sua 
sequência, com ênfase nos princípios e métodos fundamentais. 
A escolha deste tipo de abordagem é incentivada pela actual com- 
pressão do espaço atribuído às matérias tratadas neste livro.



Índice

1. REDES RESISTIVAS
1.1. Redes de Parâmetros Concentrados
1.2. Variáveis das Redes Eléctricas
1.3. Elementos Resistivos
1.4. Leis de Kirchhoff
1.5. Teoremas
1.6. Método dos Nós
1.7. Redes com Vários Acessos
Problemas

2. REDES REACTIVAS
2.1. Elementos Reactivos
2.2. Redes de La Ordem
2.3. Redes de 2: Ordem
2.4. Regime Forçado Sinusoidal
2.5 Funções de Rede
Problemas

3. AMPLIFICADOR OPERACIONAL
3.1. Características Ideais
3.2. Funcionamento Linear
3.3. Funcionamento Não-Linear
3.4. Características Não-Ideais
3.5. Elementos Singulares
Problemas

4. DÍODOS
4.1. Díodo de Junção
4.2. Rectificadores
4.3. Reguladores de Tensão
4.4. Rectificadores de Precisão
4.5. Amplificadores Logarítmicos e Exponenciais
4.6. Limitadores e Fixadores
4.7. Modelo Incremental
Problemas

5. REALIMENTAÇÃO E ESTABILIDADE
5.1. Realimentação Negativa
5.2. Quatro Topologias Básicas
5.3. Estabilidade
5.4. Compensação
5.5. Osciladores Sinusoidais
Problemas

Apêndice 1: NÚMEROS COMPLEXOS
Apêndice 2: PROBLEMAS ADICIONAIS
Apêndice 3: SOLUÇÕES DOS PROBLEMAS
Bibliografia

PREFÁCIO
RESUMO DE NOTAÇÕES

1.a PARTE - NÚMEROS REAIS, SUCESSÕES E SÉRIES
I. Números Reais
I.1 Propriedades básicas dos números reais
I.2 Noções topológicas no conjunto dos reais
Exercícios
II. Sucessões e Séries Reais
II.1 Sucessões
II.2 Séries
Exercícios

2.a PARTE – FUNÇÕES REAIS DE UMA VARIÁVEL REAL
III. Funções Contínuas. Limites.
III.1 Funções reais de variável real. Generalidades e Exemplos
III.2 Continuidade e limite
Exercícios
IV. Cálculo Diferencial
IV.I Derivação. Teoremas fundamentais
IV.2 Complementos e aplicações dos teoremas fundamentais
IV.3 Primitivação
Exercícios
V. Cálculo Integral
V.1 Integral de Riemann. Teoremas fundamentais
V.2 Outra definição do integral de Riemann. Complementos e aplicações
V.3 Integrais impróprios
Exercícios
Soluções abreviadas de alguns exercícios

Este livro foi pensado para servir de texto de apoio às disciplinas que tratam de Álgebra Linear, sejam elas semestrais ou anuais, em cursos de Engenharia, Economia, Ciências e Matemática. Com esse objectivo, a apresentação dos assuntos é feita de maneira sistemática e rigorosa, mas de forma modular. Inicialmente é abordada a parte mais concreta da Álgebra Linear: matrizes, sistemas e determinantes. Continua-se com o estudo de ?n e seus subespaços, do ponto de vista vectorial e métrico, e com breve referência ao caso abstracto. Segue-se a Geometria Analítica do 1.º grau e um longo capítulo sobre vectores próprios e valores próprios, incluindo algumas aplicações interessantes, como a compressão de imagens usando a decomposição dos valores singulares, os sistemas dinâmicos lineares discretos, a análise de componentes principais em Estatística e o funcionamento do Google. O material coberto nestes sete primeiros capítulos é adequado para nele se basear uma disciplina semestral. Os capítulos finais são dedicados à Álgebra Linear abstracta, estudando-se os espaços vectoriais gerais sobre corpos arbitrários (incluindo os espaços de dimensão infinita), as transformações lineares entre eles e os espaços com produto interno.

Este livro foi preparado especificamente para uma primeira disciplina semestral de Álgebra Linear para alunos do primeiro ano das licenciaturas em Engenharia, Física ou Matemática do IST (Universidade Técnica de Lisboa), onde tem sido utilizado desde 1985 em versões que foram revistas de ano para ano até se chegar à forma presente.