Abstract Algebra: The Basic Graduate Year

Um livro/texto razoável para  o primeiro ano  , escrito por Robert B. Ash .

Front Preface and Table of Contents (110 K)
Chapter 0 Prerequisites (194 K)
Chapter 1 Group Fundamentals (150 K)
Chapter 2 Ring Fundamentals (222 K)
Chapter 3 Field Fundamentals (135 K)
Chapter 4 Module Fundamentals (357 K)
Enrichment Chapters 1-4 (288 K)
Chapter 5 Some Basic Techniques of Group Theory (405 K)
Chapter 6 Galois Theory (480 K)
Chapter 7 Introducing Algebraic Number Theory (410 K)
Chapter 8 Introducing Algebraic Geometry(448 K)
Chapter 9 Introducing Noncommutative Algebra (350 K)
Chapter 10 Introducing Homological Algebra(437 K)
Supplement (315 K)
Solutions Chapters 1-5 (461 K)
Solutions Chapters 6-10 (449 K)
End Bibliography, List of Symbols and Index (233 K)

Euclides Elements

Um site onde tem muitas coisas sobre os elementos de Euclides.

 Euclides Elements

A=B

 Este livro centra-se no ramo da Matemática computacional , utilizando o Maple.

Escrito por

Marko Petkovsek, Herbert Wilf and Doron Zeilberger .

Para quem gosta desta área  , ou necessita de lidar com problemas que só se resolvem numericamente.

O livro pode ser baixado nestes sitios

1. From the University of Pennsylvania web site
2. From the Temple University web site
3. From the University of Ljubljana web site

A Course in Universal Algebra

** The Millennium Edition **

by

Stanley N. Burris and H.P. Sankappanavar

Download

Postscript files

• univ-algebra.ps (1.9 Megs)
• univ-algebra.ps.gz (0.6 Megs )
• univ-algebra.ps.Z (0.75 Megs)
• univ-algebra.ps.zip (0.6 Megs )

PDF file

univ-algebra.pdf (1.2 Megs )

Algorithms and Complexity

Escrito por Herbert S. Wilf .

Aqui está a página do livro

Aqui está o livro   Algorithms and Complexity

generatingfunctionology

Aqui vai mais um livro  , aqui está o link sobre o livro.

Aqui está o livro para Download 

An Introduction to Probability and Random Processes

Este livro foi escrito em 1979 , por Gian-Carlo Rota and Kenneth Baclawski , não estranhem o grafismo um pouco antiquado pois o conteúdo está lá todo .

 An Introduction to Probability and Random Processes

ELEMENTARY LINEAR ALGEBRA

Este é outro livro de algebra elementar. Escrito por Keith Matthews .

Aqui está a parte teórica

• Preface
• Title Page/Contents (pages 0, i-iv)
  • pdf version of book (747K)
• Chapter 1: Linear Equations (pages 1-21)
• Chapter 2: Matrices (pages 23-54)
• Chapter 3: Subspaces (pages 55-70)
• Chapter 4: Determinants (pages 71-88)
• Chapter 5: Complex Numbers (pages 89-114)
• Chapter 6: Eigenvalues and Eigenvectors (pages 115-128)
• Chapter 7: Identifying Second Degree Equations (pages 129-148)
• Chapter 8: Three-dimensional Geometry (pages 149-187)
• Further Reading/Bibliography (pages 189,191-193)
• Index (pages 194-196)

• Corrections

———————————————————————–

Aqui vai as respostas aos exercícios

• Title Page/Contents (pages 0/i)
  • pdf version of the solutions (437K – best read with zoom in)
• Problems 1.6: Linear Equations (pages 1-11)
• Problems 2.4: Matrices (pages 12-17)
• Problems 2.7: Matrices (pages 18-31)
• Problems 3.6: Subspaces (pages 32-44)
• Problems 4.1: Determinants (pages 45-57)
• Problems 5.8: Complex Numbers (pages 58-68)
• Problems 6.3: Eigenvalues and Eigenvectors (pages 69-82)
• Problems 7.3: Identifying Second Degree Equations (pages 83-90)
• Problems 8.8: Three-dimensional Geometry (pages 91-103)

Linear Algebra

Este livro foi escrito pelo  Professor Jim Hefferon  é um livro  que aborta muitos aspectos da Algebra linear.

Linear Algebra

E está aqui as respostas ao livro   Respostas

The Geometry and Topology of Three-Manifolds

Este não cheguei a ver , mas para quem quiser está aqui o link onde pode fazer o download dos capitulos.

Foi escrito por William Thurston e distribuido pela Universidade de Princeton

Algebraic Topology

Este livro trata de Topologia Algébrica , este livro pelo que vi parece estar bastante bem escrito , apesar de eu não perceber muito deste tema , parece-me que o texto tem muita qualidade .

O autor é Professor Allen Hatcher .

The book was published by Cambridge University Press in 2002

Opções de download:

• The whole book as a single rather large pdf file (3.5MB) of about 550 pages.
• Doublepage version with two pages side by side, reduced in size so that they fit on one sheet of paper.
• Individual chapters can be downloaded as separate pdf files.

Elements of Abstract and Linear Algebra

 Quemfez este livro foi   Professor E.H. Connell of the University of Miami  .

O livro está neste link

 Elements of Abstract and Linear Algebra

Tem os seguintes capitulos

Chapter 1: Background and Fundamentals of Mathematics

Chapter 2: Groups

Chapter 3: Rings

Chapter 4: Matrices and Matrix Rings

Chapter 5: Linear Algebra

Chapter 6: Appendix

Complex Variables

Este texto   trata de Variáveis complexas   , escrito por

Robert B. Ash
Professor Emeritus, Mathematics

Dept. of Mathematics
University of Illinois

Tem os seguintes capitulos :

Preface
Table of Contents
Chapter 1 Introduction
Chapter 2 The Elementary Theory
Chapter 3 The General Cauchy Theorem
Chapter 4 Applications of the Cauchy Theory
Chapter 5 Families of Analytic Functions
Chapter 6 Factorization of Analytic Functions
Chapter 7 The Prime Number Theorem
Solutions
List of Symbols
Index

Linear Algebra, Infinite Dimensions, and Maple

Este livro , texto , foi escrito por George Cain e aborda análise Complexa.

Os capitulos do livro são :

Chapter One – Complex Numbers
1.1 Introduction
1.2 Geometry
1.3 Polar coordinates

Chapter Two – Complex Functions
2.1 Functions of a real variable
2.2 Functions of a complex variable
2.3 Derivatives

Chapter Three – Elementary Functions
3.1 Introduction
3.2 The exponential function
3.3 Trigonometric functions
3.4 Logarithms and complex exponents

Chapter Four – Integration
4.1 Introduction
4.2 Evaluating integrals
4.3 Antiderivatives

Chapter Five – Cauchy’s Theorem
5.1 Homotopy
5.2 Cauchy’s Theorem

Chapter Six – More Integration
6.1 Cauchy’s Integral Formula
6.2 Functions defined by integrals
6.3 Liouville’s Theorem
6.4 Maximum moduli

Chapter Seven – Harmonic Functions
7.1 The Laplace equation
7.2 Harmonic functions
7.3 Poisson’s integral formula

Chapter Eight – Series
8.1 Sequences
8.2 Series
8.3 Power series
8.4 Integration of power series
8.5 Differentiation of power series
Chapter Nine – Taylor and Laurent Series
9.1 Taylor series
9.2 Laurent series

Chapter Ten – Poles, Residues, and All That
10.1 Residues
10.2 Poles and other singularities

Applications of the Residue Theorem to Real Integrals-Supplementary Material by Pawel Hitczenko

Chapter Eleven – Argument Principle
11.1 Argument principle
11.2 Rouche’s Theorem

Linear Methods of Applied Mathematics

Este livro , ou texto foi escrito por

Evans M. Harrell II and James V. Herod

Em baixo estão os links para cada capítulo .

Preface

---

Diagnostic quiz Please take this before embarking on a course from this book. Links to review materials on ordinary differential equations and linear algebra

---

1. Linearity

Also available in an Adobe Acrobat version

---

The geometry of functions

Also available in an Adobe Acrobat version The red syllabus and the yellow syllabus continue with Chapter III
The green syllabus continues with Chapter XIII

---

Fourier series. Introduction.

Also available in an Adobe Acrobat version (without links)

---

Calculating Fourier series.

Also available in an Adobe Acrobat version (without links)

---

A test at this stage.

---

Differentiating Fourier series.

Also available in an Adobe Acrobat version (without links) The red syllabus continues with Chapter VI
The yellow syllabus continues with Chapter XIII

---

Notes on a vibrating string.

Also available in an Adobe Acrobat version (without links)

---

Traveling waves.

Also available in an Adobe Acrobat version (without links)

---

A test at this stage.

---

Mathematics of hot rods.

Also available in an Adobe Acrobat version (without links)

---

PDEs in space. (includes potential equations)

Also available in an Adobe Acrobat version (without links)

---

PDEs on a disk.

Also available in an Adobe Acrobat version (without links)

---

A test at this stage.

---

Great balls of PDEs.

---

Hunting for eigenvalues.

End of the red syllabus.

---

Geometry and integral operators.

---

Solving Y = KY + f.

---

A test at this stage.

---

Ordinary differential operators.

---

Finding Green functions for ODEs.

---

A test at this stage.

---

Green functions, Fourier series, and eigenfunctions.

---

Partial differential operators – classification and adjoints.

---

The free Green function and the method of images

---

A test at this stage.

---

The fundamental solution of the heat equation

---

Using conformal mapping to construct Green functions.

---

Some advanced topics.

---

APPENDICES

• Biographical and historical notes.
• Geometry without an Inner Product
• Derivation of the
  heat equation
  wave equation for the vibrating string
  wave equation for electromagnetic waves
• Properties of solutions to potential equations (mean-value theorem and maximum principle)
• Filtering and signal processing.
• Green functions in Rⁿ (a review of matrices)
• Legendre polynomials and spherical harmonics
• Ordinary differential equations (A review as a Maple worksheet)
• Thermal properties of common materials (table)
• Vector calculus (summary)

Os links em PdF estão off  , só  dá para ver em HTML   .

Calculus

Este livro foi feito por Gilbert Strang

Aqui em baixo estão os capítulos .

1: Introduction to Calculus, pp. 1-43

1.1 Velocity and Distance, pp. 1-7
1.2 Calculus Without Limits, pp. 8-15
1.3 The Velocity at an Instant, pp. 16-21
1.4 Circular Motion, pp. 22-28
1.5 A Review of Trigonometry, pp. 29-33
1.6 A Thousand Points of Light, pp. 34-35
1.7 Computing in Calculus, pp. 36-43

2: Derivatives, pp. 44-90

2.1 The Derivative of a Function, pp. 44-49
2.2 Powers and Polynomials, pp. 50-57
2.3 The Slope and the Tangent Line, pp. 58-63
2.4 Derivative of the Sine and Cosine, pp. 64-70
2.5 The Product and Quotient and Power Rules, pp. 71-77
2.6 Limits, pp. 78-84
2.7 Continuous Functions, pp. 85-90

3: Applications of the Derivative, pp. 91-153

3.1 Linear Approximation, pp. 91-95
3.2 Maximum and Minimum Problems, pp. 96-104
3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111
3.4 Graphs, pp. 112-120
3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129
3.6 Iterations x[n+1] = F(x[n]), pp. 130-136
3.7 Newton’s Method and Chaos, pp. 137-145
3.8 The Mean Value Theorem and l’Hopital’s Rule, pp. 146-153

4: The Chain Rule, pp. 154-176

4.1 Derivatives by the Charin Rule, pp. 154-159
4.2 Implicit Differentiation and Related Rates, pp. 160-163
4.3 Inverse Functions and Their Derivatives, pp. 164-170
4.4 Inverses of Trigonometric Functions, pp. 171-176

5: Integrals, pp. 177-227

5.1 The Idea of an Integral, pp. 177-181
5.2 Antiderivatives, pp. 182-186
5.3 Summation vs. Integration, pp. 187-194
5.4 Indefinite Integrals and Substitutions, pp. 195-200
5.5 The Definite Integral, pp. 201-205
5.6 Properties of the Integral and the Average Value, pp. 206-212
5.7 The Fundamental Theorem and Its Consequences, pp. 213-219
5.8 Numerical Integration, pp. 220-227

6: Exponentials and Logarithms, pp. 228-282

6.1 An Overview, pp. 228-235
6.2 The Exponential e^x, pp. 236-241
6.3 Growth and Decay in Science and Economics, pp. 242-251
6.4 Logarithms, pp. 252-258
6.5 Separable Equations Including the Logistic Equation, pp. 259-266
6.6 Powers Instead of Exponentials, pp. 267-276
6.7 Hyperbolic Functions, pp. 277-282

7: Techniques of Integration, pp. 283-310

7.1 Integration by Parts, pp. 283-287
7.2 Trigonometric Integrals, pp. 288-293
7.3 Trigonometric Substitutions, pp. 294-299
7.4 Partial Fractions, pp. 300-304
7.5 Improper Integrals, pp. 305-310

8: Applications of the Integral, pp. 311-347

8.1 Areas and Volumes by Slices, pp. 311-319
8.2 Length of a Plane Curve, pp. 320-324
8.3 Area of a Surface of Revolution, pp. 325-327
8.4 Probability and Calculus, pp. 328-335
8.5 Masses and Moments, pp. 336-341
8.6 Force, Work, and Energy, pp. 342-347

9: Polar Coordinates and Complex Numbers, pp. 348-367

9.1 Polar Coordinates, pp. 348-350
9.2 Polar Equations and Graphs, pp. 351-355
9.3 Slope, Length, and Area for Polar Curves, pp. 356-359
9.4 Complex Numbers, pp. 360-367

10: Infinite Series, pp. 368-391

10.1 The Geometric Series, pp. 368-373
10.2 Convergence Tests: Positive Series, pp. 374-380
10.3 Convergence Tests: All Series, pp. 325-327
10.4 The Taylor Series for e^x, sin x, and cos x, pp. 385-390
10.5 Power Series, pp. 391-397

11: Vectors and Matrices, pp. 398-445

11.1 Vectors and Dot Products, pp. 398-406
11.2 Planes and Projections, pp. 407-415
11.3 Cross Products and Determinants, pp. 416-424
11.4 Matrices and Linear Equations, pp. 425-434
11.5 Linear Algebra in Three Dimensions, pp. 435-445

12: Motion along a Curve, pp. 446-471

12.1 The Position Vector, pp. 446-452
12.2 Plane Motion: Projectiles and Cycloids, pp. 453-458
12.3 Tangent Vector and Normal Vector, pp. 459-463
12.4 Polar Coordinates and Planetary Motion, pp. 464-471

13: Partial Derivatives, pp. 472-520

13.1 Surface and Level Curves, pp. 472-474
13.2 Partial Derivatives, pp. 475-479
13.3 Tangent Planes and Linear Approximations, pp. 480-489
13.4 Directional Derivatives and Gradients, pp. 490-496
13.5 The Chain Rule, pp. 497-503
13.6 Maxima, Minima, and Saddle Points, pp. 504-513
13.7 Constraints and Lagrange Multipliers, pp. 514-520

14: Multiple Integrals, pp. 521-548

14.1 Double Integrals, pp. 521-526
14.2 Changing to Better Coordinates, pp. 527-535
14.3 Triple Integrals, pp. 536-540
14.4 Cylindrical and Spherical Coordinates, pp. 541-548

15: Vector Calculus, pp. 549-598

15.1 Vector Fields, pp. 549-554
15.2 Line Integrals, pp. 555-562
15.3 Green’s Theorem, pp. 563-572
15.4 Surface Integrals, pp. 573-581
15.5 The Divergence Theorem, pp. 582-588
15.6 Stokes’ Theorem and the Curl of F, pp. 589-598

16: Mathematics after Calculus, pp. 599-615

16.1 Linear Algebra, pp. 599-602
16.2 Differential Equations, pp. 603-610
16.3 Discrete Mathematics, pp. 611-615

Agora aqui estão os links

Chapter 1 – complete (PDF – 4.1 MB)

Chapter 2 – complete (PDF – 4.3 MB)

Chapter 3 – complete (PDF – 5.9 MB)

Chapter 4 – complete (PDF – 2.0 MB)

Chapter 5 – complete (PDF – 4.8 MB)

Chapter 6 – complete (PDF – 4.9 MB)

Chapter 7 – complete (PDF – 2.6 MB)

Chapter 8 – complete (PDF – 3.4 MB)

Chapter 9 – complete (PDF – 1.7 MB)

Chapter 10 – complete (PDF – 2.9 MB)

Chapter 11 – complete (PDF – 4.0 MB)

Chapter 12 – complete (PDF – 2.2 MB)

Chapter 13 – complete (PDF – 4.9 MB)

Chapter 14 – complete (PDF – 2.5 MB)

Chapter 15 – complete (PDF – 4.3 MB)

Chapter 16 – complete (PDF – 1.8 MB)
( MIT’S OpenCourseWare electronic publishing initiative)

Este livro tem a matemática mais básica talvez a um nível do 12º ano português , primeiros anos da universidade ).

—————————————————————————————————-

É também acompanhado de um guia de estudo que tem os problemas resolvidos do  livro acima mencionado.

Chapter 1 – (PDF)

Chapter2 – (PDF)

Chapter 3- (PDF)

Chapter 4- (PDF)

Chapter 5- (PDF)

Chapter 6-(PDF)

Chapter 7-(PDF)

Chapter 8-(PDF)

Chapter 9-(PDF)

Chapter 10 -(PDF)

Chapter 11- (PDF)

Chapter 12-(PDF)

Chapter 13 -(PDF)

Chapter 14 -(PDF)

Chapter 15 – (PDF)

É também acompanhado de um guia para o professor

Chapter 1 -(PDF)

Chapter 2 – (PDF)

Chapter 3 – (PDF)

Chapter 4 – (PDF)

Chapter 5 – (PDF)

Chapter 6 – (PDF)

Chapter 7 – (PDF)

Chapter 8 – (PDF)

Chapter 9- (PDF)

Chapter 10 – (PDF)

Chapter 11- (PDF)

Chapter 12 – (PDF)

Chapter 13 – (PDF)

Chapter 14 – (PDF)

Chapter 15 -   (PDF)

Chapter 16  -(PDF)

Multivariable Calculus

Um livro de matemática que aborda os seguintes temas:

Chapter One – Euclidean Three Space
1.1 Introduction
1.2 Coordinates in Three-Space
1.3 Some Geometry
1.4 Some More Geometry–Level Sets

Chapter Two – Vectors–Algebra and Geometry
2.1 Vectors
2.2 Scalar Product
2.3 Vector Product

Chapter Three – Vector Functions
3.1 Relations and Functions
3.2 Vector Functions
3.3 Limits and Continuity

Chapter Four – Derivatives
4.1 Derivatives
4.2 Geometry of Space Curves–Curvature
4.3 Geometry of Space Curves–Torsion
4.4 Motion

Chapter Five – More Dimensions
5.1 The space Rⁿ
5.2 Functions

Chapter Six – Linear Functions and Matrices
6.1 Matrices
6.2 Matrix Algebra

Chapter Seven – Continuity, Derivatives, and All That
7.1 Limits and Continuity
7.2 Derivatives
7.3 The Chain Rule

Chapter Eight – f:Rⁿ-› R
8.1 Introduction
8.2 The Directional Derivative
8.3 Surface Normals
8.4 Maxima and Minima
8.5 Least Squares
8.6 More Maxima and Minima
8.7 Even More Maxima and Minima

Chapter Nine – The Taylor Polynomial
9.1 Introduction
9.2 The Taylor Polynomial
9.3 Error
Supplementary material for Taylor polynomial in several variables.

Chapter Ten – Sequences, Series, and All That
10.1 Introduction
10.2 Sequences
10.3 Series
10.4 More Series
10.5 Even More Series
10.6 A Final Remark

Chapter Eleven – Taylor Series
11.1 Power Series
11.2 Limit of a Power Series
11.3 Taylor Series

Chapter Twelve – Integration
12.1 Introduction
12.2 Two Dimensions
Chapter Thirteen – More Integration
13.1 Some Applications
13.2 Polar Coordinates
13.3 Three Dimensions
Chapter Fourteen – One Dimension Again
14.1 Scalar Line Integrals
14.2 Vector Line Integrals
14.3 Path Independence

Chapter Fifteen – Surfaces Revisited
15.1 Vector Description of Surfaces
15.2 Integration

Chapter Sixteen – Integrating Vector Functions
16.1 Introduction
16.2 Flux

Chapter Seventeen – Gauss and Green
17.1 Gauss’s Theorem
17.2 Green’s Theorem
17.3 A Pleasing Application

Chapter Eighteen – Stokes
18.1 Stokes’s Theorem
18.2 Path Independence Revisited

Chapter Ninteen – Some Physics
19.1 Fluid Mechanics
19.2 Electrostatics

Já agora para o post ficar completo os autores são :

George Cain & James Herod .

Scirus

Gostam do google ?? Eu gosto , mas  por vezes por ter tanta coisa torna-se difícil encontrar o que se quer , ainda mais grave se o tema que procuramos é Ciência  .

Então é aqui que o Scirus  entra é um motor de Busca  onde a sua especialidade é Ciência .

Toca a procurar…

Scirus

Reconstrução em Tomografia óptica

Este link já tem uma explicação mais abrangente que o primeiro , já dá para perceber mais qualquer coisita.

Reconstrução em Tomografia óptica

(link está em baixo)

Se não voltar a estar online eu mesmo coloco num site qualquer .

Tomografia Óptica

Esta nova categoria que vai ser aberta , espero que seja do vosso agrado pois trata-se do tema que eu  escolhi para  trabalho de fim de Curso /estágio , e como gosto deste tema e sei que existe muito poucos sítios onde se podem encontrar coisas de alguma qualidade espero conseguir manter esta categoria muito activa.

Este primeiro link é “Time Series Methods in optical Tomography”  , é um bom link para começar a ter uma ideia do que esta temática consiste.

Time Series Methods in optical Tomography

Quantum Mechanics

Este sítio  trata de um dos  temas mais interessantes em Física , mas também um dos mais complexos , pelo que eu já vi do site é muito.

Muito bom para quem se está a iniciar neste domínio. 

( está em Inglês)

Quantum Mechanics

IOP ( Institute of Physics)

Neste sítio encontram-se bastantes artigos das   seguintes áreas :

 Física Médica e Biológica , Matemática aplicada e Matemática Física,Matéria Condensada e Ciência dos Materiais, Mecânica dos Fluido, Física Nuclear e de altas energias, Ciência das medições e sensores, Física atómica , molecular ,Óptica, Física dos plasmas para além de tópicos mais gerais .

 IOP