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Sabtu, 27 Agustus 2011

Categorical Data Analysis (Wiley Series in Probability and Statistics)


By Alan Agresti


  • Publisher: Wiley-Interscience
  • Number Of Pages: 734
  • Publication Date: 2002-07-22
  • ISBN-10 / ASIN: 0471360937
  • ISBN-13 / EAN: 9780471360933
  • Binding: Hardcover



Product Description:

Amstat News asked three review editors to rate their top five favorite books in the September 2003 issue. Categorical Data Analysis was among those chosen.

A valuable new edition of a standard reference.
"A 'must-have' book for anyone expecting to do research and/or applications in categorical data analysis."
-Statistics in Medicine on Categorical Data Analysis, First Edition

The use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. Responding to new developments in the field as well as to the needs of a new generation of professionals and students, this new edition of the classic Categorical Data Analysis offers a comprehensive introduction to the most important methods for categorical data analysis.

Designed for statisticians and biostatisticians as well as scientists and graduate students practicing statistics, Categorical Data Analysis, Second Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial regression for discrete data with normal regression for continuous data. Adding to the value in the new edition is coverage of:

Three new chapters on methods for repeated measurement and other forms of clustered categorical data, including marginal models and associated generalized estimating equations (GEE) methods, and mixed models with random effects Stronger emphasis on logistic regression modeling of binary and multicategory data An appendix showing the use of SAS for conducting nearly all analyses in the book Prescriptions for how ordinal variables should be treated differently than nominal variables Discussion of exact small-sample procedures More than 100 analyses of real data sets to illustrate application of the methods, and more than 600 exercises Summary: The source to understand categorical data and moreRating: 5The text is comprehensive in covering categorical data. Other reviews make this clear so I wanted to focus on the following. I was able to understand more general topics in statistics because of Agresti's depth of coverage on CDA. For example, for repeated measurements, Agresti clearly explains marginal models, conditional models, and generalized estimating equations. When I needed to understand these topics, I used this text because I have not found clear explanations elsewhere. In addition, SAS code and R code is available for the examples presented. Summary: the masterpiece by the masterRating: 5When this book came out in 1990 it was the first book to provide a truely modern treatment of categorical data analysis for both ordinal and nominal data. It provides an excellent treatment of the asymptotic theory for binary and multinomial data. It is extremely well written and is still a favorite of statisticians and practitioners. Because of its popularity and continued value, it should soon be added to the Wiley Classic series. This is the first book to take the regression approach to categorical data analysis tieing the subject to the methods and theory of the generalized linear models. It also was one of the first to show the modern practicality of exact permutation methods. The only drawback of this book is that it is 11 years old and there have been many interesting and relevant research developments in computer-intensive methods, analysis of missing data and mixed effects linear models to make a revision useful. Some of the latest developments can be found in Lloyd's new book "Statistical Analysis of Categorical Data" that was recently published by Wiley. Agresti provides clear advice and also gives a nice historical perspective on the development of the subject. The book is authoritative and includes numerous relevant references. Each chapter contains many exercises and a wealth of practical examples for illustration of the techniques. This is a good text from both practical and theoretical perspectives. It is excellent for a graduate level course on categorical data analysis. Summary: Dense and comprehensiveRating: 4Please read this in addition to the other reviews! I agree with the other reviewers except on one aspect: I found the style of writing a little bit choppy at times. The author uses short sentences when a few connecting words like e.g. "because", "due to", would have made understanding a little easier. Also, examples are not integrated optimally into the text so that there seems to be a gap between abstract conceptual explanations and the examples. Summary: The one to haveRating: 5If you want one book on Categorical Data analysis, this is the one. But there are others that are easier to read, if your math is not great (including the same author's book with an almost identical title) Summary: Good reading, but how do I analyze my data?Rating: 2In the theoretical sense, this book provides a very thorough overview of categorical data analysis. However, this book should not be used as a reference for the scientist needing to do the occasional number crunching of categorical data. The examples are vague and the tests are not well explained. If you want to derive the tests, this book is for you. If you're not a statistician at heart and just want the answer, I suggest looking at Conover's "Practical Nonparametric Statistics" for a good explanation of which tests to use and how to use them.

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Sabtu, 13 Agustus 2011

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition



by: Robin J. Gottlieb

A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course.

Table of Contents

Preface
Contents
PART I - Functions: An Introduction
  • 1 Functions Are Lurking Everywhere
    • 1.1 Functions Are Everywhere
    • * EXPLORATORY PROBLEMS FOR CHAPTER 1: Calibrating Bottles
    • 1.2 What Are Functions? Basic Vocabulary and Notation
    • 1.3 Representations of Functions
  • 2 Characterizing Functions and Introducing Rates of Change
    • 2.1 Features of a Function: Positive/Negative, Increasing/Decreasing, Continuous/Discontinuous
    • 2.2 A Pocketful of Functions: Some Basic Examples
    • 2.3 Average Rates of Change
    • * EXPLORATORY PROBLEMS FOR CHAPTER 2: Runners
    • 2.4 Reading a Graph to Get Information About a Function
    • 2.5 The Real Number System: An Excursion
  • 3 Functions Working Together
    • 3.1 Combining Outputs: Addition, Subtraction, Multiplication, and Division of Functions
    • 3.2 Composition of Functions
    • 3.3 Decomposition of Functions
    • * EXPLORATORY PROBLEMS FOR CHAPTER 3: Flipping, Shifting, Shrinking, and Stretching: Exercising Functions
    • 3.4 Altered Functions, Altered Graphs: Stretching, Shrinking, Shifting, and Flipping
PART II - Rates of Change: An Introduction to the Derivative
  • 4 Linearity and Local Linearity
    • 4.1 Making Predictions: An Intuitive Approach to Local Linearity
    • 4.2 Linear Functions
    • 4.3 Modeling and Interpreting the Slope
    • * EXPLORATORY PROBLEM FOR CHAPTER 4: Thomas Wolfe's Royalties for The Story of a Novel
    • 4.4 Applications of Linear Models: Variations on a Theme
  • 5 The Derivative Function
    • 5.1 Calculating the Slope of a Curve and Instantaneous Rate of Change
    • 5.2 The Derivative Function
    • 5.3 Qualitative Interpretation of the Derivative
    • * EXPLORATORY PROBLEMS FOR CHAPTER 5: Running Again
    • 5.4 Interpreting the Derivative: Meaning and Notation
  • 5 The Quadratics: A ProÞle of a Prominent Family of Functions
    • 6.1 A Prole of Quadratics from a Calculus Perspective
    • 6.2 Quadratics From A Noncalculus Perspective
    • * EXPLORATORY PROBLEMS FOR CHAPTER 6: Tossing Around Quadratics
    • 6.3 Quadratics and Their Graphs
    • 6.4 The Free Fall of an Apple: A Quadratic Model
  • 7 The Theoretical Backbone: Limits and Continuity
    • 7.1 Investigating Limits - Methods of Inquiry and a Definition
    • 7.2 Left- and Right-Handed Limits; Sometimes the Approach Is Critical
    • 7.3 A Streetwise Approach to Limits
    • 7.4 Continuity and the Intermediate and Extreme Value Theorems
    • * EXPLORATORY PROBLEMS FOR CHAPTER 7: Pushing the Limit
  • 8 Fruits of Our Labor: Derivatives and Local Linearity Revisited
    • 8.1 Local Linearity and the Derivative
    • * EXPLORATORY PROBLEMS FOR CHAPTER 8: Circles and Spheres
    • 8.2 The First and Second Derivatives in Context: Modeling Using Derivatives
    • 8.3 Derivatives of Sums, Products, Quotients, and Power Functions
PART III - Exponential, Polynomial, and Rational Functions with Applications
  • 9 Exponential Functions
    • 9.1 Exponential Growth: Growth at a Rate Proportional to Amount
    • 9.2 Exponential: The Bare Bones
    • 9.3 Applications of the Exponential Function
    • * EXPLORATORY PROBLEMS FOR CHAPTER 9: The Derivative of the Exponential Function
    • 9.4 The Derivative of an Exponential Function
  • 10 Optimization
    • 10.1 Analysis of Extrema
    • 10.2 Concavity and the Second Derivative
    • 10.3 Principles in Action
    • * EXPLORATORY PROBLEMS FOR CHAPTER 10: Optimization
  • 11 A Portrait of Polynomials and Rational Functions
    • 11.1 A Portrait of Cubics from a Calculus Perspective
    • 11.2 Characterizing Polynomials
    • 11.3 Polynomial Functions and Their Graphs
    • * EXPLORATORY PROBLEMS FOR CHAPTER 11: Functions and Their Graphs: Tinkering with Polynomials and Rational Functions
    • 11.4 Rational Functions and Their Graphs
PART IV - Inverse Functions: A Case Study of Exponential and Logarithmic Functions
  • 12 Inverse Functions: Can What Is Done Be Undone?
    • 12.1 What Does It Mean for F and G to Be Inverse Functions?
    • 12.2 Finding the Inverse of a Function
    • 12.3 Interpreting the Meaning of Inverse Functions
    • * EXPLORATORY PROBLEMS FOR CHAPTER 12: Thinking About the Derivatives of Inverse Functions
  • 13 Logarithmic Functions
    • 13.1 The Logarithmic Function Dened
    • 13.2 The Properties of Logarithms
    • 13.3 Using Logarithms and Exponentiation to Solve Equations
    • * EXPLORATORY PROBLEM FOR CHAPTER 13: Pollution Study
    • 13.4 Graphs of Logarithmic Functions: Theme and Variations
  • 14 Differentiating Logarithmic and Exponential Functions
    • 14.1 The Derivative of Logarithmic Functions
    • * EXPLORATORY PROBLEM FOR CHAPTER 14: The Derivative of the Natural Logarithm
    • 14.2 The Derivative of b^x Revisited
    • 14.3 Worked Examples Involving Differentiation
  • 15 Take It to the Limit
    • 15.1 An Interesting Limit
    • 15.2 Introducing Differential Equations
    • * EXPLORATORY PROBLEMS FOR CHAPTER 15: Population Studies
PART V - Adding Sophistication to Your Differentiation
  • 16 Taking the Derivative of Composite Functions
    • 16.1 The Chain Rule
    • 16.2 The Derivative of x^n where n is any Real Number
    • 16.3 Using the Chain Rule
    • * EXPLORATORY PROBLEMS FOR CHAPTER 16: Finding the Best Path
  • 17 Implicit Differentiation and its Applications
    • 17.1 Introductory Example
    • 17.2 Logarithmic Differentiation
    • 17.3 Implicit Differentiation
    • 17.4 Implicit Differentiation in Context: Related Rates of Change
PART VI - An Excursion into Geometric Series
  • 18 Geometric Sums, Geometric Series
    • 18.1 Geometric Sums
    • 18.2 Innite Geometric Series
    • 18.3 A More General Discussion of Innite Series
    • 18.4 Summation Notation
    • 18.5 Applications of Geometric Sums and Series
PART VII - Trigonometric Functions
  • 19 Trigonometry: Introducing Periodic Functions
    • 19.1 The Sine and Cosine Functions: Denitions and Basic Properties
    • 19.2 Modifying the Graphs of Sine and Cosine
    • 19.3 The Function f(x) = tanx
    • 19.4 Angles and Arc Lengths
  • 20 Trigonometry - Circles and Triangles
    • 20.1 Right-Triangle Trigonometry: The Denitions
    • 20.2 Triangles We Know and Love, and the Information They Give Us
    • 20.3 Inverse Trigonometric Functions
    • 20.4 Solving Trigonometric Equations
    • 20.5 Applying Trigonometry to a General Triangle: The Law of Cosines and the Law of Sines
    • 20.6 Trigonometric Identities
    • 20.7 A Brief Introduction to Vectors
  • 21 Differentiation of Trigonometric Functions
    • 21.1 Investigating the Derivative of sinx Graphically, Numerically, and Using Physical Intuition
    • 21.2 Differentiating sinx and cosx
    • 21.3 Applications
    • 21.4 Derivatives of Inverse Trigonometric Functions
    • 21.5 Brief Trigonometry Summary
PART VIII - Integration: An Introduction
  • 22 Net Change in Amount and Area: Introducing the Definite Integral
    • 22.1 Finding Net Change in Amount: Physical and Graphical Interplay
    • 22.2 The Denite Integral
    • 22.3 The Denite Integral: Qualitative Analysis and Signed Area
    • 22.4 Properties of the Denite Integral
  • 23 The Area Function and Its Characteristics
    • 23.1 An Introduction to the Area Function \int_a^x f(t)
    • 23.2 Characteristics of the Area Function
    • 23.3 The Fundamental Theorem of Calculus
  • 24 The Fundamental Theorem of Calculus
    • 24.1 Denite Integrals and the Fundamental Theorem
    • 24.2 The Average Value of a Function: An Application of the Denite Integral
PART IX - Applications and Computation of the Integral
  • 25 Finding Antiderivatives - An Introduction to Indefinite Integration
    • 25.1 A List of Basic Antiderivatives
    • 25.2 Substitution: The Chain Rule in Reverse
    • 25.3 Substitution to Alter the Form of an Integral
  • 26 Numerical Methods of Approximating Definite Integrals
    • 26.1 Approximating Sums: L_n, R_n, T_n, and M_n
    • 26.2 Simpson's Rule and Error Estimates
  • 27 Applying the DeÞnite Integral: Slice and Conquer
    • 27.1 Finding "Mass" When Density Varies
    • 27.2 Slicing to Find the Area Between Two Curves
  • 28 More Applications of Integration
    • 28.1 Computing Volumes
    • 28.2 Arc Length, Work, and Fluid Pressure: Additional Applications of the Denite Integral
  • 29 Computing Integrals
    • 29.1 Integration by Parts - The Product Rule in Reverse
    • 29.2 Trigonometric Integrals and Trigonometric Substitution
    • 29.3 Integration Using Partial Fractions
    • 29.4 Improper Integrals
PART X - Series
  • 30 Series
    • 30.1 Approximating a Function by a Polynomial
    • 30.2 Error Analysis and Taylor's Theorem
    • 30.3 Taylor Series
    • 30.4 Working with Series and Power Series
    • 30.5 Convergence Tests
  • 31 Differential Equations
    • 31.1 Introduction to Modeling with Differential Equations
    • 31.2 Solutions to Differential Equations: An Introduction
    • 31.3 Qualitative Analysis of Solutions to Autonomous Differential Equations
    • 31.4 Solving Separable First Order Differential Equations
    • 31.5 Systems of Differential Equations
    • 31.6 Second Order Homogeneous Differential Equations with Constant Coefcients
APPENDIX A - Algebra
  • A.1 Introduction to Algebra: Expressions and Equations
  • A.2 Working with Expressions
  • A.3 Solving Equations
APPENDIX B - Geometric Formulas
APPENDIX C - The Theoretical Basis of Applications of the Derivative
APPENDIX D - Proof by Induction
APPENDIX E - Conic Sections
  • E.1 Characterizing Conics from a Geometric Viewpoint
  • E.2 Dening Conics Algebraically
  • E.3 The Practical Importance of Conic Sections
APPENDIX F - L' Hopital's Rule: Using Relative Rates of Change to Evaluate Limits
  • F.1 Indeterminate Forms
APPENDIX G - Newton's Method: Using Derivatives to Approximate Roots
APPENDIX H - Proofs to Accompany Chapter 30, Series

The Britannica Guide to Analysis and Calculus (Math Explained)



By Erik Gregersen

  • Publisher: Rosen Educational Publishing
  • Number Of Pages: 304
  • Publication Date: 2010-08-15
  • ISBN-10 / ASIN: 1615301232
  • ISBN-13 / EAN: 9781615301232

The dynamism of the natural world means that it is constantly changing, sometimes rapidly, sometimes gradually. By mathematically interpreting the continuous change that characterizes so many natural processes, analysis and calculus have become indispensable to bridging the divide between mathematics and the sciences. This comprehensive volume examines the key concepts of calculus, providing students with a robust understanding of integration and differentiation. Biographies of important figures will leave readers with an increased appreciation for the sometimes competing theories that informed the early history of the field.

Contents

Introduction 12

Chapter 1: Measuring Continuous Change 21
Bridging the Gap Between Arithmetic and Geometry 22
Discovery of the Calculus and the Search for Foundations 24
Numbers and Functions 25
Number Systems 25
Functions 26
The Problem of Continuity 27
Approximations in Geometry 27
Infinite Series 29
The Limit of a Sequence 30
Continuity of Functions 31
Properties of the Real Numbers 32

Chapter 2: Calculus 35
Differentiation 35
Average Rates of Change 36
Instantaneous Rates of Change 36
Formal Definition of the Derivative 38
Graphical Interpretation 40
Higher-Order Derivatives 42
Integration 44
The Fundamental Theorem of Calculus 44
Antidifferentiation 45
The Riemann Integral 46

Chapter 3: Differential Equations 48
Ordinary Differential Equations 48
Newton and Differential Equations 48
Newton’s Laws of Motion 48
Exponential Growth and Decay 50
Dynamical Systems Theory and Chaos 51
Partial Differential Equations 55
Musical Origins 55
Harmony 55
Normal Modes 55
Partial Derivatives 57
D’Alembert’s Wave Equation 58
Trigonometric Series Solutions 59
Fourier Analysis 62

Chapter 4: Other Areas of Analysis 64
Complex Analysis 64
Formal Definition of Complex Numbers 65
Extension of Analytic Concepts to Complex Numbers 66
Some Key Ideas of Complex Analysis 68
Measure Theory 70
Functional Analysis 73
Variational Principles and Global Analysis 76
Constructive Analysis 78
Nonstandard Analysis 79

Chapter 5: History of Analysis 81
The Greeks Encounter Continuous Magnitudes 81
The Pythagoreans and Irrational Numbers 81
Zeno’s Paradoxes and the Concept of Motion 83
The Method of Exhaustion 84
Models of Motion in Medieval Europe 85
Analytic Geometry 88
The Fundamental Theorem of Calculus 89
Differentials and Integrals 89
Discovery of the Theorem 91
Calculus Flourishes 94
Elaboration and Generalization 96
Euler and Infinite Series 96
Complex Exponentials 97
Functions 98
Fluid Flow 99
Rebuilding the Foundations 101
Arithmetization of Analysis 101
Analysis in Higher Dimensions 103

Chapter 6: Great Figures in the History of Analysis 106
The Ancient and Medieval Period 106
Archimedes 106
Euclid 112
Eudoxus of Cnidus 115
Ibn al-Haytham 118
Nicholas Oresme 119
Pythagoras 122
Zeno of Elea 123
The 17th and 18th Centuries 125
Jean Le Rond d’Alembert 125
Isaac Barrow 129
Daniel Bernoulli 131
Jakob Bernoulli 133
Johann Bernoulli 134
Bonaventura Cavalieri 136
Leonhard Euler 137
Pierre de Fermat 140
James Gregory 144
Joseph-Louis Lagrange, comte de l’Empire 147
Pierre-Simon, marquis de Laplace 150
Gottfried Wilhelm Leibniz 153
Colin Maclaurin 158
Sir Isaac Newton 159
Gilles Personne de Roberval 167
Brook Taylor 168
Evangelista Torricelli 169
John Wallis 170
The 19th and 20th Centuries 173
Stefan Banach 173
Bernhard Bolzano 175
Luitzen Egbertus Jan Brouwer 176
Augustin-Louis, Baron Cauchy 177
Richard Dedekind 179
Joseph, Baron Fourier 182
Carl Friedrich Gauss 185
David Hilbert 189
Andrey Kolmogorov 191
Henri-Léon Lebesgue 195
Henri Poincaré 196
Bernhard Riemann 200
Stephen Smale 203
Karl Weierstrass 205

Chapter 7: Concepts in Analysis and Calculus 207
Algebraic Versus Transcendental Objects 207
Argand Diagram 209
Bessel Function 209
Boundary Value 211
Calculus of Variations 212
Chaos Theory 214
Continuity 216
Convergence 217
Curvature 218
Derivative 220
Difference Equation 222
Differential 223
Differential Equation 223
Differentiation 226
Direction Field 227
Dirichlet Problem 228
Elliptic Equation 229
Exact Equation 230
Exponential Function 231
Extremum 233
Fluxion 234
Fourier Transform 234
Function 235
Harmonic Analysis 238
Harmonic Function 240
Infinite Series 241
Infinitesimals 243
Infinity 245
Integral 249
Integral Equation 250
Integral Transform 250
Integraph 251
Integration 251
Integrator 252
Isoperimetric Problem 253
Kernel 255
Lagrangian Function 255
Laplace’s Equation 256
Laplace Transform 257
Lebesgue Integral 258
Limit 259
Line Integral 260
Mean-Value Theorem 261
Measure 261
Minimum 263
Newton and Infinite Series 263
Ordinary Differential Equation 264
Orthogonal Trajectory 265
Parabolic Equation 266
Partial Differential Equation 267
Planimeter 269
Power Series 269
Quadrature 271
Separation of Variables 271
Singular Solution 272
Singularity 273
Special Function 274
Spiral 276
Stability 278
Sturm-Liouville Problem 279
Taylor Series 280
Variation of Parameters 280

Glossary 282
Bibliography 285
Index 289

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