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Categorical Data Analysis (Wiley Series in Probability and Statistics)

noreply@blogger.com (math) — Sat, 27 Aug 2011 07:05:00 +0000

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

noreply@blogger.com (math) — Sat, 13 Aug 2011 13:52:00 +0000

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

Index

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The Britannica Guide to Analysis and Calculus (Math Explained)

noreply@blogger.com (math) — Sat, 13 Aug 2011 13:38:00 +0000

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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Practice Makes Perfect Calculus (Practice Makes Perfect Series)

noreply@blogger.com (math) — Sat, 13 Aug 2011 13:35:00 +0000

by: Dr. William Clark, Sandra McCune

Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: Calculus is not focused on any particular test or exam, but complementary to most calculus curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied it. Its all-encompassing approach will appeal to both U.S. and international students.William Clark has contributed to Practice Makes Perfect Calculus as an author. William Clark is visiting assistant professor of history at the University of California, Los Angeles, and coeditor of "The Sciences in Enlightened Europe," also published by the University of Chicago Press.

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Applied Linear Algebra and Matrix Analysis (Undergraduate Texts in Mathematics)

noreply@blogger.com (math) — Sat, 13 Aug 2011 12:53:00 +0000

By Thomas S. Shores

Publisher: Springer
Number Of Pages: 388
Publication Date: 2006-12-06
Sales Rank: 1244973
ISBN / ASIN: 0387331948
EAN: 9780387331942
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating:
Total Reviews:

Book Description: )

This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms.

Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics

*Gaussian elimination and other operations with matrices

*basic properties of matrix and determinant algebra

*standard Euclidean spaces, both real and complex

*geometrical aspects of vectors, such as norm, dot product, and angle

*eigenvalues, eigenvectors, and discrete dynamical systems

*general norm and inner-product concepts for abstract vector spaces

For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable.

Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory.

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Introduction to Calculus and Classical Analysis

noreply@blogger.com (math) — Sat, 13 Aug 2011 12:42:00 +0000

by Omar Hijab (Author)
# Hardcover: 375 pages
# Publisher: Springer Third Edition (April 2011)
# Language: English
# ISBN-10: 1441994874
# ISBN-13: 9781441994875 [Hardcover]

Intended for an honors calculus course or for an introduction to analysis, this is an ideal text for undergraduate majors since it covers rigorous analysis, computational dexterity, and a breadth of applications. The book contains many remarkable features: * complete avoidance of /epsilon-/delta arguments by using sequences instead * definition of the integral as the area under the graph, while area is defined for every subset of the plane * complete avoidance of complex numbers * heavy emphasis on computational problems * applications from many parts of analysis, e.g. convex conjugates, Cantor set, continued fractions, Bessel functions, the zeta functions, and many more * 344 problems with solutions in the back of the book.

ISSN 0172-6056
ISBN 978-1-4419-9487-5 e-ISBN 978-1-4419-9488-2
DOI 10.1007/978-1-4419-9488-2
Library of Congress Control Number: 2011923653
Mathematics Subject Classification (2010): 41-XX, 40-XX, 33-XX, 05-XX

Contents

Preface

1 The Set of Real Numbers
1.1 Sets and Mappings
1.2 The Set R
1.3 The Subset N and the Principle of Induction
1.4 The Completeness Property
1.5 Sequences and Limits
1.6 Nonnegative Series and Decimal Expansions
1.7 Signed Series and Cauchy Sequences

2 Continuity
2.1 Compactness
2.2 Continuous Limits
2.3 Continuous Functions

3 Differentiation
3.1 Derivatives
3.2 Mapping Properties
3.3 Graphing Techniques
3.4 Power Series
3.5 Trigonometry
3.6 Primitives

4 Integration
4.1 The Cantor Set
4.2 Area
4.3 The Integral
4.4 The Fundamental Theorem of Calculus
4.5 The Method of Exhaustion

Applications
5.1 Euler’s Gamma Function
5.2 The Number π
5.3 Gauss’ Arithmetic–Geometric Mean (AGM)
5.4 The Gaussian Integral
5.5 Stirling’s Approximation of n!
5.6 Infinite Products
5.7 Jacobi’s Theta Functions
5.8 Riemann’s Zeta Function
5.9 The Euler–Maclaurin Formula

A Solutions
A.1 Solutions to Chapter 1
A.2 Solutions to Chapter 2
A.3 Solutions to Chapter 3
A.4 Solutions to Chapter 4
A.5 Solutions to Chapter 5

References

Index

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Cliffs Quick Review Calculus

noreply@blogger.com (math) — Sat, 13 Aug 2011 12:36:00 +0000

We take great notes–and make learning a snap

When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core Calculus concepts–from functions, limits, and derivatives to differentials, integration, and definite integrals– and get the best possible grade.

At CliffsNotes, we’re dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented writers who know how to cut to the chase– and zero in on the essential information you need to succeed.

Make the grade with CliffsQuickReviews

CliffsQuickReviews are available for more than 30 introductory level courses. See inside for a complete listing of these and other bestselling Cliffs titles.

Summary: Great primer, supplement, and refresher for calculus
Rating: 4

Having completed the standard three semesters of calculus as a teenager, many years ago, I periodically need a refresher, and this book was perfect. However, it only reviews the basic calculus normally covered in the first semester of calculus, and part of the second semester. Topics, for example, which are not covered in this book include: sequences and series, parametric equations and polar coordinates, vectors and spatial geometry, partial derivatives, multiple integrals, and vector calculus. However, this book is a nice refresher that can be completed in a short period of time.

Because it covers the essentials, you don't have to spend more time covering topics than necessary to grasp the tools and concepts. I worked all the problems at the end of each chapter, and at the end of the book. I felt that the number of problems was just right: not too few and not too many. Answers are provided. There is an appendix that briefly revisits some examples given in the book, to show how your graphing calculator help you out with these problems. If you read all of the chapters in this book, I definitely recommend that you also read this review of graphing calculators in the appendix. The technology enhances one's study of mathematics tremendously.

For students entering calculus, I think this book is valuable as both a primer and a course supplement. If you only need the first semester of calculus, then this book covers all of the basics. However, you will need a textbook for thorough and in-depth coverage, as well as ample problem sets, to become proficient in the subject. After you've had one semester of calculus, then this book serves as a handy reference.

This book is not without some occasional errors, which are usually in the answers to problems. This is unfortunate for the new student unable to recognize these errors. There is no errata page published on the CliffsNotes website. Of the 42 review questions at the end of the book, the answers provided to six of these questions say, "Provide your own answer." Although these are critical thinking and proof questions, it is still annoying that an extra half-page, or less, wasn't included to provide solutions to these problems.

Summary: Good little book
Rating: 4

I didn't purchase my Calculus text book, but I did get this. This is way cheaper and covered pretty much all the material I needed. I did find myself using online resources a little, but this book explains the concepts well and provides good practice problems. Well worth it. There's also a free version online at the Cliffs Notes website.

Summary: Useful only if you are reviewing for an examination of "plug and chug" differentiation and integration problems
Rating: 2

Unless you are preparing to take a calculus exam consisting of a series of basic differentiation and integration problems, then I really don't see any use for this book. The reviews of what differentiation and integration really are have no depth to them, so those sections are of limited use in bringing you back up to speed in calculus.
This makes the book almost totally a collection of sections of the form:

Here is a type of mathematical expression and this is how we differentiate (integrate) it, with some examples.

One of my college math professors referred to these problems as "plug and chug", where you simply execute the rules without having any real understanding of the concept. Therefore, if you are trying to refresh your understanding of calculus, then this book will be of little value.

Summary: Unhelpful
Rating: 1

I purchased this book because I had a good experience with both the Algebra and Algebra II Quick Review. This book, however has not helped me one bit. It's worse than using the textbook to learn!
The formulas it gives are too complicated and it doesn't even give you any shortcut techniques. I do not recommend this book to anyone who needs supplementary instruction in Calculus.

Summary: Great supplement for Calc!
Rating: 5

I used this book as a supplement to Calculus I and II courses. Cliffs breaks down limits, derivatives and integration in a very simple way. You don't have to be a "math nerd" to grasp this book. During calculus lectures I would reference the book in class to make sure I understood the professor. There were even a few times when the professor asked to use my Cliffs in class because he knew the book had great examples. Needless to say I got an A in the course. Now as a senior electrical engineering student, I still use it if I need to reference stuff that I forgot.

Just a warning though, if you want to be good in calculus don't just read the Cliffs and your textbook. Dig into the text or cliffs and work a ton of problems (beyond just the assigned homework) and you will pass the course.

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A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)

noreply@blogger.com (math) — Sat, 13 Aug 2011 11:32:00 +0000

By Sudhir R. Ghorpade, Balmohan V. Limaye

Publisher: Springer
Number Of Pages: 432
Publication Date: 2006-06-05
ISBN-10 / ASIN: 0387305300
ISBN-13 / EAN: 9780387305301
Binding: Hardcover

Product Description:

This book provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. Throughout the book, the authors highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps students get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis.

The only prerequisites for reading this book are topics that are normally covered in high school; however, the reader is expected to possess some mathematical maturity and an ability to understand and appreciate proofs. This book can be used as a textbook for a serious undergraduate course in calculus, while parts of the book can be used for advanced undergraduate and graduate courses in real analysis. Each chapter contains several examples and a large selection of exercises, as well as "Notes and Comments" describing salient features of the exposition, related developments and references to relevant literature.

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Foundations of Differential Calculus

noreply@blogger.com (math) — Sat, 13 Aug 2011 09:41:00 +0000

By L. Euler

Publisher: Springer
Number Of Pages: 194
Publication Date: 2000-05-23
Sales Rank: 376288
ISBN / ASIN: 0387985344
EAN: 9780387985343
Binding: Hardcover
Manufacturer: Springer
Studio: Springer
Average Rating: 5
Total Reviews: 2

Book Description:

The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.

Date: 2004-12-12 Rating: 5
Review:

PART 1 OF BOOK

I was disappointed when I opened the box to find a skinny hardcover 6" by 8" book. I was expecting a full blown thick textbook for the price of $60. This is more of a novelty item for those of you who wish to find out how the theory of differentiation started from scratch. The book has the first steps and analysis that lead to the power rule etc. There is lot of useful information but the notations are a bit a different. This is not a text book with problems and solution. There are examples but these examples are nothing like you'd find in a calculus class. I think this book should be sold for $25 tops. Another thing is that when Euler wrote this book, it had 23 chapters, this is only the first 9 chapters so it leaves you shy of the whole picture. There is about 15 pages on solving Linear Differential equations. I have not read the book word per word yet. So for the intelligent ones, there may be more information they could harvest out of this book. This book is definitely over priced!

Date: 2000-06-19 Rating: 5
Review:

A Classic and a Current

While Newton (arguably) founded the subject, Euler (pronounced 'oiler') developed all the methods used today in Differential Calculus. Not only was Leonhard Euler the greatest Mathematician of his day (he actually wrote over a quarter of the tracts from the 18th century!), but he wrote in a humbling and readable manner such that anyone with a foundation may approach his proofs. And this text is no different; simply a book any mathematician should own. Truly one of the milestones of Calculus.

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Government Student Loan Consolidation

noreply@blogger.com (math) — Tue, 22 Mar 2011 16:02:00 +0000

The price of higher education has continued to rise even as the importance of furthering one's education has skyrocketed. As a result, more students and graduates are incurring student loans. For these individuals, government student loan consolidation offers one option which may reduce their burden in some circumstances.

Government Student Loan Consolidation: Who's Eligible

All students with federal student loans are eligible for government student loan consolidation. However, some requirements must be met in advance. First, the student must have more than one federal student loan. If he or she only have one now, then consolidation is unnecessary. Second, students must be in good standing with their loans. That means the student must either still be in his or her six-month post-graduate grace period or have made three full monthly payments on time for each of the loans being consolidated.

Both subsidized and unsubsidized student loans can be consolidated. According to the Federal Consolidation Loan Information section of the Carnegie Mellon web site, however, those loans will be consolidated in two separate loans so that lenders can monitor them separately as they are required to do by law. Despite that, the payments for those loans will be combined so the student still only pays one payment per month.

Government Student Loan Consolidation: Repayment

Loans consolidated through government student loan consolidation must still be repaid. One of the advantages of consolidation, however, is that the repayment period is often extended so students have longer to pay off their loans. That means students will need to make lower monthly payments. Maximum repayment periods for consolidated loans vary from 10 to 30 years depending on how much is owed. The cost of the monthly payments depends on the repayment period, total loan amount, and interest rate.

Students should keep in mind that while a longer repayment period and lower monthly payments can be useful now they will end up paying more in the long run because of the additional accumulated interest.

To learn more about government student loan consolidation, read "Student Loan Consolidation Programs", "Student Loan Consolidations," or "A Primer on Loan Consolidation".

Soal UTS Matematika Ekonomi

noreply@blogger.com (math) — Mon, 21 Mar 2011 07:15:00 +0000

Berikut lampira soal uts matematika ekonomi 2

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