Fractals Everywhere

 2.ª edição

Michael F. Barnsley

Morgan Kaufmann Publishers | 2000 | 534 páginas |  PDF | 15,3 Mb

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This volume is the second edition of the highly successful Fractals Everywhere. The Focus of this text is how fractal geometry can be used to model real objects in the physical world.
This edition of Fractals Everywhere is the most up-to-date fractal textbook available today.
Fractals Everywhere may be supplemented by Michael F. Barnsley's Desktop Fractal Design System (version 2.0) with IBM for Macintosh software. The Desktop Fractal Design System 2.0 is a tool for designing Iterated Function Systems codes and fractal images, and makes an excellent supplement to a course on fractal geometry
* A new chapter on recurrent iterated function systems, including vector recurrent iterated function systems.* Problems and tools emphasizing fractal applciations.* An all-new answer key to problems in the text, with solutions and hints.

Mathematics for Physicists and Engineers: Fundamentals and Interactive Study Guide

Klaus Weltner, Wolfgang J. Weber, Jean Grosjean and Peter Schuster 


Springer  |  2009 | 596 páginas |  PDF | 5,5 Mb 

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This textbook offers an accessible and highly-effective approach which is characterised by the combination of the textbook with a detailed study guide on an accompanying CD. This study guide divides the whole learning task into small units which the student is very likely to master successfully. Thus he or she is asked to read and study a limited section of the textbook and then to return to the study guide. Through interactive learning with the study guide, the results are controlled, monitored and deepened by graded questions, exercises, repetitions and finally by problems and applications of the content studied. Since the degree of difficulties is slowly rising, the students gain confidence and experience their own progress in mathematical competence thus fostering motivation. Furthermore in case of learning difficulties, he or she is given supplementary explanations and, in case of individual needs, supplementary exercises and applications. So the sequence of the studies is individualized according to the individual’s performance and needs and can be regarded as a total tutorial experience. More than that, the study guide aims to satisfy two objectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offers advice on the improvement of study skills. Empirical studies have shown that the student’s competence for using written information has improved significantly by using the combination of textbook and study guide.

Teach Yourself VISUALLY Calculus

Dale W. Johnson M.A.

Visual | 2008  | 291 páginas | PDF | 10,1 Mb 

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Calculus can test the limits of even the most advanced math students. This visual, easy-to-follow book deconstructs complex mathematical concepts in a way that's infinitely easier to grasp. With clear, color-coded methods, you'll get step-by-step instructions on solving problems using limits, derivatives, differentiation, curve sketching, and integrals. Easy access to concepts means you don't have to sort through lengthy instructions text, and you can refer to the Appendix for a look at common differentiation rules, integration formulas, and trigonometric identities. 

Livro da mesma colecção, disponível no blog

Teach Yourself VISUALLY Algebra (2008)

Limits, Limits Everywhere: The Tools of Mathematical Analysis

David Applebaum 

Oxford University Press | 2012 | 217 páginas | RAR - PDF | 1,09 Mb

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201208182

A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series. 

Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and ?, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject. 

A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.

Contents

PART I APPROACHING LIMITS
1. A Whole Lot of Numbers 2
1.1 Natural Numbers 2
1.2 Prime Numbers 3
1.3 The Integers 9
1.4 Exercises for Chapter 1 12
2. Let’s Get Real 14
2.1 The Rational Numbers 14
2.2 Irrational Numbers 17
2.3 The Real Numbers 23
2.4 A First Look at Infinity 24
2.5 Exercises for Chapter 2 26
3. The Joy of Inequality 28
3.1 Greater or Less? 28
3.2 Intervals 33
3.3 The Modulus of a Number 34
3.4 Maxima and Minima 38
3.5 The Theorem of the Means 38
3.6 Getting Closer 41
3.7 Exercises for Chapter 3 42
4. Where Do You Go To, My Lovely? 45
4.1 Limits 45
4.2 Bounded Sequences 54
4.3 The Algebra of Limits 56
4.4 Fibonacci Numbers and the Golden Section 59
4.5 Exercises for Chapter 4 62
5. Bounds for Glory 65
5.1 Bounded Sequences Revisited 65
5.2 Monotone Sequences 69
5.3 An Old Friend Returns
5.4 Finding Square Roots 73
5.5 Exercises for Chapter 5 75
6. You Cannot be Series 78
6.1 What are Series? 78
6.2 The Sigma Notation 79
6.3 Convergence of Series 82
6.4 Nonnegative Series 84
6.5 The Comparison Test 88
6.6 Geometric Series 92
6.7 The Ratio Test 95
6.8 General Infinite Series 98
6.9 Conditional Convergence 99
6.10 Regrouping and Rearrangements 102
6.11 Real Numbers and Decimal Expansions 104
6.12 Exercises for Chapter 6 105
PART II EXPLORING LIMITS
7. Wonderful Numbers – e,π and γ 110
7.1 The Number e 110
7.2 The Number π 118
7.3 The Number γ 123
8. Infinite Products 126
8.1 Convergence of Infinite Products 126
8.2 Infinite Products and Prime Numbers 130
8.3 Diversion – Complex Numbers and the Riemann Hypothesis 134
9. Continued Fractions 138
9.1 Euclid’s Algorithm 138
9.2 Rational and Irrational Numbers as Continued Fractions 139
10. How Infinite Can You Get? 145
11. Constructing the Real Numbers 151
11.1 Dedekind Cuts 151
11.2 Cauchy Sequences 152
11.3 Completeness 153
12. Where to Next in Analysis? The Calculus 157
12.1 Functions 157
12.2 Limits and Continuity
12.3 Differentiation 163
12.4 Integration 166
13. Some Brief Remarks About the History of Analysis 171
Further Reading 175
Appendices 181
Appendix 1: The Binomial Theorem 181
Appendix 2: The Language of Set Theory 183
Appendix 3: Proof by Mathematical Induction 186
Appendix 4: The Algebra of Numbers 188
Hints and Solutions to Selected Exercise 190
Index 195

First Course In Vector Mathematics

Kirstie Jacks , Jae Calabrese

 World Technologies | 2012 | 162 páginas | PDF | 2,85 Mb

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This book provides a First Course in Vector Mathematics.


Table of Contents
Chapter 1 - Euclidean Vector
Chapter 2 - Basic Properties of Euclidean Vector
Chapter 3 - Cross Product
Chapter 4 - Pseudovector & Vector Calculus
Chapter 5 - Covariance and Contravariance of Vectors
Chapter 6 - Vector Field
Chapter 7 - Bivector
Chapter 8 - Conservative Vector Field
Chapter 9 - Curl (Mathematics)
Chapter 10 - Del
Chapter 11 - Divergence
Chapter 12 - Divergence Theorem

Problemas elementales de máximo y mínimo, Suma de cantidades infinitamente pequeñas

I. P. Natanson

Ed MIR | 1977 | 112 páginas | PDF | 16,6 Mb

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Se exponen algunos procedimientos elementales para solución, de problemas de máximo y mínimo. La obra está destinada a los alumnos de los grados superiores de la escuela secundaria que deseen adquirir algunas nociones respecto al carácter de los problemas que se examinan en las matemáticas superiores. El material que se expone puede utilizarse en el trabajo de los círculos matemáticos escolares

Obstacles épistémologiques relatifs à la notion de limite

Anka Sierpinska

Recherches en Didactique des Mathematiques, Vol. 6, n°1, pp. 5-67, 1985

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Résumé

La recherche dont il est question dans le présent article se place dans la voie des recherches indiquée par Guy Brousseau dans son article (1983). Découvrir les obstacles épistémologiques lié aux mathématiques à enseigner à l’école et trouver les moyens didactiques pour aider les élèves à les surmonter - voilà, brièvement, deux principaux problèmes de ce programme de recherche. Ici, il s’agit du cas particulier de la notion de limite et l’article ne touche qu’au premier de ces problèmes : on propose une liste d’obstacles épistémologiques relatifs à la notion de limite présents encore chez des élèves d’aujourd’hui ; on ne propose pas les situations didactiques qui permettraient aux élèves de franchir ces obstacles.

Abstract

The present paper is concerned with a research the direction of which was indicated by Guy Brousseau in his 1983. To discover the epistemological obstacles connected with mathematics to be taught at school and to.elaborate didactical means to help the students to overcome them- these are, briefly, two main problems of this research programme. In this paper, the particular case of the notion of limit is considered and only the first of the two above mentionned problems is dealt with : a list of epistemological obstacles relative to the notion of limit is proposed ; there are no proposals of didactical situations enabling the students to overcome these.

Resumen

La investigación que trata este artículo se situa dentro de la línea de investigaciones indicadas por Guy Brousseau (1983). Descubrir los obstáculos epistemológicos ligados a las matemáticas que se enseñan en la escuela y encontrar los medios didácticos para ayudar los alumnos a superarlos. Brevemente presentamos aqui dos problemas principales de ese programa de investigación. Se trata del caso particular de la noción de limite y el artículo toca solamente el primero de esos problemas : se propone una lista de obstáculos epistemológicos relativos a la noción de límite presentes todavía en los alumnos de hoy en dia ; no se proponen situaciones didácticas que permitirian a los alumnos de superar esos obstáculos.

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What Is Calculus About?

(New Mathematical Library)

Mathematical Association of America | 1962| 118 Páginas | PDF | 4,01 Mb

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Whenever I teach calculus, my emphasis is always on the fact that the basic ideas of calculus can be understood by almost anyone. While I am not always successful in proving this to the students, Sawyer certainly would be. His explanations of the basics of a derivative are the clearest, most understandable that I have ever seen. There are many diagrams, and each one has a specific purpose and they are well integrated into the textual explanations.
This is not a book that you could use to teach a college calculus course. The mandatory epsilons and deltas that form the backbone of basic calculus are mentioned only as an incidental. Sawyer sets out to explain the foundation ideas of calculus in terms of everyday occurrences and for that reason it is better suited to someone who is curious about calculus. However, it could be used as a supplemental text in the foundations of science, as calculus is used in all areas of change, which describes almost all of nature.
While the notation of mathematics is concise, abstract and often appears esoteric, many of the ideas expressed in that notation are quite easy to follow. In this book, Sawyer explains what calculus is all about in terms that anyone who understands motion can follow. There needs to be more people like him writing books like this.

The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time

Jason Socrates Bardi

Thunder's Mouth Press | 2006 | 288 páginas | Djvu | 1,48 Mb

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Now regarded as the bane of many college students’ existence, calculus was one of the most important mathematical innovations of the seventeenth century. But a dispute over its discovery sewed the seeds of discontent between two of the greatest scientific giants of all time — Sir Isaac Newton and Gottfried Wilhelm Leibniz.

Today Newton and Leibniz are generally considered the twin independent inventors of calculus, and they are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret.

This long and bitter dispute has been swept under the carpet by historians — perhaps because it reveals Newton and Leibniz in their worst light — but The Calculus Wars tells the full story in narrative form for the first time. This vibrant and gripping scientific potboiler ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad and, in the end, completely

Calculus DeMYSTiFieD

Steven Krantz 

2.ª edição

McGraw-Hill Professional | 2011 | 416 páginas | RAR - PDF | 1,6 Mb

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Calculate this: learning CALCULUS just got a whole lot easier!

Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject.

Written in a step-by-step format, this practical guide begins by covering the basics--number systems, coordinates, sets, and functions. You'll move on to limits, derivatives, integrals, and indeterminate forms. Transcendental functions, methods of integration, and applications of the integral are also covered. Clear examples, concise explanations, and worked problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce key concepts.

It's a no-brainer! You'll get:
Applications of the derivative and the integral
Rules of integration
Coverage of improper integrals
An explanation of calculus with logarithmic and exponential functions
Details on calculation of work, averages, arc length, and surface area

Simple enough for a beginner, but challenging enough for an advanced student, Calculus Demystified, Second Edition, is one book you won't want to function without!
20120701

1.ª edição

McGraw-Hill Professional | 2002 | 356 páginas | PDF | 12 Mb

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Here’s an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math background you need inside and uses practical examples, real data, and a totally different approach to mastering calculus. With CalculusDemystified you ease into the subject one simple step at a time — at your own speed. A user-friendly, accessible style incorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important concepts.

From the Calculus to Set Theory 1630-1910

I. Grattan-Guinness

Princeton University Press | 2000 | 306 páginas | DJVU | 3,45 Mb

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From the Calculus to Set Theory traces the development of the calculus from the early seventeenth century through its expansion into mathematical analysis to the developments in set theory and the foundations of mathematics in the early twentieth century. It chronicles the work of mathematicians from Descartes and Newton to Russell and Hilbert and many, many others while emphasizing foundational questions and underlining the continuity of developments in higher mathematics. The other contributors to this volume are H. J. M. Bos, R. Bunn, J. W. Dauben, T. W. Hawkins, and K. Møller-Pedersen.

Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus

M. . W. Tent

A K Peters/CRC Press | 2011 | 260 páginas | PDF | 2,4 Mb

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Gottfried Wilhelm Leibniz: The Polymath Who Brought Us Calculus focuses on the life and accomplishments of one of the seventeenth century’s most influential mathematicians and philosophers. The book, which draws on Leibniz’s written works and translations, and reconstructs dialogues Leibniz may have had based on the historical record of his life experiences, portrays Leibniz as both a phenomenal genius and a real person.

Suitable for middle school age readers, the book traces Leibniz’s life from his early years as a young boy and student to his later work as a court historian. It discusses the intellectual and social climate in which he fought for his ideas, including his rather contentious relationship with Newton (both claimed to have invented calculus). The text describes how Leibniz developed the first mechanical calculator that could handle addition, subtraction, multiplication, and division. It also examines his passionate advocacy of rational arguments in all controversial matters, including the law, expressed in his famous exclamation calculemus: let us calculate to see who is right.

Leibniz made groundbreaking contributions to mathematics and philosophy that have shaped our modern views of these fields.

Precalculus: Functions and Graphs

4.ª Edição

Mark Dugopolski

Addison Wesley | 2012 | 960 páginas | PDF | 27,8 Mb

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  Dugopolski’s Precalculus: Functions and Graphs, Fourth Edition gives students the essential strategies they need to make the transition to calculus. The author’s emphasis on problem solving and critical thinking is enhanced by the addition of 900 exercises including new vocabulary and cumulative review problems. Students will find carefully placed learning aids and review tools to help them learn the math without getting distracted. Along the way, students see how the algebra connects to their future calculus courses, with tools like Foreshadowing Calculus and Concepts of Calculus.

Table of Contents

P. Prerequisites

P.1 Real numbers and Their Properties

P.2 Integral Exponents and Scientific Notation

P.3 Rational Exponents and Radicals

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

P.7 Complex Numbers

Chapter P Highlights

Chapter P Review Exercises

Chapter P Test

1. Equations, Inequalities, and Modeling

1.1 Equations in One Variable

1.2 Constructing Models to Solve Problems

1.3 Equations and Graphs in Two Variables

1.4 Linear Equations in Two Variables

1.5 Scatter Diagrams and Curve Fitting

1.6 Complex Numbers

1.7 Quadratic Equations

1.8 Linear and Absolute Value Inequalities

Chapter 1 Highlights

Chapter 1 Review Exercises

Chapter 1 Test

Concepts of Calculus: Limits

2. Functions and Graphs

2.1 Functions

2.2 Graphs of Relations and Functions

2.3 Families of Functions, Transformations, and Symmetry

2.4 Operations with Functions

2.5 Inverse Functions

2.6 Constructing Functions with Variation

Chapter 2 Highlights

Chapter 2 Review Exercises

Chapter 2 Test

Tying it all Together

Concepts of Calculus: Instantaneous Rate of Change

3. Polynomial and Rational Functions

3.1 Quadratic Functions and Inequalities

3.2 Zeroes of Polynomial Functions

3.3 The Theory of Equations

3.4 Miscellaneous Equations

3.5 Graphs of Polynomial Functions

3.6 Rational Functions and Inequalities

Chapter 3 Highlights

Chapter 3 Review Exercises

Chapter 3 Test

Tying it all Together

Concepts of Calculus: Instantaneous Rate of Change of the Power Functions

4. Exponential and Logarithmic Functions

4.1 Exponential Functions and Their Applications

4.2 Logarithmic Functions and Their Applications

4.3 Rules of Logarithms

4.4 More Equations and Applications

Chapter 4 Highlights

Chapter 4 Review Exercises

Chapter 4 Test

Tying it all Together

Concepts of Calculus: The Instantaneous Rate of Change of f(x)= ex

5. The Trigonometric Functions

5.1 Angles and Their Measurements

5.2 The Sine and Cosine Functions

5.3 The Graphs of the Sine and Cosine Functions

5.4 The Other Trigonometric Functions and Their Graphs

5.5 The Inverse Trigonometric Functions

5.6 Right Triangle Trigonometry

Chapter 5 Highlights

Chapter 5 Review Exercises

Chapter 5 Test

Tying it all Together

Concepts of Calculus: Evaluating Transcendental Functions

6. Trigonometric Identities and Conditional Equations

6.1 Basic Identities

6.2 Verifying Identities

6.3 Sum and Difference Identities

6.4 Double-Angle and Half-Angle Identities

6.5 Product and Sum Identities

6.6 Conditional Trigonometric Equations

Chapter 6 Highlights

Chapter 6 Review Exercises

Chapter 6 Test

Tying it all Together

Concepts of Calculus: Area of a Circle and π

7. Applications of Trigonometry

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Vectors

7.4 Trigonometric Form of Complex Numbers

7.5 Powers and Roots of Complex and Numbers

7.6 Polar Equations

Chapter 7 Highlights

Chapter 7 Review Exercises

Chapter 7 Test

Tying it all Together

Concepts of Calculus: Limits and Asymptotes

8. Systems of Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Nonlinear Systems of Equations

8.4 Partial Fractions

8.5 Inequalities and Systems of Inequalities in Two Variables

8.6 The Linear Programming Model

Chapter 8 Highlights

Chapter 8 Review Exercises

Chapter 8 Test

Tying it all Together

Concepts of Calculus: Instantaneous Rate of Change and Partial Fractions

9. Matrices and Determinants

9.1 Solving Linear Systems Using Matrices

9.2 Operations with Matrices

9.3 Multiplication of Matrices

9.4 Inverses of Matrices

9.5 Solution of Linear Systems in Two Variables Using Determinants

9.6 Solution of Linear Systems in Three Variables Using Determinants

Chapter 9 Highlights

Chapter 9 Review Exercises

Chapter 9 Test

Tying it all Together

10. The Conic Sections

10.1 The Parabola

10.2 The Ellipse and the Circle

10.3 The Hyperbola

10.4 Rotation of Axes

10.5 Polar Equations of the Conics

Chapter 10 Highlights

Chapter 10 Review Exercises

Chapter 10 Test

Tying it all Together

Concepts of Calculus: The Reflection Property of a Parabola

11. Sequences, Series, and Probability

11.1 Sequences

11.2 Series

11.3 Geometric Sequences and Series

11.4 Counting and Permutations

11.5 Combinations, Labeling, and the Binomial Theorem

11.6 Probability

11.7 Mathematical Induction

Chapter 11 Highlights

Chapter 11 Review Exercises

Chapter 11 Test

Concepts of Calculus: Limits of Sequences

A. Appendix: Basic Algebra Review

A.1 Real Numbers and Their Properties

A.2 Exponents and Radicals

A.3 Polynomials

A.4 Factorials Polynomials

A.5 Rational Expressions

B. Appendix: Solutions to Try This Exercises

Credits

Answers to Selected Exercises

Index of Applications

Index

Precalculus: Functions and Graphs

12.ª edição

Earl Swokowski, Jeffery Cole

Brooks Cole  | 2011 | 796 páginas | PDF | 13 Mb

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The latest edition of Swokowski and Cole's PRECALCULUS: FUNCTIONS AND GRAPHS retains the elements that have made it so popular with instructors and students alike: clear exposition, an appealing and uncluttered layout, and applications-rich exercise sets. The excellent, time-tested problems have been widely praised for their consistency and their appropriate level of difficulty for precalculus students. The book also provides calculator examples, including specific keystrokes that show students how to use various graphing calculators to solve problems more quickly. The Twelfth Edition features updated topical references and data, and continues to be supported by outstanding technology resources. Mathematically sound, this book effectively prepares students for further courses in mathematics.

Each chapter ends with Review Exercises, Discussion Exercises, and a Chapter Test.
1. TOPICS FROM ALGEBRA.
Real Numbers. Exponents and Radicals. Algebraic Expressions. Equations. Complex Numbers. Inequalities.
2. FUNCTIONS AND GRAPHS.
Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Polynomial Functions of Degree Greater Than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation.
4. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS.
Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations.
5. TRIGONOMETRIC FUNCTIONS.
Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of the Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems.
6. ANALYTIC TRIGONOMETRY.
Verifying Trigonometric Identities. Trigonometric Equations. The Additions and Subtraction of Formulas. Multiple-Angle Formulas. Product-To-Sum and Sum-To-Product Formulas. The Inverse Trigonometric Functions.
7. APPLICATIONS OF TRIGONOMETRY.
The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers.
8. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More Than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions.
9. SEQUENCES, SERIES, AND PROBABILITY.
Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability.
10. TOPICS FROM ANALYTICAL GEOMETRY.
Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics.
Appendix I: Common Graphs and Their Equations.
Appendix II: A Summary of Graph Transformations.
Appendix III: Graphs of the Trigonometric Functions and Their Inverses.
Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle.

Elementary Mathematics From an Advanced Standpoint: Arithmetic, Algebra, Analysis

Felix Klein

Dover | 1945 | 283 páginas |  djvu |  2,9 Mb

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This book, a translation of the first of Klein's three volumes entitled Elementarmathematik vom höheren Standpunkte aus, is a series of lectures that Klein gave for teachers of mathematics in secondary schools. The material is presented under the headings of arithmetic, algebra, analysis, and a supplement. The section on arithmetic treats the extensions of the number system and the laws of operation, beginning with integers and ending with complex numbers and quaternions. The treatment seeks to explain the how and why of the subject. As an example, we note the discussion of the little understood rule of signs: "minus times minus gives plus." The section on algebra is devoted to the solution of equations. First, some geometric methods are explained for investigating the real roots of rational integral equations containing parameters. Then complex roots are considered, especially of those equations whose solutions lead to a consideration of the groups of motions connected with the regular bodies. Free use is made of Riemann surfaces and other parts of the theory of functions of a complex variable. The section on analysis is devoted to the logarithmic, exponential, and trigonometric functions, and a discussion of the infinitesimal calculus proper. A wide variety of subjects is treated, however, in connection with these general topics: the construction of the early logarithmic and trigonometric tables, expansions in Fourier series, Taylor's Theorem, and Newton's and Lagrange's interpolation formulas will serve as samples. Finally, the supplement contains proofs of the transcendence of e and ir, and a discussion of assemblages.

Precalculus Functions and Graphs: A Graphing Approach

5th Edition

Ron Larson, Robert P. Hostetler

Brooks Cole | 2007 | 1138 pages | PDF | 25,9 MB

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Part of the market-leading Graphing Approach Series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs: A Graphing Approach, 5/e, is an ideal student and instructor resource for courses that require the use of a graphing calculator. The quality and quantity of the exercises, combined with interesting applications and innovative resources, make teaching easier and help students succeed. Continuing the series' emphasis on student support, the Fifth Edition introduces Prerequisite Skills Review. For selected examples throughout the text, the Prerequisite Skills Review directs students to previous sections in the text to review concepts and skills needed to master the material at hand. In addition, prerequisite skills review exercises in Eduspace are referenced in every exercise set. The Larson team achieves accessibility through careful writing and design, including examples with detailed solutions that begin and end on the same page, which maximizes the readability of the text. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles.

Calculus: Concepts and Contexts

4 edition
(Stewart's Calculus Series)

Brooks Cole | 2009 |1152 pages | PDF | 226 MB

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Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Dreams of Calculus: Perspectives on Mathematics Education

Johan Hoffman, Claes Johnson, Anders Logg

Springer | 2004 | 158 páginas | pdf | 5,6 Mb

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Descrição: What is the relationship between modern mathematics - more precisely computational mathematics - and mathematical education? It is this controversal topic that the authors address with an in-depth analysis. In fact, what they present in an extremely well-reasoned account of the development of mathematics and its culture giving concrete recommendation for a much-needed reform of the teaching of mathematics. The book is essential reading for everybody involved in mathematics and science, and mathematics teaching.

How Does One Cut a Triangle?

Alexander Soifer

Springer | 2009 - 2ª edição | 174 páginas | PDF | 1,6 Mb

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Revisões:
How Does One Cut a Triangle? is a work of art, and rarely, perhaps never, does one find the talents of an artist better suited to his intention than we find in Alexander Soifer and this book.
—Peter D. Johnson, Jr.This delightful book considers and solves many problems in dividing triangles into n congruent pieces and also into similar pieces, as well as many extremal problems about placing points in convex figures. The book is primarily meant for clever high school students and college students interested in geometry, but even mature mathematicians will find a lot of new material in it. I very warmly recommend the book and hope the readers will have pleasure in thinking about the unsolved problems and will find new ones.—Paul ErdosIt is impossible to convey the spirit of the book by merely listing the problems considered or even a number of solutions. The manner of presentation and the gentle guidance toward a solution and hence to generalizations and new problems takes this elementary treatise out of the prosaic and into the stimulating realm of mathematical creativity. Not only young talented people but dedicated secondary teachers and even a few mathematical sophisticates will find this reading both pleasant and profitable.—L.M. KellyMathematical Reviews [How Does One Cut a Triangle?] reads like an adventure story. In fact, it is an adventure story, complete with interesting characters, moments of exhilaration, examples of serendipity, and unanswered questions. It conveys the spirit of mathematical discovery and it celebrates the event as have mathematicians throughout history.—Cecil RousseauThe beginner, who is interested in the book, not only comprehends a situation in a creative mathematical studio, not only is exposed to good mathematical taste, but also acquires elements of modern mathematical culture. And (not less important) the reader imagines the role and place of intuition and analogy in mathematical investigation; he or she fancies the meaning of generalization in modern mathematics and surprising connections between different parts of this science (that are, as one might think, far from each other) that unite them.—V.G. BoltyanskiSIAM Review Alexander Soifer is a wonderful problem solver and inspiring teacher. His book will tell young mathematicians what mathematics should be like, and remind older ones who may be in danger of forgetting.—John Baylis

Spirals: From Theodorus to Chaos

Philip J. Davis, Walter Gautschi, Arieh Iserles


A K Peters Ltd | 1993 | 256 páginas | DjVu | 2,3 Mb

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Descrição: Although loosely organized around the study of a differential equation that Davis dubs Theodorus of Cyrene, the book takes an eclectic whirlwind tour of history, philosophy, anecdote, and mathematic.