Master Math: Calculus: Calculus [NOOK Book]

Overview

Get ready to master the concepts and principles of geometry! Master Math: Geometry is a comprehensive reference guide that explains and clarifies the principles of geometry in a simple, easy-to-follow style and format. You'll begin with the language of geometry, deductive reasoning and proofs, and key axioms and postulates. And as you understand the most basic fundamental topics you'll progress through to the more advanced topics, with step-by-step procedures and solutions, along with examples and applications, ...
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Master Math: Calculus: Calculus

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Overview

Get ready to master the concepts and principles of geometry! Master Math: Geometry is a comprehensive reference guide that explains and clarifies the principles of geometry in a simple, easy-to-follow style and format. You'll begin with the language of geometry, deductive reasoning and proofs, and key axioms and postulates. And as you understand the most basic fundamental topics you'll progress through to the more advanced topics, with step-by-step procedures and solutions, along with examples and applications, to help you as you go. A complete table of contents and a comprehensive index enable you to quickly find specific topics, and the approachable style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Geometry will help you master everything from deductive reasoning and proofs to constructions and analytic geometry.
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Editorial Reviews

Library Journal
This book, the fourth in the "Master Math" series, describes every major topic in the calculus, from functions through vector integral theorems, in a terse, no-nonsense manner, but the amateurish format is disappointing. Despite the availability of word-processing software that can do an excellent job on mathematical expressions, many of the formulae in this book are badly printed. Students accustomed to the new computerized graphics in most textbooks will find the diagrams and graphs rudimentary and unappealing. The text contains little in the way of motivation, few interesting examples, and no exercises. In the end, it feels more like the outline of a calculus text than an instructional book on the subject, and the student or practitioner who wants one would probably be better served (and save money) by picking up a used copy of any popular calculus textbook. Not recommended.--Harold D. Shane, Baruch Coll., CUNY
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Product Details

  • ISBN-13: 9781435455191
  • Publisher: Course Technology PTR
  • Publication date: 1/6/2009
  • Series: Master Math
  • Sold by: CENGAGE LEARNING
  • Format: eBook
  • Edition number: 1
  • Pages: 344
  • Sales rank: 1,053,522
  • File size: 4 MB

Meet the Author

Debra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and and MS in Chemical Engineering from Stanford University. Debra's career encompasses biology, chemistry, biochemistry, engineering, biosensors, pharmaceutical drug discovery, and intellectual property. She is the author of the popular Master Math books, The 3:00 PM Secret: Live Slim and Strong Live Your Dreams, The 3:00 PM Secret: Ten Day Dream Diet (2009), and Arrows Through Time: A Time Travel Tale of Adventure, Courage, and Faith (2009).

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Table of Contents

Introduction 1

Chapter 1 Functions 3

1.1 Functions: Types, Properties, and Definitions 3

1.2 Exponents and Logarithms 8

1.3 Trigonometric Functions 10

1.4 Circular Motion 20

1.5 Relationship Between Trigonometric and Exponential Functions 25

1.6 Hyperbolic Functions 26

1.7 Polynomical Functions 28

1.8 Functions of More Than One Variable and Contour Diagrams 29

1.9 Coordinate Systems 33

1.10 Complex Numbers 36

1.11 Parabolas, Circles, Ellipses, and Hyperbolas 38

Chapter 2 The Derivative 47

2.1 The Limit 47

2.2 Continuity 50

2.3 Differentiability 52

2.4 The Definition of the Derivative and Rate of Change 53

2.5 (delta) Notation and the Definition of the Derivative 57

2.6 Slope of a Tangent Line and the Definition of the Derivative 58

2.7 Velocity, Distance, Slope, Area, and the Definition of the Derivative 60

2.8 Evaluating Derivatives of Constants and Linear Functions 63

2.9 Evaluating Derivatives Using the Derivative Formula 64

2.10 The Derivatives of a Variable, a Constant with a Variable, a Constant with a Function, and a Variable Raised to a Power 66

2.11 Examples of Differentiating Using the Derivative Formula 68

2.12 Derivatives of Powers of Functions 69

2.13 Derivatives of ax, ex, and ln x 71

2.14 Applications of Exponential Equations 77

2.15 Differentiating Sums, Differences, and Polynomials 80

2.16 Taking Second Derivatives 81

2.17 Derivatives of Products: The Product Rule 82

2.18 Derivatives of Quotients: The Quotient Rule 85

2.19 The Chain Rule for Differentiating Complicated Functions 86

2.20 Rate Problem Examples 90

2.21 Differentiating Trigonometric Functions 91

2.22Inverse Functions and Inverse Trigonometric Functions and Their Derivatives 95

2.23 Differentiating Hyperbolic Functions 99

2.24 Differentiating Multivariable Functions 101

2.25 Differentiation of Implicit Vs. Explicit Functions 101

2.26 Selected Rules of Differentiation 102

2.27 Minimum, Maximum, and the First and Second Derivatives 103

2.28 Notes on Local Linearity, Approximating Slope of Curve, and Numerical Methods 109

Chapter 3 The Integral 113

3.1 Introduction 113

3.2 Sums and Sigma Notation 114

3.3 The Antiderivative or Indefinite Integral and the Integral Formula 117

3.4 The Definite Integral and the Fundamental Theorem of Calculus 120

3.5 Improper Integrals 122

3.6 The Integral and the Area Under a Curve 124

3.7 Estimating Integrals Using Sums and the Associated Error 128

3.8 The Integral and the Average Value 131

3.9 Area Below the X-axis, Even and Odd Functions, and The Integrals 131

3.10 Integrating a Function and a Constant, the Sum of Functions, a Polynomial, and Properties of Integrals 134

3.11 Multiple Integrals 136

3.12 Examples of Common Integrals 138

3.13 Integrals Describing Length 139

3.14 Integrals Describing Area 140

3.15 Integrals Describing Volume 145

3.16 Changing Coordinates and Variables 152

3.17 Applications of the Integral 157

3.18 Evaluating Integrals Using Integration by Parts 162

3.19 Evaluating Integrals Using Substitution 164

3.20 Evaluating Integrals Using Partial Fractions 172

3.21 Evaluating Integrals Using Tables 177

Chapter 4 Series and Approximation 179

4.1 Sequences, Progressions, and Series 179

4.2 Infinite Series and Tests for Convergence 183

4.3 Expanding Functions Into Series, the Power Series, Taylor Series, Maclaurin Series, and the Binomial Expansion 188

Chapter 5 Vectors, Matrices, Curves, Surfaces, and Motion 195

5.1 Introduction to Vectors 195

5.2 Introduction to Matrices 202

5.3 Multiplication of Vectors and Matrices 205

5.4 Dot or Scalar Products 208

5.5 Vector or Cross Product 211

5.6 Summary of Determinants 215

5.7 Matrices and Linear Algebra 217

5.8 The Position Vector Parametric Equations, Curves, and Surfaces 224

5.9 Motion, Velocity, and Acceleration 230

Chapter 6 Partial Derivatives 243

6.1 Partial Derivatives: Representation and Evaluation 243

6.2 The Chain Rule 246

6.3 Representation on a Graph 247

6.4 Local Linearity, Linear Approximations, Quadratic Approximations, and Differentials 250

6.5 Directional Derivative and Gradient 255

6.6 Minima, Maxima, and Optimization 259

Chapter 7 Vector Calculus 267

7.1 Summary of Scalars, Vectors, the Directional Derivative, and the Gradient 267

7.2 Vector Fields and Field Lines 271

7.3 Line Integrals and Conservative Vector Fields 276

7.4 Green's Theorem: Tangent and Normal (Flux) Forms 282

7.5 Surface Integrals and Flux 287

7.6 Divergence 295

7.7 Curl 300

7.8 Stokes' Theorem 304

Chapter 8 Introduction to Differential Equations 307

8.1 First-Order Differential Equations 308

8.2 Second-Order Linear Differential Equations 312

8.3 Higher-Order Linear Differential Equations 315

8.4 Series Solutions to Differential Equations 317

8.5 Systems of Differential Equations 319

8.6 Laplace Transform Method 321

8.7 Numerical Methods for Solving Differential Equations 322

8.8 Partial Differential Equations 324

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Customer Reviews

Average Rating 4
( 22 )
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See All Sort by: Showing 1 – 20 of 22 Customer Reviews
  • Anonymous

    Posted November 8, 2007

    The Best Algebra Book Available!

    This is the best book on learning basic algebra. It is thorough yet concise. The information is presented very clearly. The author has obviously tried to explain the concepts so that they `make sense¿ to students - and their parents. I use the book to explain algebra to my students. Like the other Master Math books by Ross, the topics flow logically and build in difficulty. What a breath of fresh air after the often confusing text books students are given in school. This book is helpful for students struggling with algebra and the parents who are tutoring them. This book is also extremely useful for older students who did not adequately learn algebra, yet find they need to know it later. Topics can easily be looked up and reviewed or learned. I highy recommend this book!

    5 out of 7 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Posted October 10, 2009

    ALG 101 Launchpad

    Splendid clarity and progression.
    A cherry on top of this fine sundae,
    maybe a single page of exponential,
    radical,and complex properties for
    a quick reference,( but that's nitpicking).

    3 out of 5 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted November 20, 2007

    Outstanding Trigonometry Presentation!

    This is the best book out there on learning trigonometry. I especially appreciate the visually-oriented focus. Each concept is described in all its forms, such as sine. Do you know each of the different ways sine can be described? Like the other Master Math books by Ross, the topics flow logically and are in context with what precedes and follows. It is thorough yet concise, and packed full of everything you, as tutor, or your kids need to know. The real world and fun applications are wonderful! The information is explained clearly and in a way that makes sense, so that a given concept is explained in such a way you understand what is being discussed rather than just memorizing formulas. What a breath of fresh air after the often confusing text books I was and my children are given in school. I really feel I can explain trigonometry to young people using this book! if I were going back to school, and taking math or science, this book would be in my backpack.

    3 out of 5 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted November 21, 2012

    page 14 e reader

    i am not sure if i am missing something but on page 14 the book says x times $1.00 per glass will equal 20. then shows this equation
    X + ($1.00 per glass)=$20.00

    1 out of 1 people found this review helpful.

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  • Anonymous

    Posted February 12, 2012

    the internet is more helpful

    This book is terrible. There are many books that are better. I found websites more helpful.

    1 out of 3 people found this review helpful.

    Was this review helpful? Yes  No   Report this review
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