Technical Math Demystified. McGraw-Hill



I extend thanks to my nephew Tony Boutelle, a student at Macalester College in
St. Paul. He spent many hours helping me proofread the manuscript, and he

offered insights and suggestions from the point of view of the intended audience.

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Technical Math Demystified

This book is written for people who want to refresh or improve their mathematical
skills, especially in fields applicable to science and engineering. The course
can be used for self-teaching without the aid of an instructor, but it can also be
useful as a supplement in a classroom, tutored, or home-schooling environment.
If you are changing careers, and your new work will involve more mathematics
than you’ve been used to doing, this book should help you prepare.
If you want to get the most out of this book, you should have completed
high-school algebra, high-school geometry and trigonometry, and a first-year
course in calculus. You should be familiar with the concepts of rational, real, and
complex numbers, linear equations, quadratic equations, the trigonometric functions,
coordinate systems, and the differentiation and integration of functions in a single variable.

This book contains plenty of examples and practice problems. Each chapter
ends with a multiple-choice quiz. There is a multiple-choice final exam at the
end of the course. The questions in the quizzes and the exam are similar in format
to the questions in standardized tests.

The chapter-ending quizzes are open-book. You may refer to the chapter texts
when taking them. When you think you’re ready, take the quiz, write down your
answers, and then give your list of answers to a friend. Have the friend tell you
your score, but not which questions you got wrong. The answers are listed in
the back of the book. Stick with a chapter until you get most, and preferably all,
of the quiz answers correct.

The final exam contains questions drawn uniformly from all the chapters. It
is a closed-book test. Don’t look back at the text when taking it. A satisfactory
score is at least three-quarters of the answers correct (I suggest you shoot for
90 percent). With the final exam, as with the quizzes, have a friend tell you your
score without letting you know which questions you missed. That way, you will
not subconsciously memorize the answers. You can check to see where your
knowledge is strong and where it is weak.

I recommend that you complete one chapter a week. An hour or two daily
ought to be enough time for this. When you’re done with the course, you can use
this book as a permanent reference.
Suggestions for future editions are welcome.


Table of Contents
Preface xiii
Acknowledgments xv
CHAPTER 1 Numbering Systems
Sets 1
Denumerable Number Sets 6
Bases 10, 2, 8, and 16 10
Nondenumerable Number Sets 15
Special Properties of Complex Numbers 20
Quick Practice 24
Quiz 27
CHAPTER 2 Principles of Calculation
Basic Principles 29
Miscellaneous Principles 33
Advanced Principles 37
Approximation and Precedence 42
Quick Practice 46
Quiz 47
CHAPTER 3 Scientific Notation
Powers of 10 51
Calculations in Scientific Notation 57
Significant Figures 61
Quick Practice 65
Quiz 67
CHAPTER 4 Coordinates in Two Dimensions
Cartesian Coordinates 71
Simple Cartesian Graphs 74
Polar Coordinates 80
Navigator’s Coordinates 87
Coordinate Conversions 89
Other Coordinate Systems 92
Quick Practice 99
Quiz 101
CHAPTER 5 Coordinates in Three Dimensions
Cartesian 3-Space 105
Other 3D Coordinate Systems 108
Hyperspace 113
Quick Practice 119
Quiz 122
CHAPTER 6 Equations in One Variable
Operational Rules 125
Linear Equations 127
Quadratic Equations 130
Higher-Order Equations 134
Quick Practice 137
Quiz 139
CHAPTER 7 Multivariable Equations
2×2 Linear Equations 143
3×3 Linear Equations 148
2×2 General Equations 152
Graphic Solution of Pairs of Equations 154
Quick Practice 158
Quiz 160
CHAPTER 8 Perimeter and Area in Two Dimensions
Triangles 163
Quadrilaterals 166
Regular Polygons 171
Circles and Ellipses 172
Other Formulas 175
Quick Practice 180
Quiz 182
CHAPTER 9 Surface Area and Volume in Three Dimensions
Straight-Edged Objects 185
Cones and Cylinders 191
Other Solids 198
Quick Practice 202
Quiz 204
CHAPTER 10 Boolean Algebra
Operations, Relations, and Symbols 207
Truth Tables 212
Some Boolean Laws 216
Quick Practice 220
Quiz 223
CHAPTER 11 Trigonometric Functions
The Unit Circle 227
Primary Circular Functions 229
Secondary Circular Functions 232
The Right Triangle Model 234
Trigonometric Identities 237
Quick Practice 245
Quiz 248
CHAPTER 12 Vectors in Two and Three Dimensions
Vectors in the Cartesian Plane 251
Vectors in the Polar Plane 256
Vectors in Cartesian 3-Space 259
Standard Form of a Vector 264
Basic Properties 267
Other Properties 275
Quick Practice 278
Quiz 280
CHAPTER 13 Logarithmic and Exponential Functions
Logarithmic Functions 284
How Logarithmic Functions Behave 287
Exponential Functions 290
How Exponential Functions Behave 293
Quick Practice 298
Quiz 300
CHAPTER 14 Differentiation in One Variable
Definition of the Derivative 305
Properties of Derivatives 311
Properties of Curves 315
Derivatives of Wave Functions 323
Quick Practice 329
Quiz 331
CHAPTER 15 Integration in One Variable
What Is Integration? 337
Basic Properties of Integration 341
A Few More Formulas 343
Integrals of Wave Functions 348
Examples of Definite Integration 354
Quick Practice 358
Quiz 361
Final Exam 365
Answers to Quiz and Exam Questions 395
Suggested Additional Reading 399
Index 401


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 2006 by The McGraw-Hill Companies, Inc 

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