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Everyday Calculus: Discovering the Hidden Math All around Us

Oscar E. Fernandez
Princeton University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Schulte
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The author earnestly and excitedly seeks to make the principles of calculus near and natural, without the intimidation of a five-pound textbook dense with equations. Oscar Fernandez describes the math in a cooling cup of coffee, falling rain drops, population growth, and the stars of the night sky. Asking no more of the reader than concepts such as the derivative and the chain rule, the author celebrates the calculus in the familiar through calculating the ideal number of hours for sleeping, the optimal route to reach work and, in what is becoming an old saw, selecting a seat in the theater for best viewing.

Most of the observations herein are prose, with an average of around one equation per page. For more ardent math enthusiasts, there are more rigorous appendices on calculus fundamentals. Fernandez invites the reader along on this work day and telegraphs an enthusiasm for seeing calculus, with hints of differential equations, presented to him. This excitement will communicate itself to the math enthusiast becoming acquainted with calculus through the author’s style, which is both lively and confident.

Tom Schulte confidently delivers lively lectures to students of mathematics at Oakland Community College.

Preface ix
Calculus Topics Discussed by Chapter xi

CHAPTER 1 Wake Up and Smell the Functions 1
What's Trig Got to Do with Your Morning? 2
How a Rational Function Defeated Thomas Edison, and Why Induction Powers the World 5
The Logarithms Hidden in the Air 10
The Frequency of Trig Functions 14
Galileo's Parabolic Thinking 17

CHAPTER 2 Breakfast at Newton's 21
Introducing Calculus, the CNBC Way 21
Coffee Has Its Limits 25
A Multivitamin a Day Keeps the Doctor Away 30
Derivatives Are about Change 34

CHAPTER 3 Driven by Derivatives 35
Why Do We Survive Rainy Days? 36
Politics in Derivatives, or Derivatives in Politics? 39
What the Unemployment Rate Teaches Us about the Curvature of Graphs 41
America's Ballooning Population 44
Feeling Derivatives 46
The Calculus of Time Travel 47

CHAPTER 4 Connected by Calculus 51
E-Mails, Texts, Tweets, Ah! 51
The Calculus of Colds 53
What Does Sustainability Have to Do with Catching a Cold? 56
What Does Your Retirement Income Have to Do with Traffic? 58
The Calculus of the Sweet Tooth 61

CHAPTER 5 Take a Derivative and You'll Feel Better 65
I "Heart" Differentials 65
How Life (and Nature) Uses Calculus 67
The Costly Downside of Calculus 73
The Optimal Drive Back Home 75
Catching Speeders Efficiently with Calculus 77

CHAPTER 6 Adding Things Up, the Calculus Way 81
The Little Engine That Could . . . Integrate 82
The Fundamental Theorem of Calculus 90
Using Integrals to Estimate Wait Times 93

CHAPTER 7 Derivatives Integrals: The Dream Team 97
Integration at Work-Tandoori Chicken 98
Finding the Best Seat in the House 101
Keeping the T Running with Calculus 104
Look Up to Look Back in Time 108
The Ultimate Fate of the Universe 109
The Age of the Universe 113

Epilogue 116
Appendix A Functions and Graphs 119
Appendices 1-7 125
Notes 147
Index 149

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