Everyday Calculus
Discovering the Hidden Math All around Us
1st Edition
Published on 6. March 2017
168 pages
978-1-4008-8566-4 (ISBN)
Description
A fun look at calculus in our everyday lives
Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun and accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes. The book features a new preface that alerts readers to new interactive online content, including demonstrations linked to specific figures in the book as well as an online supplement. Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus will convince even die-hard skeptics to view this area of math in a whole new way.
Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun and accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes. The book features a new preface that alerts readers to new interactive online content, including demonstrations linked to specific figures in the book as well as an online supplement. Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus will convince even die-hard skeptics to view this area of math in a whole new way.
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Book
03/2017
Princeton University Press
€20.00
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Persons
Oscar E. Fernandez is assistant professor of mathematics at Wellesley College. He is the author of The Calculus of Happiness (Princeton).
Content
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
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
