Everyday Calculus

Everyday Calculus: Discovering the Hidden Math All around Us

OSCAR E. FERNANDEZ
Copyright Date: 2014
Pages: 176
https://www.jstor.org/stable/j.ctt5hhrp2
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  • Book Info
    Everyday Calculus
    Book Description:

    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, accessible, and surrounds us everywhere we go. InEveryday Calculus, Oscar Fernandez shows us how to see the math in our coffee, on the highway, and even in the night sky.

    Fernandez uses our everyday experiences to skillfully reveal the hidden calculus behind a typical day's events. He guides us through how math naturally emerges from simple observations-how hot coffee cools down, for example-and in discussions of over fifty familiar events and activities. 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.

    Whether you're new to mathematics or already a curious math enthusiast,Everyday Calculusinvites you to spend a day discovering the calculus all around you. The book will convince even die-hard skeptics to view this area of math in a whole new way.

    eISBN: 978-1-4008-5008-2
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. PREFACE
    (pp. ix-x)
    Oscar Edward Fernandez
  4. CALCULUS TOPICS DISCUSSED BY CHAPTER
    (pp. xi-xiv)
  5. CHAPTER 1 WAKE UP AND SMELL THE FUNCTIONS
    (pp. 1-20)

    It’s Friday morning. The alarm clock next to me reads 6:55 a.m. In five minutes it’ll wake me up, and I’ll awake refreshed after sleeping roughly 7.5 hours. Echoing the followers of the ancient mathematician Pythagoras—whose dictum was “All is number”—I deliberately chose to sleep for 7.5 hours.But truth be told, I didn’t have much of a choice. It turns out that a handful of numbers, including 7.5, rule over our lives every day. Allow me to explain.

    A long time ago at a university far, far away I was walking up the stairs of my college dorm...

  6. CHAPTER 2 BREAKFAST AT NEWTON’S
    (pp. 21-34)

    Everyone has a morning routine. After my shower, I like to tune to the financial news network CNBC while I get dressed. Its morning show is the closest I can get to a daily TV show about mathematics.viiiIn five minutes of watching it you’re likely to see changes in interest rates, rising and falling stock market prices, fluctuating currency exchange rates, and, well, lots of other numbers flashing red and green.

    After years of starting my mornings like this, I’m used to this barrage of information. But not my wife, Zoraida; this particular channel gives her a headache. “There...

  7. CHAPTER 3 DRIVEN BY DERIVATIVES
    (pp. 35-50)

    I’m now ready to head out to work. The last thing to do is to grab a pair of shoes from my shoe “collection”—a line of pairs of shoes on the floor ordered by color from light brown to black. Oftentimes I just pick a random pair, but now that it’s started to rain I decide to go for the usually neglected pair of waterproof shoes. I slip them on, pick up the umbrella, and finally leave my house.

    I open my door and, unlike my shoe collection, I am instantly met with a world of disorder. It’s pouring...

  8. CHAPTER 4 CONNECTED BY CALCULUS
    (pp. 51-64)

    If you’re like me, one of the first things you do when you get to work is check your e–mail. Honestly, I don’t know how some jobs ever got done before e–mail. I can’t imagine my students writing meletterswith their questions on the homework, or me making costly international calls to my collaborators to discuss research. With e-mail it’s now become much easier—and faster—to communicate with each other. But it’s not just ease of communication that this new technology has produced. In this age of Facebook and Twitter we’re all connected to each other....

  9. CHAPTER 5 TAKE A DERIVATIVE AND YOU’LL FEEL BETTER
    (pp. 65-80)

    My office is on the third floor of the building I work in. As I walk in, hot chocolate about half–way gone, I head toward the stairwell. I climb these three flights of stairs many times during the day. Naturally, the first couple of steps are easy, but as I keep moving up the stairs my heart beats faster. It’s compensating for the sudden increase in oxygen demand, and quickly distributing that oxygen across my blood vessels to my muscles. But this requires very special plumbing. For starters, my blood vessels need to expand to accommodate the greater volume...

  10. CHAPTER 6 ADDING THINGS UP, THE CALCULUS WAY
    (pp. 81-96)

    My drive home took me about 20 minutes. I’m making a quick pit stop inside my house to change out of my work clothes. For me, changing into “non–work clothes” basically means just changing into jeans. And since I own only four pairs of jeans, five quick minutes later I’m changed and ready to catch the T.

    I never used public transportation until I moved up north, having grown up in Miami, Florida. But since our home is a one–minute walk from the nearest T station, it’s a no–brainer. The Massachusetts Bay Transportation Authority (MBTA) operates the...

  11. CHAPTER 7 DERIVATIVES AND INTEGRALS: THE DREAM TEAM
    (pp. 97-115)

    After first discussing derivatives in Chapter 2 we not only found them everywhere, but as our discussion of time dilation showed, they were powerful enough to literally change our view of reality. Similarly, after introducing integration in the last chapter we already have seen how it naturally appears all around us via probability. Imagine, then, the possibilities of using both derivatives and integrals in mathematizing a situation. As we’ll soon find out, this dream team can answer some of the most fundamental questions posed in the history of civilization. But I’ll have to build up to that crescendo first. So...

  12. EPILOGUE
    (pp. 116-118)
    Oscar Edward Fernandez

    If you’ve made it this far, let me be the first to say that I’m proud of you. As I mentioned in the preface, many of us are unfortunately intimidated by mathematics, thinking that it’s either too abstract or too difficult to understand. I hope that what you’ve read in this book has helped you see that you’re already familiar with a lot of mathematics; the only prerequisite is curiosity. Next time you have coffee, take some time to notice how the temperature cools, or study the patterns that the milk you put in it makes as you swirl it...

  13. APPENDIX A FUNCTIONS AND GRAPHS
    (pp. 119-124)
  14. APPENDIX 1
    (pp. 125-126)
  15. APPENDIX 2
    (pp. 127-127)
  16. APPENDIX 3
    (pp. 128-132)
  17. APPENDIX 4
    (pp. 133-137)
  18. APPENDIX 5
    (pp. 138-141)
  19. APPENDIX 6
    (pp. 142-144)
  20. APPENDIX 7
    (pp. 145-146)
  21. NOTES
    (pp. 147-148)
  22. INDEX
    (pp. 149-150)