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The Manga Guide to Calculus

By Hiroyuki Kojima, Shin Togami, and Becom Co., Ltd.

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In The Manga Guide to Calculus, Noriko discovers that hard-hitting journalism requires a lot more mathematical know-how than she has. Luckily, her boss teaches her everything she needs to know about calculus, like integration, differentiation, Taylor expansions, and more.

Description

Noriko is just getting started as a junior reporter for the Asagake Times. She wants to cover the hard-hitting issues, like world affairs and politics, but does she have the smarts for it? Thankfully, her overbearing and math-minded boss, Mr. Seki, is here to teach her how to analyze her stories with a mathematical eye.

In The Manga Guide to Calculus, you’ll follow along with Noriko as she learns that calculus is more than just a class designed to weed out would-be science majors. You’ll see that calculus is a useful way to understand the patterns in physics, economics, and the world around us, with help from real-world examples like probability, supply and demand curves, the economics of pollution, and the density of Shochu (a Japanese liquor).

Mr. Seki teaches Noriko how to:

  • Use differentiation to understand a function’s rate of change
  • Apply the fundamental theorem of calculus, and grasp the relationship between a function’s derivative and its integral
  • Integrate and differentiate trigonometric and other complicated functions
  • Use multivariate calculus and partial differentiation to deal with tricky functions
  • Use Taylor Expansions to accurately imitate difficult functions with polynomials

Whether you’re struggling through a calculus course for the first time or you just need a painless refresher, you’ll find what you’re looking for in The Manga Guide to Calculus.

This EduManga book is a translation from a bestselling series in Japan, co-published with Ohmsha, Ltd. of Tokyo, Japan.

 

DETAILS

August 2009, 256 pp.
ISBN-13: 978-1-59327-194-7

TABLE OF CONTENTS

Prologue: What is a Function?

Chapter 1: Let’s Differentiate a Function!
Chapter 2: Let’s Learn Differentiation Techniques!
Chapter 3: Let’s Integrate a Function!
Chapter 4: Let’s Learn Integration Techniques!
Chapter 5: Let’s Learn About Taylor Expansions!
Chapter 6: Let’s Learn About Partial Differentiation!

Index

View the detailed Table of Contents (PDF)
View the Index (PDF)

AUTHOR BIO

Hiroyuki Kojima was born in 1958. He received his PhD in Economics from the Graduate School of Economics, Faculty of Economics, at the University of Tokyo. He has worked as a lecturer and is now an associate professor in the Faculty of Economics at Teikyo University in Tokyo, Japan. While highly appraised as an economist, he is also active as an essayist and has published a wide range of books on mathematics and economics at the fundamental, practical, and academic levels.

UPDATES

Page 40:

Exercise 2 should read. “The derivative of f(x) at x = a is…” The first alpha in the equation below it should also be an “a”.

Page 69:

In Futoshi’s speech bubble in the upper right panel, the equation should read:

E(r) = -r3 + 3r2

Page 75:

Formula 2-7 should read:

h'(x) = g'(f(x))f'(x)

Page 90:

In the top panel, Step 6, q'(x) should be equal to 2/(x+1)2.

Page 112:

The general rule of finding the antiderivative F(x) of f(x) = xn is:

(x^(n+1))/(n+1)

Page 137:

When we substitute f(h) for f(0)(h+1), those equations are approximately equal (˜).

Page 141:

The second equation indented on the page should read:

f(g(1)) = 1 = a0

Page 169:

The exponent for the equation in the top panel should be (n-x) not (n-1).

Page 171:

Throughout this exercise, our function hn is now with respect to the variable z or hn(z).

Page 195:

The second term of the equation at (5) should not include t.

Page 196:

When we imitate the concentration of sugar syrup given y grams of sugar in x grams of water:

 

REVIEWS

“A fun, different approach to a subject that’s always a hard sell.”
Jennifer Ouellette, author of The Calculus Diaries

The Manga Guide to Calculus is an entertaining comic with colorful characters and a fun strategy to teach its readers calculus.”
Dr. Dobb’s CodeTalk (Read More)

The Manga Guide to Calculus would make an excellent supplement for
anyone seeking a firmer intuitive grasp of the subject. It is entertaining, and it does an excellent job of exploring the meaning and relevance of calculus to the physical world.”
Math Horizons, a periodical from the Mathematical Association of America

“An excellent, calculus-savvy and user-friendly guide for any student needing to brush up on their calculus, whether tackling a course for the first time or seeking a refresher.”
The Midwest Book Review (Read More)

“I like this book. A lot.”
Wild About Math! (Read More)

“I never took calculus in high school or college, yet I was able to get through the Guide and come out at the end with a pretty fair understanding of it. Moreover, I actually enjoyed the learning journey!”
FrazzledDad (Read More)

“What this book does better than any calculus book I have seen is give a context to the processes and concepts.”
Matthew Helmke (dot) Net (Read More)

“This book does exactly what it is supposed to: offer a fun, interesting way to learn calculus concepts that would otherwise be extremely bland to memorize.”
DailyTech (Read More)

“The book is primarily for those who want to understand calculus, especially where some prior exposure has been a bad experience. However, anyone interested in technical communication, regardless of the subject, should find this guide a great source of ideas.”
Linux Users of Victoria (Read More)

“The Manga Guides series is a fantastic way of breaking down some of the barriers to learning and making the content accessible to all!”
GirlyGeekdom (Read More)

“This book is exceptional in that I actually read it and understood most of it in the first reading.”
MacCompanion (Read More)

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