xii Preface
presents the notion of what calculus really does. You will never
understand this through the teaching methods that stick to limits
(or ε-δ logic). Unless you have a clear image of what calculus really
does and why it is useful in the world, you will never really under-
stand or use it freely. You will simply fall into a miserable state of
memorizing formulas and rules. This book explains all the formu-
las based on the concept of the first-order approximation, helping
you to visualize the meaning of formulas and understand them
easily. Because of this unique teaching method, you can quickly
and easily proceed from differentiation to integration. Further-
more, I have adopted an original method, which is not described in
ordinary textbooks, of explaining the differentiation and integra-
tion of trigonometric and exponential functions—usually, this is
all Greek to many people even after repeated explanations. This
book also goes further in depth than existing manga books on
calculus do, explaining even Taylor expansions and partial dif-
ferentiation. Finally, I have invited three regular customers of
calculus—physics, statistics, and economics—to be part of this
book and presented many examples to show that calculus is truly
practical. With all of these devices, you will come to view calculus
not as a hardship, but as a useful tool.
I would like to emphasize again: All of this has been made
possible because of manga. Why can you gain more information
by reading a manga book than by reading a novel? It is because
manga is visual data presented as animation. Calculus is a branch
of mathematics that describes dynamic phenomena—thus, calcu-
lus is a perfect concept to teach with manga. Now, turn the pages
and enjoy a beautiful integration of manga and mathematics.
Hiroyuki Kojima
November 2005
Note:
For ease of understanding, some figures are not drawn
to scale.
Prologue:
What Is A Function?
2 Prologue
The Asagake
Times’s Sanda-cho
Oice must be
around here.
Just think me,
Noriko Hikima, a
journalist! My
carr starts
here!
It’s a sma
newspaper and
just a branch
oice. But Im
sti a journalist!
I’ work
hard!!
What Is a Function? 3
Sanda-cho Oice...
do I have the
wrong map?
A newspaper
distributor?
Youre lking
for the Sanda-cho
branch oice?
Everybody mistakes
us for the oice
because we are
larger.
It’s next
dr.
The Asagake Times
Sanda-Cho Distributor
4 Prologue
Dont...don’t get
upset, Noriko.
It’s a branch
oice, but it’s
sti the real
Asagake Times.
Whsh
Oh, no!!
It’s a prefab!
The Asagake Times
Sanda-Cho Branch Oice

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