Prologue
How to read this book

Chapter 1: Perspectives from Calculus

1-1 Virus Infection Through Calculus
1-2 Calculus used in automobiles
1-3 Analyzing the flow of money using calculus
1-4 Calculus in Smartphones

Chapter 2 What is Calculus?

2-1 Calculus of the relationship between the continuation
2-2 What is integration? The "huge multiplication" that calculates area.
What is Differentiation 2-3? The "Huge Division" for Finding Slope
Differentiation for predicting the orbit of a comet 2-4
2-5 Calculus for controlling oil temperature

Chapter 3 Why Use Formulas?

3-1 Write a formula to predict the future.
3-2 What is a function?
(One point) Inverse function
Get used to the 3-3 graph
How to create a 3-4 formula
3-5 Simulation involves differential equations.
3-6 Differential equations supporting science and technology
Features of Formula 3-7
(One Point) How to Read Algebraic Graphs

Chapter 4 Calculus in the World of Mathematics

4-1 Finding the area by integration
4-2 Finding the slope by differentiation
4-3 The derivative is a 'function of the slope'
4-4 Integration is the inverse operation of differentiation.
4-5 Structure of Calculus
4-6 Symbols used in calculus
4-7 Calculus Calculation Method
4-8 Why are Napier numbers important?

Chapter 5: Calculus Becomes Perfect with Infinite Power

5-1 Is the formula for the area of ​​a circle true?
5-2 Reasons for thinking about extremes
5-3 Thinking about differentiation using limits
(One point) f ′(x)=nxn-1 is also true for n other than natural numbers.
5-4 Thinking about integration using limits
(One point) How to use the Σ symbol

Chapter 6: Predicting the Future with Differential Equations

6-1 What is a differential equation?
6-2 The motion equations can be used to predict the movement of objects.
6-3 The age of a fossil can be determined using differential equations.
6-4 Finding Individual Creatures
6-5 Weight difference at the equator and the North Pole
6-6 Limitations of Differential Equations

Chapter 7 Another Calculus Story

7-1 Exponents, Logarithmic Functions, and Calculus
7-2 Trigonometry and Calculus
7-3 Increase and decrease of function
7-4 Various Calculus Techniques
7-5 You can find the volume or length of a curve by integration.

Differentiating and integrating reveals the solution to the problem and the future.

Knowing the meaning and structure
My first differentiation and integration in my life

What are differentiation and integration? Literally, differentiation is about the minute details, and integration is about accumulating and combining those minute details.
But why is calculus called the foundation of modern civilization? Indeed, it's an essential tool for cutting-edge IT, infectious disease prediction, wireless communications, rocket launches, artificial intelligence, and even the smartphones we always hold in our hands.
The author of this book says that calculus is also the part of the mathematics we learn in school that can be most practically helpful.
He says that calculus thinking is crucial for analyzing the most important numbers in our daily lives and work, and for determining areas for improvement or directions for work advancement. He also says that there is an unbridgeable gap between those who utilize it and those who do not.

When discussing the development of modern society and the future to come, computers and artificial intelligence are things that cannot be left out.
Artificial intelligence is the only thing in this world, other than living things, that is considered capable of 'thinking and reasoning'.
Artificial intelligence functions are working hard in home appliances like smartphones, cars, refrigerators, vacuum cleaners, and washing machines, whether we know it or not.
They are like our closest and most important colleagues who have already become a part of our lives and will play an even greater role in the future.
Understanding how these precious beings think and reason can be crucial to our personal development.
However, the basis of this artificial intelligence's thinking circuit is mathematics, and the one that plays the biggest role among them is calculus.
This is why the author of this book emphasizes that studying calculus can help us understand the 'mind' of artificial intelligence.

How does calculus move the world?

This book consists of seven chapters.
The author believes that the reason beginners find calculus difficult is largely due to the complex formulas that create preconceptions, so he explains the concepts in an easy-to-understand manner using examples without using formulas at all up to Chapter 2.
I can confidently say that I explained the concept of calculus so that even those who dislike formulas could clearly understand it.
The book is structured to help you think in calculus with easy content in the beginning, and to become more in-depth as you progress. It is structured so that even if you get stuck along the way, you can still get help with the knowledge you have accumulated so far.
It explains the concepts using familiar examples of calculus, how to use formulas to predict the future, how to find area through integration, how to find slope through differentiation, the structure of calculus, the symbols used, and calculation methods, etc., and explains calculus, which is abundant in real life, in an easy-to-understand way.

Welcome to the world of calculus.
A minimal mathematics textbook for understanding the world

Most universities structure their curricula to require first-year science and engineering students to take calculus as a required subject, regardless of their major.
This is because calculus is an essential tool for analyzing and tracking trends and changes in almost all fields, including social and natural phenomena, economics, and engineering in the world we live in.
The author says that knowing calculus allows you to obtain more diverse information than just numbers.
For example, let's say someone runs a ramen shop.
If you make a profit of 5 million won this month, you need to compare it to last month's profit to see if it's a lot or a little.
Knowing the increase or decrease in profit is differentiation.
You can also integrate the profits for one year.
If you simply look at the profit numbers, you can only get one piece of information, which is the monthly profit, but through differentiation, you can get the information of 'change', and through integration, you can get the information of 'accumulation'.
If we came into the world without a proper understanding of calculus during our school days, this is why we need to understand and study calculus now.
If you aspire to personal success or advancement at work, I hope this book will help you master the magical tool that is calculus, the path to success, before it's too late.