Preface 4
Introductory remarks 6

Chapter 1: The Birth of Calculus
1. Traces of Calculus Hidden in Ancient Civilizations 16
2 Two Geniuses Who Changed the World: Newton vs. Leibniz 22
3 The Mathematical Revolution That Continues to This Day 25

Chapter 2: Learning the Basic Concepts of the Language of Calculus
1 Infinity, an invitation to an endless world 30
2 Extremes, Beyond the Boundaries: A Math Journey 32
3 Differentiation, the power to capture momentary changes 34
4 Integration, putting pieces together to draw the whole 37
5 Secret Formulas for Differential Calculus 39
6 The Secret Key to Integral Calculations 43
7 Pi, the Hidden Ratio of the Universe 48
8 Natural constant e, the magic number that calculates the world 51
9 Partial Differentiation and Multiple Integration, Exploring the Multidimensional World 54

Chapter 3: The Eye of Differentiation: Reading Nature
1 Animal Movement, Trajectories Drawn by Mathematics 60
2 The Secrets of Bird Flight Paths and Energy 63

Chapter 4 Environmental Analysis
1 Population Change: Predicting the Future with Mathematics 70
2. How do pollutants spread? 72
3 Climate Change: Earth's Warning in Formulas 76
4 Resource Consumption Patterns Revealed in Graphs 79
5 Calculus Hidden in Weather Forecasting 83
6 Savings and Investments: The Calculation Behind the Numbers 85
7 Anatomy of Currency Circulation and the Flow of the Economy 89
8 Differential Equations 93

Chapter 5: Adventures in Calculus in Technology and Engineering
1 Sky-piercing architecture, designed with mathematics 100
2 Calculus 103 in a Pixel of a Display
3 Game Physics Engines: The Secret to Realistic Play 106
4 Medical Innovations: Saving Lives with Calculus 109
5 MRI and CT: The Math Behind Creating Images 111
6 Curves drawing the movement of drugs 115
7 Human Modeling: Inside the Virtual Body Created by Mathematics 119
8 Perfect Lenses, Equations for Light, Calculus 122
9 Hidden Optimization Formulas in Cooking Calculus 126
10 Earthquake Waves, Warnings from Curves 130
11 Marine Engineering: Designing the Underwater 134
12 Traffic Enforcement Systems: The Math Behind the Cameras 138
13 Deep Learning, the Heart of Artificial Intelligence 142
14 The Magnus Effect: Governing Ball Trajectories 145
15 Topographic Analysis, Mathematics in Maps, Guide 149
16 Roller Coasters and Ferris Wheels: A Calculus-Inspired Thrill 153
17 Unraveling the Mysteries of Static Electricity with Calculus Formulas 157
18 Aurora, Waves of Light in the Sky 161

Chapter 6: Calculus for Designing the Future
1 Smartwatch, a math engine on your wrist 168
2 Fire Patrol Robots Calculate Safety 171
3 CG Innovations: The Magic of Cinema Created by Partial Differential Equations 174
4 Space Exploration: Mathematics Reaching Stars and Planets 178
5 Hidden Formulas for Explosive Instagram Follower Growth Calculus 181
6 The Black-Scholes Model: A Game Changer in Financial Markets 183
7 Rocket Equations, a Key Tool of the Space Age 187
8 Deep Learning, the Brain of Future Industries 190
9 Lanchester's Law, The Mathematics of Strategic Study 194
10 Predator-Prey Relationships, the Curve Drawing an Ecosystem 198
11 Radiometric Dating: A Mathematical Clock that Reads the Past 202
12 The Butterfly Effect: Small Changes Create Big Waves 206
13 The Emergence Effect, Chaos and Creation in Order 211
14 Hidden Mathematical Codes for Solving Fine Dust Problems 214
15 Calculus 217: Finding the Lagrange Points, the Key to Unraveling the Balance of the Universe

Minimize formulas, maximize fun and interest, and learn life-style mathematics.
“Isn’t calculus just a math full of complicated formulas?”
Many people think this way and avoid calculus.
However, 『Calculus in Your Hands』 completely overturns that prejudice.
This book explains calculus in an easy and fun way, minimizing mathematical formulas and using everyday examples that anyone can relate to.
The author demonstrates calculus through the 'change' and 'sum' that occur naturally around us.
The moment you decide whether to bring an umbrella when it rains, how roller coasters operate safely, how electricity is supplied reliably, how chocolate is made in a factory, even how long a smartphone battery lasts? These are all scenes where calculus is hidden.
As the reader turns the page, he or she nods and says, “Ah, so this is calculus!”
〈Calculus in Your Hands〉 is not a textbook-like, rigid explanation, but rather unfolds the story as if telling an interesting story.
Important concepts appear repeatedly and become naturally ingrained in our minds.
The simple definition that "differentiation is the study of the rate of change, and integration is the study of the whole by putting together small details" is repeated in various examples, such as soccer ball trajectories, weather forecasts, and health data, leading readers on the path to understanding.
This book is not for people who are good at math.
Rather, it is more useful for those who find math difficult and unfamiliar.
Elementary school students can also find it interesting, and adult readers can broaden their general knowledge while simultaneously rediscovering the necessity of mathematics in real life.
"Calculus in Your Hands" is not just a simple math book; it is a guide that introduces another language for reading the world.
By the time the reader closes the book, they will be amazed to find that calculus is so close to their daily lives, and will realize that mathematics is a power that goes beyond mere knowledge.
Math is no longer a scary subject.
"Calculus at Your Fingertips" invites readers beyond boring and difficult mathematics to a world of fun, friendly, and knowledge-enhancing liberal arts mathematics.