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Tuesday, August 1, 2017

Lesson 1. What is Calculus? Why do we study Calculus?

Scared?

"I study mathematics.'' Being able to say this is the first step to study mathematics. Say "mathematics'' rather than "math'' because that way, it sounds more serious. You are serious about studying the subject. You do not have to be good at it, and no one should expect that when you say this sentence. Don't be scared. This book is created in order to get rid of math-phobia among first year college students or high school seniors, who want to get a feeling of what calculus is. This does not mean that the book will teach you all the essentials that a standard calculus curriculum should teach. Please do NOT rely on this book for your exams.

What is calculus?

Roughly speaking, calculus is the study of slopes and areas. You will make sense of this slowly, so this remark is not too important.

Why do you study calculus?

Why do you study calculus? Even before you start studying calculus, you must ask this yourself, your classmates, and your teachers. Here is one answer, or before I give you an answer, let me ask: if you are a businessperson, is it important to maximize profit? Without some special reasons, you are likely to say "yes". Or, let me ask again, is it important to minimize deficit? Again, you are probably going to say "yes". Hence, here is one reason to study calculus: you study calculus to learn how to maximize or minimize.

Another reason may sound somewhat technical: you study calculus to learn how to measure quantity, area, volume, etc. Undoubtedly, it is important to measure various quantities in life. Now, you should ask then "What do we maximize / minimize / measure?" Roughly, we maximize / minimize / measure what we call functions.

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