# Normal textbooks suck

### ... so I wrote a better one

This is the deal. Give me three weeks of your attention and I will teach you everything you need to know about equations, functions, vectors, limits, derivatives, integrals, and forces.

Contents

• High school math
• Vectors
• Mechanics
• Derivatives
• Integrals

## Why?

### Textbooks are too long

Traditional textbooks are too long, too expensive and too boring.

You don't need to read thousands of pages in order to learn mechanics and calculus, so why are the required textbooks so long?

The reason why textbook publishers produce such large textbooks is so that they can charge you 150\$for each textbook. They want to get 300\$ from you in order to teach you some basic math and physics.

Something must be done!

### A new type of textbook

A compact textbook that explains calculus and mechanics clearly and intuitively.

#### Calculus and mechanics together

Calculus and mechanics are often taught as separate subjects. It shouldn't be like that. If you learn calculus without mechanics, it will be boring. If you learn physics without calculus, you won't truly understand.

By learning both subjects in parallel, you will be able to understand concepts much better.

## OK cool but ...

Can't I just learn math from the web?

Isn't math hard?

I am in Arts. I don't care about math.

### Funny

First of all, I love the book. My only problem has been when I am working through it in the library and start laughing out loud --- you have great examples.
- Miriam Aczel, McGill student

### Compact

It is literally two heavy textbooks packed into a very light and small book.
- Alexandra Shearon, McGill student

### Tone

I like the conversational tone of your writing. It's almost like I'm learning math from a friend.
- Kevin Del Castillo

## How?

Through short tutorials on each of the topics in mechanics and calculus.

#### Structured writing

In order to learn mechanics, you need to understand calculus. To learn calculus, you need to know about functions and other high school math stuff.

The goal of this book is to be self-contained. Towards this goal, the book begins with a series of tutorials which review the most important concepts of high school math. This is what makes this book special: it comes with prerequisites included.

#### Prerequisites

Anyone can pick up this book and learn, regardless of their mathematical background.

## Gimme some of that...

### Real-world example

You are downloading a 720[MB] file from the Internet. At $t=0$[s] you clicked "Save as..." to initiate the download and at $t=600$[s] (10 minutes later) the download completes.

### Mathematical modelling

Let the function $f(t)$ represent the file size of the file. Suppose that you monitor the file size during the entire download and observe that it is described by the function: $f(t) = 0.002\,t^2 \qquad \textrm{[MB]}.$ We can verify that this function correctly predicts the initial file size at $t=0$[s] ($f(0)=0$[MB]) and the final size at $t=600$[s] ($f(600)=720$[MB]) by plotting its graph:

## Q:

The download rate corresponds to the slope of the function $f(t)$. Since you have the graph of $f(t)$, you can use it to find the slope of $f(t)$ at any point. Recall that the slope of a function is computed as the rise-over-run for the function. In order to make the slope calculation easier, you can zoom in on the graph of $f(t)$ near $t=400$[s] and draw a triangle with the same slope as the function.

Observe that that slope of the triangle is exactly the same as the slope of the function at the point where they touch. We can compute the slope of the triangle using the rise-over-run calculation: $\textrm{slope}_f(400) = \frac{ \Delta f }{ \Delta t } \approx 1.6 \quad \textrm{ [MB/s]}.$ Therefore, the download rate at $t=400$[s] is 1.6[MB/s].

The derivative function $f'(t)$ describes the change in $f(t)$ at all times. In this case, the change in $f(t)$ is given by the download rate. Thus, in calculus speak, the questions is asking you to find $f'(400)$.

We will do this in two steps. First we compute the derivative using the general formula: \begin{align*} f(t) = A t^n \quad &\Rightarrow \quad f'(t)= An t^{n-1}. \end{align*} We can use this formula by identifying the variable $A$ with the number $0.002$ and the variable $n$ with the number two. The derivative of the file size is: \begin{align*} f(t)=0.002t^2 \textrm{ [MB]} \ \ \Rightarrow \ \ f'(t)=0.004t^1 \textrm{ [MB/s]}. \end{align*}

The second step is to evaluate $f'(t)$ at $t=400$[s]: $f'(400) = 0.004(400) = 1.6 \quad \textrm{ [MB/s]}.$ You can verify these calculation using the computer.

### Discussion

It is important to see the connections between the three different ways of finding the answer: the intuitive notion of download speed that we are all familiar with, the graphical notion of "slope of a function", and the abstract notion of the derivative operation which computes the slope any function. This example serves to illustrate how knowing calculus is useful for solving real world problems. The notion of rate of change is also important in biology, chemistry, business and many other areas of life.

Trust me on this one, investing time in learning about abstract concepts like derivatives and integrals is time well spent.

## What?

### Textbook

size
5½[in] x 8½[in] x 327[pages]
price
\\$29 (available in print and PDF)
author
Ivan Savov, B.Eng., M.Sc., Ph.D.
preview
Print version / eBook version
contents
subjects covered
• High school math (Precalculus)
• Vectors
• Mechanics (Physics 101)
• Differential calculus (Calculus I)
• Integral calculus (Calculus II)
publisher
Minireference Co.
edition
Third edition
prerequisites
Included

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## The author

Ivan Savov has been tutoring math and physics privately for more than twelve years. He did his undergraduate studies at McGill University in Electrical Engineering, then did a M.Sc. in Physics and recently completed a Ph.D. in CS. He is the founder of ''Minireference Publishing Co.'' and is out on a mission to revolutionize the textbook industry.