Math books Applied for Good

Math books and more books on math

Following the path of applied mathematics and popular science with math inclination I want to bring to your attention a couple of books that some of you may find helpful if not insightful.

Oliver Heaviside’s Maxwell’s Equations

Actually, I would rather start from a book which is an amalgam of history and mathematical physics in one and it’s a book about the self-taught mathematical physicist Oliver Heaviside who brought to you the so called Four Maxwell’s equations.

equations

book_heaviside

The book is Oliver Heaviside: The Life, Work, and Times of an Electrical Genius of the Victorian Age written by Paul J. Nahin an emeritus prof. of Electrical Engineering in University Of New Hampshire which we’ll return to later in the post.  What is interesting about the books is that it has a right amount of math for readers who are interested not only to know who Oliver Heaviside was,  but also what he did as a physicist and engineer.

 

 

 

 

Okay, the books

While reading very interesting Applied Mathematics book by David J. Logan (3rd edition, Ch. 4.4 Green’s Functions, p. 253)

step_function

I was, as always, diverged by the mentioning of the Heaviside Step function in the text that I felt an urgent surge to check a biography of this incredible person and, lo an behold, I was able to find the Paul Nahin’s book mentioned above and also quite interesting and short  article in the Physics Today magazine Oliver Heaviside: A first-rate oddity

David J. Logan

Having mentioned, David Logan I should say that I am reading the 3rd edition of his book, which is available in Scribd if you have a membership there, and even for free for 30 days trial period. It is always possible to buy the 4th edition, but the price is, quite frankly, astronomical.

logan

Applied Mathematics 4th edition by David J. Logan. What I like about this book is the detailed examples that help you understand the content of the book better, but even more I like the way David Logan explains the physical rational behind the differential equations. It helps very much to know how and why this or that math technique is applied in practice. In addition, another applied mathematician Mark H. Holmes book’s is also mentioned by David Logan which you also may find useful.

 

 

 

Paul J. Nahin

Now that’s get back to Paul Nahin. It turn’s out he produced a whole series of books on Physics, Mathematics, Electrical Engineering and Computer Science which can be called popular, but actually are an essays full of wonderful applied mathematics. Paul is able to explain things in engaging and easy to understand manner. As people like to say, I wish I had come across his books earlier in my life, but it is what it is and it’s good that I was able to find them. Thanks to the Scribd digital library I was able to glimpsed through all of his books available there and I’d recommend to math inclined readers to check the following books.

simple_physics

 In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions will take you into the physics journey that you could have been missing since your school or collage years. Maybe, you weren’t able  to understand it back then or had no time, but this time it will be different thanks to Paul’s ability to explain physics in an easy to grasp way.

 

 

 

 

And one additional book that I find quite impressing 

crunchung numbers

Number-Crunching: Taming Unruly Computational Problems from Mathematical Physics to Science Fiction as all books by Paul J. Nahin this one draws examples from different areas of exact sciences and engineering that will keep you awake at night following the stories and trying to solve the puzzles yourself.

 

 

 

 

Mark H. Holmes

holmes

Remember, I’ve mentioned Mark H. Holmes so he also wrote a couple of books on applied math, and I’d recommend you to check his Introduction to Numerical Methods in Differential Equations which I find also very useful and a helper while reading aforementioned books on applied math. Unlike his Introduction to the Foundations of Applied Mathematics, which I find cryptic due to the lack of detailed examples, Introduction to Numerical Methods has quite a few of them. This makes the book kind of easy to digest.

 

 

 

Last, but not least

To make sense in this whole unfamiliar forest of applied mathematics there is a nice book that has all you need in one place classified and summarized to be your guidance on your quest to master the math and apply it for good. It is

all_of_it

The Princeton Companion To Applied Mathematics.

 

 

 

 

 

 

 

Dare think, keep on going, and be carried forward on wings of math muse.

References

Fixing a broken zipper slider. Fill your boots

slider_bigger

Do it yourself

This post is a little be unexpected, but nevertheless it may be useful to some of the readers of this blog.

The issue is that last weekend while having fun with my family outdoors I was skillful enough to brake the zipper slider of one of my beloved winter boots. Even though the boots weren’t new and showed early signs of wear and tear replacing them with a new pair of similar ones would cost me about 115 CAD. I knew that throwing the old boots only because of a broken slider wasn’t an option, so I resorted to trying to reattach it myself without first watching how to do it on the YoutTube. The result wasn’t encouraging, so I watched a couple of videos there, the most useful, I’ve attached at the bottom of the post. Following the video advice I ended up with a zipper slider in a really broken state as in the image above.

A fork stuck in the road

Having found myself and the boots in this awkward situation, the options were to buy a couple of new zipper sliders of varying sizes. The issue was I wasn’t sure what slider to chose on the Internet, since there were quite a few, and frankly speaking, I’m not a shoemaker expert. I was curious enough to notice that some descriptions for sliders had a Vislon term in them. So I searched for it and hooray a number of posts clarified that a zipper is more then meets the eye, and there are some things to know about them before any purchase.

Zipper sciences

Zippers have a number of distinct physical parameters:

  • Type
  • Size
  • Markings or absence of which
  • Lock mechanism

Below comes a more detailed description of each parameter.

Types

It turns out that there are two kind of zippers: Vislon and Coil. While the Vislon zipper has distinguishable teeth, the Coil more resembles a coil, hence its name.

zippers_shape

 

Sizes

As for the sizes, zippers are numbered starting from #1 to #10. The sizes are measured in inches or millimeters.  When the size is measured in a following fashion as it’s shown in the image below

size_zippers

To find a mapping from zipper number to zipper size, and vice versa, in inches/mm search the Internet.

Roughly it’s

Markings

If you think that determining the size of your zipper is easy, it’s yes or no.

Best case scenario – good markings

There are zippers, such as YKK that have proper markings on the back side of the zipper slider. Where the number, for example 5, stands for the zipper size number and CN or VS/V post-fixes stand for the zipper type. CN stands for Coil type and V/VS stands for Vislon type. In the image below it’s size number 5, Coil type YKK zipper slider.

ykk_marking

So – so scenario – some markings in unexpected places

Some zippers have no apparent markings, but upon thorough investigation it can be found at the front side of the slider like on the image below, which has size number 8 shown (though it resembles a letter B in this case)

marking_on_the_side

 

No markings – use your engineering skills, i.e. the ruler

Since the slider on my boots was a stealth one, it had no markings, I resorted to measuring the size using a good old ruler. And it measured to about 6.5-7 mm which could be size #6 or #7.

Locking mechanism

Some zipper sliders have a retractable pin or other means to lock the slider in place to prevent it from sliding. Other zippers can’t have this functionality and are plain non-locking sliders. My broken slider had the pin configuration as in the image below.

lock_pin

 

An ideal solution

Having watched on the YouTube a couple of video tutorials on how to reattach a slider or attach a new one, I got that it wasn’t gonna be an easy task. So I searched a little bit more and found a kind of ideal solution.

As you would expect the robust solution should be adjustable and easy to install zipper slider. The good news are that there is such a thing already in three sizes to rule them all. It’s a FixnZip.

This FixnZip consists of two metal parts that are easily install-able and work just like it should provided you had a correct size for the boots in hand. Actually, it is applicable to jacket, bags and other kinds of zippers. 

So in the end having the small size FixnZip for 25 CAD saved me about 90 CAD spared on not buying a new pair of boots. The lesson is do it yourself, and be happy.

shoes

 

References