# How Can I Read Engineering Textbooks?

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Hi , I have a huge problem...

I need to study engineering textbooks written in english. I usually have no problems with technical terms, as long as I can find their pronunciation in a dictionary, but when it comes to formulae...uh-oh...

Now, here's the problem: how can ESL students read engineering, mathematics or physics textbooks if they are learning english by themselves, studying in their own country?

I have been learning english by myself, no teachers, no courses at all. Unfortunately I can't afford to study abroad, and now I'm really stuck. I'll give you some examples. How should a student read:

(2bx+a)4b ok, this is simple, two B X plus A multiplied by four B, for example... but now...

25 (A^2 m)/V^4 umm... twenty-five amperes squared meters over volts to the forth, or maybe twenty-five square amperes meters over volts to the forth...

10 m^2/kg^2 ten square meters over square kilogram(s), or ten meters squared per square kilogram, etc.

(+3x)(-b) positive three X times negative B, or positive three X times minus B, or plus three X multiplied by minus B, etc.

That was pretty easy stuff compared to other topics. So, as you can see, the problems are about reading formulae or reading everything that is not written in words. Of course, that kinds of things are taught in school, but I wasn't taught in english! I also searched the Net for something useful, but I found almost nothing (lots of mathematics textbooks that can't solve my problem).

Now I just need some advice. What should I do? I hope you know a book, a website or a person that can help me. Anyway, I feel these kinds of things shouldn't be really difficult, it's just I can't find nothing for learners on the Net and now I don't know what to do. I'd be disappointed if I had to give in.

Thank you very much in advance.
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Hi, Kooyeen

I sent your e-mail to my father, who used to be an electrical engineer and a physics teacher. This is what he wrote.

(I think other people who use this forum will have some ideas, also.)

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If the notation the student is reading is like the notation in the email, I see some of the problem.

1. It looks like he is confusing the variable x with the multiplication sign x. i.e. In the first example (2bx+a)4b I think the x is a variable and that expression would simplify to 8(b^2)x + 4ab. If the problem was written in a good text book or with Microsoft Word it could be written with superscripts instead of using simplified computer symbols like ^.

2. He says he is studying engineering text books. A large part of engineering is algebra. From what he says I would recommend studying an algebra book - with worked out examples.

3. He also is not familiar enough with the symbols to differentiate Unit Symbols from Variable Symbols and from mathematical Operation Symbols. Sticking with a beginning engineering book should help some of this.

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I don't know if this link will be helpful or not. You might want to search under "operators" first, and go from there.

http://mathforum.org/library/view/3747.html
Thank you very much Nef.

I'm so sorry, I've read my post again and I see I didn't express myself very well, my post isn't really clear. Anyway, I partly solved my problem by myself. I'll show you what I should have asked:

My question should have been: How can I read, spell out or pronounce mathematical formulae and symbols?

I found something useful myself, so an example of reply could have been: check out in wikipedia at , for example.

I didn't make clear that my problem was only about the English language (i.e. reading a formula like a native speaker) and not about the meaning or the usage of a particular formula.

Even though I found some useful websites on the Net, I still can't find how to pronounce some symbols. Anyway I think I'll post some questions later, but I'll post them in another section of this forum because I realized that few people check this section.

Thank you again Nef
Students: We have free audio pronunciation exercises.
Neat table

I'm sorry I misunderstood you.

If some symbols are still bothering you, maybe you could list them here a few at a time.
Hi Koyeen,

Thank you guys.

I'm writing this post for those who will read this thread in the future and will face the same problems as me.

This link, will be useful. If you need something else, try to take a look at other articles in wikipedia ( for example Partial Derivative, Integral,etc.).

It could be useful to try searching for examples with Google. There are a lot of websites and free e-books about mathematics, there you'll find some more expressions aand terms. Here's a simple book to begin with: http://www.themathpage.com /

If you want to follow some brief lessons, here's some videos: http://www.sci.uidaho.edu/polya / . Search that website for "course material" and "online lectures".

A last tip: there are a lot of ways to express the same concept in mathematics, so you will find that every professor has their own style.

Site Hint: Check out our list of pronunciation videos.
Kooyeen, I have just found your inquiry, and I hope it's not too late to answer. If I grasp what you have asked us, you are looking for the technique of reading formulas and equations aloud, in English. As I look at your very first post, I see that you have most of the technique in mind with simple variables, but you need a way to handle parenthetical groupings, divisions, exponentiation, and so forth.

One way is simply to read each element in an expression, left to right, top to bottom, and pronounce or state each bit of punctuation as it occurs. For example, (2bx+a)4b would be open parenthesis 2BX plus A close parenthesis times 4B. (I used capital letters for variables to avoid confusion with ordinary letters.) And 25 (A^2 m)/V^4 would be 25 times open parens (I abbreviate) A squared M close parens over (or divided by) V to the 4th.

Sometimes when the expression in parentheses is of a few variables, you could say quantity[...all] like this:
25 times the quantity A squared times M all over V to the 4th, where all is used to combine the 25 and the expression in parentheses.

10 m^2/kg^2 is simply ten meters squared per kilogram squared (not square kilogram).

If you would like to throw a few expressions this way, with or without your versions of spoken English equivalents, I will be happy to transform them into spoken English. We can compare. I will be happy to help you learn this.
Hi Tartan , what a coincidence, I just checked this forum section... it's been two months since I last took a look at this section! In some ways I've already found what I was looking for, however I'm still unsure about some things. If you feel like taking a look at these... I just need to know the usual ways to deal with this stuff. I hope you understand, since I can't type strange symbols here, I'll write the formulae the best way I can.

Negative numbers: minus or negative?

• 2^(-x) two to the negative/minus ex (I think it's usually "minus")

• 10^-6 ten to the negative/minus six (I think it's usually "minus")

• The integral of f of x dee x from minus/negative b to minus/negative one (both can be used)

• The limit of f of x, as x approaches negative/minus one (both can be used)

• 3-(-2) three minus minus/negative two (I think it's usually "negative")
Derivatives: what are the usual ways to read them?

• d^2 y/d x^2 (this is a second derivative, I'd say "dee squared why by/over dee ex squared", where "by/over" could be omitted)

• d^3 y/d x^3 (this is a third derivative, I don't know how to read this, I think it's more usual to just say "the third derivative of y with respect to x", instead of reading the symbols)

• d^4 y/d x^4 (same comment as above)
Partial derivatives: I can't write the partial derivative symbol (the cyrillic letter "de"), I just need to know how that notation can be read.

• Partial derivative of f with respect to x (I'd say "dee f by/over dee x", like a classic derivative. Also "partial f by/over partial x")

• second, third, etc. partial derivatives (I don't know how to read this, I think it's more usual to just say "the second, third, etc. derivative of f with respect to x", instead of reading the symbols)
Integrals: do I integrate over, in, along, inside, etc. a domain?

• The line integral over/along/on a closed path/curve (I think it's usually "over" and "path")

• The integral over/in/on the interval (a,b) (I think it's usually "over")

• The volume integral over/in/inside the volume/region R ( I think it's usually "over" and "region", but also "volume" can be used, especially in cases like "...over the volume of the sphere S")

• The surface integral over/on the surface S (I think it's usually "over")
Simplifying and reducing:

• ab(2x + 2y) ------> 2ab(x+y) What did I do? How would you describe that step? (I would say "I took out a two")

• 2x + 4y + 8z -------> 2(x + 2y + 4z) How would you describe that step? ( I'd say "I took out a two", or "I got a two by itself")

• 2a/2b -----> a/b How would you describe this semplification? ( I'd say "Those two's cancel", "the two in the denominator cancels with the two in the numerator", "The two in the numerator cancels the other two")
Maybe it's too much stuff for a post, anyway there's no need to hurry (of course ), feel free to answer to what you like (or even not to answer!) Thank you very much in advance.
Negative numbers: minus or negative?
• 2^(-x) two to the negative/minus ex (I think it's usually "minus") minus is good.
• 10^-6 ten to the negative/minus six (I think it's usually "minus") ditto
• The integral of f of x dee x from minus/negative b to minus/negative one (both can be used) minus may be more common
• The limit of f of x, as x approaches negative/minus one (both can be used) ditto
• 3-(-2) three minus minus/negative two (I think it's usually "negative") negative is good
Derivatives: what are the usual ways to read them?
• d^2 y/d x^2 (this is a second derivative, I'd say "dee squared why by/over dee ex squared", where "by/over" could be omitted) Omitting by/over is risky--leads to misinterpretation.
• d^3 y/d x^3 (this is a third derivative, I don't know how to read this, I think it's more usual to just say "the third derivative of y with respect to x", instead of reading the symbols) I recall saying dee third why over dee why third (I was in engineering school forty years ago)
• d^4 y/d x^4 (same comment as above) ditto as dee fourth, etc.
Partial derivatives: I can't write the partial derivative symbol (the cyrillic letter "de"), I just need to know how that notation can be read. Can you cut and paste this: ∂y/∂x ?

• Partial derivative of f with respect to x (I'd say "dee f by/over dee x", like a classic derivative. Also "partial f by/over partial x")
• second, third, etc. partial derivatives (I don't know how to read this, I think it's more usual to just say "the second, third, etc. derivative of f with respect to x", instead of reading the symbols)
Integrals: do I integrate over, in, along, inside, etc. a domain?
• The line integral over/along/on a closed path/curve (I think it's usually "over" and "path")
• The integral over/in/on the interval (a,b) (I think it's usually "over")
• The volume integral over/in/inside the volume/region R ( I think it's usually "over" and "region", but also "volume" can be used, especially in cases like "...over the volume of the sphere S")
• The surface integral over/on the surface S (I think it's usually "over")
For derivatives and integrals, here are some clips from Wikipedia, one of my favorite quick resources.

«The definite integral...is read "the integral from a to b of f-of-x dx".» http://en.wikipedia.org/wiki/Calculus
«The derivative of a function y = f(x) with respect to x is usually expressed as either y ′ (read "y-prime"), f ' (x) (read "f-prime of x") or as d/dx (y) which is commonly shortened to: dy/dx»

dy/dx
«is pronounced in various ways such as "dee why by dee ex" or "dee why over dee ex". The form "dee why dee ex" is also used conversationally, although it may be confused with the notation for element of area.» http://en.wikipedia.org/wiki/Derivative

«Partial derivatives are represented as ∂/∂x (where ∂ is a rounded 'd' known as the 'partial derivative symbol'). Some people pronounce the partial derivative symbol as 'der' rather than the 'dee' used for the standard derivative symbol, 'd'.»

Given f(x(1),...,x(i))and ∂f/∂x(i), we can say: With f of x sub 1 to x sub n, {der|dee} f over {der|dee} x sub i is the [partial] derivative of f with respect to x sub i, with all other variables kept constant. Adapted from

Symbols: [abc] means optional; and {a|b|c} means choose one.