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This topic is available for NewMars members who might wish to contribute to a body of knowledge about calculus.
This topic is NOT limited to English.
The issue addressed by this topic is the art of correct pronunciation of mathematical terms, in whatever language they may appear.
We open with a conversation with Gemini about audio books for calculus in English.
The book I just received about OpenFOAM was written by two Italian professors, and it was translated to English (with some success).
Regardless of the language, my experience has been that I do not know the correct pronunciation of many terms / expressions.
I just guess, and try to pick up hints from video or the occasional live person.
It appears that there may be guidelines / resources available for persons who create audio books of mathematical subjects.
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Post #3: Conversation with Google's Gemini about audio books for calculus, and related options
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This post contains a transcript of a conversation with Gemini 2.5 about audio books for calculus.
Conversation with Gemini
Audio Book Calculus - Hi Again! Thank you for all your help with many previous requests! Today's question is just a search request, with a nuance. I'm wondering if there might be audio books of calculus texts?
***That's an excellent and very specific question! The short answer is yes, but with a significant caveat.
The Nuance:
You'll find that there are two main types of "audiobooks" related to calculus.
Audiobooks about calculus: These are narrative books that discuss the history, concepts, and applications of calculus in a more accessible, prose-based format. They are designed for a general audience and are much better suited for listening without a visual aid. Examples include:
A Tour of the Calculus by David Berlinski
Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz
Change Is the Only Constant: The Wisdom of Calculus in a Madcap World by Ben Orlin
These are great for gaining a conceptual understanding and appreciation for the subject, but they won't teach you how to solve problems.
Audiobooks of classic calculus textbooks: These are verbatim readings of older, public-domain textbooks. The most famous example is "Calculus Made Easy" by Silvanus P. Thompson. This book, originally published in 1910, is a classic for its clear and straightforward approach. You can find audio versions on platforms like:
YouTube
Internet Archive
LibriVox (a great source for free, public-domain audiobooks)
The Challenge with Calculus Audiobooks:
As you can probably imagine, listening to a textbook that is heavily reliant on visual information (equations, graphs, diagrams) is extremely difficult. Many people in online forums and reviews point this out. A narrator reading "the derivative of f(x) equals the limit as h approaches zero of the quantity f(x + h) minus f(x) all divided by h" is almost impossible to follow without seeing the notation.
Summary:
For a conceptual, big-picture understanding of calculus, look for narrative audiobooks on Audible or similar platforms.
If you're looking for an actual textbook in audio form, your best bet is "Calculus Made Easy," but be prepared to supplement your listening with a physical or digital copy of the book to follow along with the equations and diagrams.
For a truly effective "audio" experience, many people recommend video lectures (like those on YouTube) as a better alternative, as they combine audio explanations with visual demonstrations.
***Thank you ** very ** much! What I am actually looking for may be available in the answers you kindly provided. I want to be able to ** say ** (pronounce) the equations correctly, while I have the actual book in front of me. As one of countless students who have to work remotely, I do not have exposure to a knowledgeable speaker so I can learn the correct pronunciation. It certainly sounds as though "Calculus Made Easy" might be an answer, provided that the hard copy is still available as well.
***That's an excellent clarification! Your goal of learning to "say" the equations correctly while looking at the hard copy is a perfect use case for these audio resources.
You've hit on a key challenge for students learning remotely—the lack of an audible role model for mathematical notation.
Here is a breakdown of how the resources can help and what other options you have:
1. "Calculus Made Easy" as a Solution
Audiobook: As we discussed, the LibriVox audio version of "Calculus Made Easy" by Silvanus P. Thompson is a fantastic starting point. The narrator will read the text, including the mathematical expressions, out loud.Hard Copy: You are in luck. Because the book is in the public domain, it has been reprinted by many different publishers, so it is widely available in both new and used formats. You can find copies on sites like Amazon, AbeBooks, and ThriftBooks for very reasonable prices. You can also find free PDF or HTML versions of the text online through sites like Project Gutenberg.
How to Use It: Simply open the hard copy to the section you are studying and listen to the audiobook. When the narrator gets to an equation, they will say it out loud, providing you with the correct pronunciation. For example, they might say "The derivative of x n is nx n−1 ." This will allow you to connect the visual symbols with the spoken words.
2. Other Resources for Pronunciation
While the audiobook is a great direct solution, you can also benefit from resources specifically designed to teach you how to read math notation.Narrators' and ESL Guides: Many websites created for audiobook narrators or for people learning English as a second language have guides on how to pronounce mathematical terms and symbols. These are incredibly useful and can teach you the conventions for things like "summation of," "for all," and "there exists."
Example: A guide might show you how to read the expression
x→a lim f(x) and tell you the proper way to say it is "the limit of f(x) as x approaches a."
YouTube Videos: Many math professors and tutors on YouTube read equations out loud as they write them on a whiteboard. This is an excellent way to see the notation being formed and hear the correct way to say it in real-time. Searching for "how to read math equations" or "calculus lecture" will bring up thousands of videos.
Text-to-Speech Software with MathML Support: More advanced accessibility tools are available that can read mathematical equations aloud. Some of these are integrated into learning management systems (LMS) or available as separate software. They can parse the underlying code of a math equation (like MathML or LaTeX) and convert it to spoken language. An example of such a tool is EquatIO, which has a screenshot reader that can read math aloud.
In conclusion, your strategy of using an audiobook with the physical book is a sound one, and "Calculus Made Easy" is a perfect candidate. Combining this with online resources for specific symbol pronunciation will give you a comprehensive way to learn the correct "language" of mathematics. Good luck!
***Awesome! Thank you ** very ** much. Our discussion contains so much valuable content I've decided to publish it in a small international forum whose members come from around the world, and for whom English is not necessarily the first language.
***
That's a wonderful idea! I'm truly glad the information was helpful and that you've found a way to share it with a wider audience. The challenge of learning the pronunciation of mathematical notation is a global one, and a resource like this could be incredibly valuable for students everywhere, especially those who don't have access to in-person instruction.I wish you and your forum members the best of luck with your studies and mathematical endeavors. Thank you for the opportunity to have this insightful discussion!
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This topic includes "calculus" in the title.... The topic is available for NewMars members who might wish to contribute to a collection of links, images and text that might help a reader to master this important set of ideas.
This post is about the difference between an algebraic equation and a differential equation.
In study of the CFD tool "OpenFOAM" I find myself confronted with differential equations that must be solved within every cell of a matrix of cells through which gas or fluid might flow in a simulation of the Real Universe.
In thinking about how to explain what is going on, it occurred to me that most folks are familiar with algebraic equations.
I had never thought about what the difference might be, so I asked Google and it came back with an answer that I would like to offer to our members to see if anyone can add texture to the answer.
what is a differential equation as compared to an algebraic equation
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An algebraic equation seeks specific numerical values for an unknown variable, like finding x in 3x = 15, whereas a differential equation seeks an entire unknown function that satisfies a relationship involving its own derivatives, such as y = sin(x) + c for the equation y' = cos(x). The key difference lies in the nature of the solution: numbers for algebraic equations and functions for differential equations.
Algebraic Equations
Unknown: A single number or a set of numbers.
Purpose: To find the specific value(s) of the unknown variable(s) that make the equation true.
Example: In the equation x² + 5x + 6 = 0, the solutions are the numbers x = -2 or x = -3.
Nature: The variables represent fixed, unchanging quantities.Differential Equations
Unknown:
An unknown function and its derivatives.
Purpose:
To find the function (or a family of functions) that satisfies the relationship involving its derivatives at every point in its domain.
Example:
For y' = cos(x), the solution is the function y = sin(x) + c, where c is any constant.
Nature:
The unknown function describes how something is changing over time or with respect to a variable, such as a changing volume or an evolving system.
In the case of OpenFOAM (or probably any CFD package) the events of interest involve flowing mass.
Measurements of interest include pressure and temperature, along with mass in the flow and other factors I've not yet learned. My impression is that it is not unusual to have to solve six differential equations to describe the flow of gas through an individual cell.
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My explanation for beginning students is that there are two kinds of numbers that you have to book-keep correctly, one being the numbers big enough to see (from math and algebra), and the others too tiny to see, called "differentials". You have to track them separately, but the two sets interact in two very specific ways.
First, if you ratio two of the tiny differentials to create a fraction, that fraction has a value that is a big number you can see, called a derivative. That is the fundamental notion behind differential calculus, and equations that have these ratios in them are called differential equations.
Second, if you add up an infinite number of these tiny little differential things, each too small to see any one of them, you get a sum that is a big number that you can see, and that summation process result is called an "integral". This is the fundamental notion behind integral calculus, and there are various formulas and procedures for actually computing those integrals.
Doing these same things with enough variable names to cover coordinates in 3-space (or more) is what we call "multivariate calculus".
The rest is merely learning all the rules and procedures to do these things correctly. It's very much like card games: you cannot win if you don't know the rules and procedures. Simple as that.
GW
Last edited by GW Johnson (Today 09:58:42)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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