A lesson in vector mathematics

In summary, the person in the conversation has started work on a textbook with about 100 pages and is looking for opinions on its clarity and understanding. They have included a link to one of the chapters and have received feedback on the writing being too personal, the lack of a definition of unit directions, and the absence of direction cosines in the explanation of unit vectors. There is also a suggestion to leave the section on units as a separate chapter and to consider the reader's level of knowledge on integration and differentiation.
  • #1
abercrombiems02
114
0
Hey everyone, I eventually would like to write a textbook. I've started some work, and have about 100 pages total. There is a link here to one of the chapters in my book. It still needs to be edited of course, but I would like any opinions...Is it understandable, clear, and direct? If some of the figures the text did not display correctly. Typically I label my base points with ), the location of particles with P, and horizontal displacments are labeled with x, and vertical displacements are labeled with y. Here is the link

http://www.geocities.com/abercrombiems02/Index/Chapter2.pdf

Thank you to all that responds!
 
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  • #2
I did a quick read through of it. I had a few things pop into mind (just my opinions):

1. The writing is a bit too "personal" for my tastes. The usage of terms like "I want to make side notes..." or "If I integrate..." If that was your aim, well then I guess you did well there.

2. You didn't really give a definition of what the 3 unit directions are at the very beginning. You just throw out e1, e2, e3 and eT. I'd take a paragraph and explain the orthagonal directions a bit.

3. You don't mention the direction cosines when talking about unit vectors.

4. I'd personally leave the section on units as a separate chapter. It confuses things a bit to be talking about the make up of a vector and operations and throw in units. One can learn how to operate with vectors and not have to worry about units just yet.

5. I honestly can't remember, but is it safe to assume that the reader knows about integration and differentiation at this level? I'm not sure there.

Again, these are just my opinions, so don't take them too seriously.
 
  • #3


First of all, congratulations on working towards writing a textbook! That is a great accomplishment. I took a look at the chapter you provided and I have some feedback for you.

Overall, the content is clear and direct. I appreciate the use of diagrams and examples to illustrate the concepts. However, there are a few areas that could use some improvement.

Firstly, I noticed some grammatical errors and typos throughout the chapter. It would be beneficial to have someone proofread your work before publishing it to ensure a professional and polished final product.

Additionally, some of the equations and mathematical notation may be difficult for beginners to understand. It would be helpful to provide more explanations and step-by-step breakdowns of the formulas and concepts. This will make it easier for readers to follow along and grasp the material.

I also noticed that the figures in the text did not display correctly. This can be confusing for readers and may hinder their understanding of the material. It would be best to fix these figures before publishing the textbook.

Lastly, I suggest labeling the figures and equations consistently throughout the chapter. For example, you mentioned labeling base points with parentheses, but I noticed that some figures had different labels. This can be confusing for readers and may result in misunderstandings.

Overall, I think your chapter has potential, but it could use some refinement before publishing. Keep up the good work and don't be afraid to ask for feedback from others to improve your writing. Good luck with your textbook!
 

1. What is vector mathematics?

Vector mathematics is a branch of mathematics that deals with the study of vectors, which are mathematical quantities that have both magnitude and direction. It involves operations such as addition, subtraction, and multiplication of vectors to solve problems in various fields such as physics, engineering, and computer science.

2. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. For example, temperature is a scalar quantity as it only has a numerical value, but velocity is a vector quantity as it has both magnitude (speed) and direction (e.g. north, east, etc.).

3. How are vectors represented in mathematics?

Vectors can be represented in mathematics using various methods, such as geometrically with arrows or algebraically with coordinates. In the geometric representation, the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. In the algebraic representation, a vector is written as an ordered list of numbers, usually in the form of (x, y, z).

4. What are some common operations used in vector mathematics?

Some common operations used in vector mathematics include addition, subtraction, scalar multiplication, dot product, and cross product. Addition and subtraction of vectors involve adding or subtracting the corresponding components of two vectors to get a new vector. Scalar multiplication involves multiplying a vector by a scalar (a number) to change its magnitude. The dot product and cross product are used to calculate the angle between two vectors and to find a vector that is perpendicular to two given vectors, respectively.

5. How is vector mathematics used in real-life applications?

Vector mathematics has a wide range of applications in various fields, such as physics, engineering, computer graphics, and navigation. For instance, it is used in physics to calculate forces and velocities, in engineering to design structures and analyze motion, and in computer graphics to create 3D images and animations. It is also used in navigation systems to determine the location and direction of an object or person.

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