Vector analysis textbook

In summary, the conversation discusses the search for a book on vector analysis that covers spherical and cylindrical coordinates, as well as the calculation of volume, surface area, and curve length using differential surface and volume elements. The speaker mentions that most books in the library only use cartesian coordinates and curvilinear coordinates are not used much. They also express a preference for a book that uses all coordinate systems throughout the text. Another person suggests the book "Vector Calculus" by Marsden, but notes that it may not be well-liked by some. They also suggest "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach" by Hubbard. The original speaker mentions that they are not a fan of Marsden and asks if the Vector
  • #1

iampaul

93
0
Can you suggest me a book in vector analysis which covers spherical and cylindrical coordinates. My professor discusses the calculation of volume, surface area and curve length, by integrating differential surface and volume elements in terms of cartesian, spherical and cylindrical coordinates. All the books I find in our library only uses cartesian. Curvilinear coordinates are introduced but not used much. I have the same problem with surface and line integrals. It would be better if the book uses all coordinate systems throughout the text.
 
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  • #2
Based on what it sounds like the level of the course is, you may enjoy Vector Calculus by Marsden. A lot of people I know disliked it however.
 
  • #3
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  • #4
Have you looked at the Vector Analysis textbook by Victor and Alice S. Textbook?
 
  • #5
I was in your exact situation about 20 years ago - I found that the Schaum's Outline of Vector Analysis fit the bill quite well. Discusses curvilinear coordinates and has enough examples to help you out. Cheap, too!

good luck,

jason
 
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1. What is vector analysis?

Vector analysis is a branch of mathematics that deals with the study of geometric objects known as vectors. It involves the use of mathematical operations such as addition, subtraction, and scalar multiplication to analyze and manipulate these vectors.

2. What are some applications of vector analysis?

Vector analysis has numerous applications in fields such as physics, engineering, and computer graphics. It is commonly used to analyze forces and motion, electric and magnetic fields, and fluid flow.

3. What topics are typically covered in a vector analysis textbook?

A vector analysis textbook will typically cover topics such as vector algebra, vector calculus, vector fields, line and surface integrals, and theorems such as Green's theorem and Stokes' theorem. It may also include applications of vector analysis in different fields.

4. Is vector analysis difficult to learn?

Vector analysis can be challenging for some students, especially those who are new to the concept of vectors. However, with practice and a solid understanding of basic mathematical concepts, it can be easily mastered.

5. How can I improve my understanding of vector analysis?

To improve your understanding of vector analysis, it is important to practice solving problems and working through examples. You can also seek help from a tutor or join a study group to discuss and clarify any concepts you may find difficult.

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