Vector Calculus: Dots, Crosses & Triple Products Explained

In summary, the conversation is about suggestions for a good book that covers topics such as vectors, dots, cross and triple products, gradient, divergence, and their applications. Some recommended books include "Linear Algebra," "Multivariable and Vector Calculus," "div, grad, curl, and all that," and "The General Fundamental Theorem of Calculus." Physics books, such as "Feynman vol 2," can also provide a good understanding of these concepts.
  • #1
pona24
2
0
Can anybody please suggest me a good book which covers following topics in detail

Vectors - Dots, Cross and triple products, Gradient, divergence and applications.

thnx in advance
 
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  • #3
"div, grad, curl, and all that"
 
  • #4
thrill3rnit3 said:
"div, grad, curl, and all that"

What kind of reply is that?
 
  • #5
AC130Nav said:
What kind of reply is that?

Lol, it's a book title... google it :smile:
 
  • #8
I don't really see your problem with the reply. The OP was asking for books, the reply gave a book...
 
  • #9
Essentially all several variable calculus books cover these topics: Stewart, Edwards-Penney, Hass Weir Thomas, either at the end or in volume 2. Stronger treatments are in apostol vol.2, Courant vol.2, Fleming, or even spivak's calculus on manifolds, or the derivative evrsion in guillemin and pollack. Indeed almost every differential geometry book on ym shelf covers this material. I found 10-15 books on my shelf with this theorem in it. this must be the most important theorem in mathematics. Of course that is no surpriz=se since it is the general fundamental theorem of calculus. (Stokes thm).

So if you own almost any calculus book, look in it for this stuff.

Physics books are also good for telling you what the theorem means physically. E.g. after learming the vector algebra try Feynman vol 2.
 
  • #10
thnk u all
 

1. What is vector calculus?

Vector calculus is a branch of mathematics that deals with the study of vector fields and their properties. It involves the use of vectors, which are mathematical quantities that have both magnitude (size) and direction, to solve problems related to calculus.

2. What are the basic operations in vector calculus?

The basic operations in vector calculus include addition, subtraction, scalar multiplication, and vector multiplication. Addition and subtraction are performed by combining or subtracting the corresponding components of vectors. Scalar multiplication involves multiplying a vector by a scalar (a real number). Vector multiplication includes the dot product, cross product, and triple product, which are used to calculate the angle between vectors, the area of a parallelogram formed by two vectors, and the volume of a parallelepiped formed by three vectors, respectively.

3. What is a dot product?

A dot product is a type of vector multiplication that results in a scalar (a single numerical value). It is calculated by multiplying the corresponding components of two vectors and then adding the products together. The dot product is used to find the angle between two vectors and to determine if the vectors are perpendicular (have an angle of 90 degrees between them).

4. What is a cross product?

A cross product is another type of vector multiplication that results in a vector. It is calculated by taking the determinant of a 3x3 matrix formed by the components of two vectors and then assigning the resulting vector a direction determined by the right-hand rule. The cross product is used to find the area of a parallelogram formed by two vectors and to determine the direction of a vector perpendicular to two given vectors.

5. What is a triple product?

A triple product is a type of vector multiplication that results in a scalar (a single numerical value). It is calculated by taking the dot product of one vector with the cross product of the other two vectors. The triple product is used to find the volume of a parallelepiped formed by three vectors and is also known as the scalar triple product.

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