Is It Acceptable to Use Angle Braces in Vector Integration?

In summary, it seems that using angle braces when integrating a vector function is not commonly used in textbooks, but it may be a matter of convention and personal preference.
  • #1
radiogaga35
34
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A quick question -- is it acceptable to use angle braces when integrating a vector function, instead of expressing the vector i.t.o unit vectors?

E.g. say ∫<x,2x,3x> dx

This form seems far more convenient and suggestive than ∫ [xi + 2xj + 3xk] dx. Especially with ugly functions. However I've looked though a few textbooks and I've never seen this notation used with integration (or differentiation?) of a vector fxn...is there some reason, or is it just convention?
 
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  • #2
is there some reason, or is it just convention?

I suspect it is just convention. Math texts tend to use (a,b,c) while physics texts tend toward the i,j,k unit vector notation.
 
  • #3


It is acceptable to use angle braces when integrating a vector function, instead of expressing the vector in terms of unit vectors. This notation is commonly used and can be more convenient and suggestive, especially when dealing with complex vector functions. However, it is important to note that this notation is not commonly used in textbooks and may not be recognized by all readers. It is ultimately a matter of personal preference and convention. Some textbooks may use this notation, while others may stick to the more traditional form of expressing the vector in terms of unit vectors. As long as the notation is clear and consistent, either form can be used in vector integration.
 

FAQ: Is It Acceptable to Use Angle Braces in Vector Integration?

What is vector integration notation?

Vector integration notation is a mathematical notation used to represent vector calculus operations, such as integration, in a concise and efficient manner. It involves using symbols and operators, such as the dot and cross product, to manipulate vectors and perform calculations.

How is vector integration notation different from regular integration notation?

Vector integration notation differs from regular integration notation in that it takes into account the direction and magnitude of vectors. In regular integration, only scalar quantities are integrated, while in vector integration, both scalar and vector quantities can be integrated.

What is the purpose of vector integration notation?

The purpose of vector integration notation is to simplify and streamline calculations involving vector calculus. It allows for the representation of complex vector operations in a compact and efficient manner, making it easier to solve problems in physics, engineering, and other fields.

How is vector integration notation used in real-world applications?

Vector integration notation is used in various real-world applications, such as analyzing forces and motion in physics, calculating electric and magnetic fields in engineering, and modeling fluid flow in aerodynamics. It is also used in computer graphics to represent and manipulate 3D objects.

Can vector integration notation be used in any coordinate system?

Yes, vector integration notation can be used in any coordinate system, including Cartesian, polar, cylindrical, and spherical coordinates. However, the specific notation and formulas used may vary depending on the coordinate system being used.

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