Multivariate Function Integration

In summary, when taking multiple integrals of a multivariable function, the order in which you integrate does not matter for "nice" integrands. There is a notation for partially integrating a multivariable function with respect to a single variable, which is indicated by the differentials used. Fubini theorem can provide more information on this topic.
  • #1
gordonj005
56
0
Quick Question

When taking multiple integrals of a multivariable function, does the order in which you integrate (in terms of the variable) matter?

Also, is there a notation for partially integrating a multivariable function with respect to a single variable?

Thanks for your help
 
Mathematics news on Phys.org
  • #2
The order will not matter for "nice" integrands.

I'm not sure what you are looking for in your second question. You can integrate with respect to some variables and leave others alone. This would be indicated by what differentials you use. For example the integral of f(x,y)dx means integrate with respect to x and leave y alone.
 
Last edited:
  • #3
What do you mean by "nice" integrands?

Ah right, that's what I thought. Thanks a lot man.
 
  • #4
Look up Fubini theorem.
 
  • #5
For the second question, this might help you understand:

http://www.cliffsnotes.com/study_guide/Partial-Integration.topicArticleId-19736,articleId-19707.html
 
Last edited by a moderator:

FAQ: Multivariate Function Integration

What is a multivariate function?

A multivariate function is a mathematical function that takes multiple variables as inputs and produces a single output. It is used to describe relationships between multiple variables and is commonly used in fields such as economics, physics, and engineering.

What is integration of a multivariate function?

Integration of a multivariate function involves finding the area under the curve of the function in a multi-dimensional space. It is a mathematical process used to calculate the total value of a function by dividing it into smaller parts and summing them up. Integration is used to solve a variety of problems, such as finding volumes, areas, and probabilities.

What are the methods for integrating multivariate functions?

The two main methods for integrating multivariate functions are multiple integrals and iterated integrals. Multiple integrals involve integrating over multiple variables at once, while iterated integrals involve breaking down a multivariate integral into a series of single variable integrals. Other methods include using change of variables, polar coordinates, and numerical integration techniques such as the trapezoidal rule and Simpson's rule.

What are the applications of multivariate function integration?

Multivariate function integration has many applications in various fields of science and engineering. It is commonly used in physics to calculate the work done by a force on an object, in economics to calculate consumer and producer surplus, and in biology to model population growth. It is also used in probability and statistics to calculate joint probabilities and expected values.

What are the challenges in integrating multivariate functions?

Integrating multivariate functions can be challenging due to the increased complexity of working with multiple variables. It requires a solid understanding of calculus and algebra, as well as the ability to visualize and work in multi-dimensional spaces. Additionally, finding closed-form solutions for multivariate integrals can be difficult, and numerical methods may be necessary for more complex functions.

Similar threads

Calculus Multivariable calculus PDF books
Replies
10
Views
2K
I Can Schwarz's Theorem be used "Backwards" to prove continuity?
Replies
21
Views
1K
Operators On Multivariable Wave Functions
Replies
8
Views
1K
Correct Usage of Partial Derivative Symbols in PDEs
Replies
10
Views
1K
Nice Resource to learn Advanced Calculus
Replies
2
Views
7K
B Limitations of Multivariate Linear Regression
Replies
6
Views
2K
I A doubt about the multiplicity of polynomials in two variables
Replies
8
Views
2K
I Multivariable optimization problem
Replies
6
Views
2K
I Exploring the Identity Matrix in Multivariable Control Theory
Replies
7
Views
2K
I Second derivative of chained function
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top