- #1
erzagildartz
- 1
- 0
how to solve triple integrals in cylindrical, spherical and rectangular coordinates ..easy ways
How to Integrate Triple Integrals in Different Coordinate Systems?
- Context: Undergrad
- Thread starter erzagildartz
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SUMMARY
This discussion focuses on solving triple integrals in cylindrical, spherical, and rectangular coordinates. The process involves converting Cartesian coordinates (x, y, z) to their respective spherical or cylindrical forms and multiplying by the Jacobian of the new coordinate system. Participants emphasized the importance of integrating each component sequentially and provided links to resources for further understanding, including examples and tutorials on triple integrals.
PREREQUISITES- Understanding of triple integrals
- Familiarity with coordinate systems: Cartesian, cylindrical, and spherical
- Knowledge of Jacobian transformations
- Basic calculus skills
- Study the process of converting Cartesian coordinates to cylindrical coordinates
- Learn about the Jacobian determinant and its application in coordinate transformations
- Explore examples of triple integrals in spherical coordinates
- Review the provided resources: Math Insight and Lamar University tutorials on triple integrals
Students and educators in mathematics, particularly those studying calculus and integral calculus, as well as professionals needing to apply triple integrals in various coordinate systems.
- #2
Mr-R
- 123
- 23
Welcome to PF
You should provide us with your mathematical background first, right?
What do you mean by easy ways?
Well, you just integrate each of the components normally one at a time. Depending on your limits.
Assuming you have Cartesian coordinates (x,y,z). Convert each component to its Spherical/Cylindrical counterpart and multiply by the Jacobian of the new coordinate system. So, just convert to the new coordinate system, multiply by the Jacobian and then integrate normally.
Check this link, it has some nice examples for you:
http://mathinsight.org/triple_integral_introduction (read this first)
http://tutorial.math.lamar.edu/Classes/CalcIII/TISphericalCoords.aspx
You should provide us with your mathematical background first, right?
What do you mean by easy ways?
Well, you just integrate each of the components normally one at a time. Depending on your limits.
Assuming you have Cartesian coordinates (x,y,z). Convert each component to its Spherical/Cylindrical counterpart and multiply by the Jacobian of the new coordinate system. So, just convert to the new coordinate system, multiply by the Jacobian and then integrate normally.
Check this link, it has some nice examples for you:
http://mathinsight.org/triple_integral_introduction (read this first)
http://tutorial.math.lamar.edu/Classes/CalcIII/TISphericalCoords.aspx
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