MISCELLANEOUS > MULTIPLE INTEGRALS
Finding the mass of a nebula in space.
While the ideas of Calculus were certainly a breakthrough in mathematics, the mathematicians at that time where comtemplating on the idea of using the same notions and processes but applying it to a situation with multiple variables.
This brought forth a whole now dimension of analysis where multiple variables are used, and no longer were we restricted to one variable. Multiple integrals are in essence, taking the limiting value of infinite sums in a space described by two or three variables.
We start of by revisiting the age old concepts of Calculus, extending it to two and three variables and look at a few problems which uses multiple integrals.
Take a look at any physics phenomena or engineering problem and you would see that multiple integrals greatly facilitates the analysis of the situation. The selling point of its uses comes from the fact that most physical problems are described by more than one variable. In the real world, a certain result is affected by different factors, and the only way to study the cumulative result of these factors is to perform integral calculus on all the variables.
Pierre-Simon de Laplance
Triple Integral formulas
Coordinates Transformation
Finding Moment of Inertia
Most areas of Calculus that uses multple variables
Finding the mass of a nebula in space.
This brought forth a whole now dimension of analysis where multiple variables are used, and no longer were we restricted to one variable. Multiple integrals are in essence, taking the limiting value of infinite sums in a space described by two or three variables.
We start of by revisiting the age old concepts of Calculus, extending it to two and three variables and look at a few problems which uses multiple integrals.
Take a look at any physics phenomena or engineering problem and you would see that multiple integrals greatly facilitates the analysis of the situation. The selling point of its uses comes from the fact that most physical problems are described by more than one variable. In the real world, a certain result is affected by different factors, and the only way to study the cumulative result of these factors is to perform integral calculus on all the variables.
CONCEPT CONTENTS
> DEFINITION OF THE DOUBLE INTEGRAL
> EVALUATING DOUBLE INTEGRALS
> SIMPLE EXAMPLES OF DOUBLE INTEGRALS
> DOUBLE INTEGRALS OVER NONRECNTANGULAR REGIONS
> LIMITS OF REGION R (TYPE I)
> LIMITS OF REGION R (TYPE II)
> REVERSING THE ORDER OF INTEGRATION
> INTERPRETATIONS AND USES OF THE DOUBLE INTEGRAL
> FINDING VOLUME PROBLEMS
> HUNTING GOLD, DOUBLE INTEGRAL PROBLEM
> HUNTING GOLD, ALTERNATIVE APPROACH
Notable Mathematicians
Isaac Newton Pierre-Simon de Laplance
Important Theorems
Double Integral formulas Triple Integral formulas
Coordinates Transformation
Applications
Finding Center of Mass Finding Moment of Inertia
Most areas of Calculus that uses multple variables
