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Calculus III (Notes) / Multiple Integrals   [Notes] [Practice Problems] [Assignment Problems]

Calculus III - Notes
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 Multiple Integrals

In Calculus I we moved on to the subject of integrals once we had finished the discussion of derivatives.  The same is true in this course.  Now that we have finished our discussion of derivatives of functions of more than one variable we need to move on to integrals of functions of two or three variables.

 

Most of the derivatives topics extended somewhat naturally from their Calculus I counterparts and that will be the same here.  However, because we are now involving functions of two or three variables there will be some differences as well.  There will be new notation and some new issues that simply don’t arise when dealing with functions of a single variable. 

 

Here is a list of topics covered in this chapter.

 

Double Integrals  We will define the double integral in this section.

 

Iterated Integrals  In this section we will start looking at how we actually compute double integrals.

 

Double Integrals over General Regions  Here we will look at some general double integrals.

 

Double Integrals in Polar Coordinates  In this section we will take a look at evaluating double integrals using polar coordinates.

 

Triple Integrals  Here we will define the triple integral as well as how we evaluate them.

           

Triple Integrals in Cylindrical Coordinates  We will evaluate triple integrals using cylindrical coordinates in this section.

            .

Triple Integrals in Spherical Coordinates  In this section we will evaluate triple integrals using spherical coordinates.

 

Change of Variables  In this section we will look at change of variables for double and triple integrals.

 

Surface Area  Here we look at the one real application of double integrals that we’re going to look at in this material.

 

Area and Volume Revisited  We summarize the area and volume formulas from this chapter.

Lagrange Multipliers Previous Section   Next Section Double Integrals
Applications of Partial Derivatives Previous Chapter   Next Chapter Line Integrals

Calculus III (Notes) / Multiple Integrals    [Notes] [Practice Problems] [Assignment Problems]

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