{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lecture28-09

# lecture28-09 - 18.02 Multivariable Calculus(Spring 2009...

This preview shows pages 1–3. Sign up to view the full content.

18.02 Multivariable Calculus (Spring 2009): Lecture 28 Triple Integrals. Cylindrical Coordinates April 16 Reading Material: From Simmons : 20.5 and 20.6. Last time: Simply Connected Regions. Today: Triple Integrals. Cylindrical Coordinates. 2 What we did in 2D and what we need to do in 3D 2D 3D Double integrals Triple integrals Polar coordinates Cylindrical & spherical coordinates 2D Applications 3D Applications Line integrals Line integrals in 3D Surface integrals Green’s Theorem for flux Gauss (divergence) Theorem Green’s Theorem for work Stoke’s Theorem 3 Introduction to triple integrals The 2D case: We recall that given a function f ( x, y ) and a region R 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
we can write R f ( x, y ) dA = b a g ( x ) h ( x ) f ( x, y ) dy dx. To determine the limits of the outer variable we look at the shadow of R on the axis relative to the outer variable. We also recall that R 1 dA = Area( R ) . The 3D case: Here usually we have a function f ( x, y, z ) and a 3D region D We want to define D f ( x, y, z ) dV where dV denotes the infinitesimal element of volume. The definition of the integral above should
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern