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2006 Fall MATH 100 Lecture 221 MATH 100 Lecture 22 Introduction to surface integrals.

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Presentation on theme: "2006 Fall MATH 100 Lecture 221 MATH 100 Lecture 22 Introduction to surface integrals."— Presentation transcript:

1 2006 Fall MATH 100 Lecture 221 MATH 100 Lecture 22 Introduction to surface integrals

2 2006 Fall MATH 100 Lecture 222 Definition of density function:

3 2006 Fall MATH 100 Lecture 223 MATH 100 Lecture 22 Introduction to surface integrals

4 2006 Fall MATH 100 Lecture 224 MATH 100 Lecture 22 Introduction to surface integrals

5 2006 Fall MATH 100 Lecture 225 MATH 100 Lecture 22 Introduction to surface integrals

6 2006 Fall MATH 100 Lecture 226 MATH 100 Lecture 22 Introduction to surface integrals

7 2006 Fall MATH 100 Lecture 227 MATH 100 Lecture 22 Introduction to surface integrals

8 2006 Fall MATH 100 Lecture 228 MATH 100 Lecture 22 Introduction to surface integrals

9 2006 Fall MATH 100 Lecture 229 MATH 100 Lecture 22 Introduction to surface integrals

10 2006 Fall MATH 100 Lecture 2210 MATH 100 Lecture 22 Introduction to surface integrals

11 2006 Fall MATH 100 Lecture 2211 MATH 100 Lecture 22 Introduction to surface integrals

12 2006 Fall MATH 100 Lecture 2212 Surface integral of vector functions, we have studied line (curve) integral with orientation, now we go to surface with orientation. In general, a surface is given by G(x,y,z) = 0 The particular cones are MATH 100 Lecture 22 Introduction to surface integrals

13 2006 Fall MATH 100 Lecture 2213 There are 2 unit normal vectors A surface has 2 orientation, corresponding to the 2 normal direction. The orientation should be chosen in the way that there is no sudden change in the normal direction when we transverse along the surface. MATH 100 Lecture 22 Introduction to surface integrals

14 2006 Fall MATH 100 Lecture 2214 The 2 possible orientation: inward normal and outward normal MATH 100 Lecture 22 Introduction to surface integrals

15 2006 Fall MATH 100 Lecture 2215 Surface integral

16 2006 Fall MATH 100 Lecture 2216 MATH 100 Lecture 22 Introduction to surface integrals (continuous next page)

17 2006 Fall MATH 100 Lecture 2217 MATH 100 Lecture 22 Introduction to surface integrals

18 2006 Fall MATH 100 Lecture 2218 MATH 100 Lecture 22 Introduction to surface integrals

19 2006 Fall MATH 100 Lecture 2219 MATH 100 Lecture 22 Introduction to surface integrals

20 2006 Fall MATH 100 Lecture 2220 MATH 100 Lecture 22 Introduction to surface integrals

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