16 MULTIPLE INTEGRALS

More documents

Recommendations

Info

$C:\Documents and Settings\BabyGator\.TeXmacs\system\tmp$

GROUP WORK 3, SECTION 16.4 FunwithPolarVolume 1. Find the volume of the region bounded above by the upper hemisphere of the sphere x 2 +y 2 +(z − 1) 2 = 1 and bounded below by the xy-plane. 2. Find the volume of the region bounded above by the sphere x 2 + y 2 + z 2 = 1 and below by the sphere x 2 + y 2 + (z − 1) 2 = 1. 898
16.5 APPLICATIONS OF DOUBLE INTEGRALS SUGGESTED TIME AND EMPHASIS 1 class Optional material POINTS TO STRESS I recommend stressing one of the following topics: 1. Density, mass, and centers of mass (for an engineering- or physics-oriented course) 2. Probability and expected values (for a course oriented toward biology or the social sciences) QUIZ QUESTIONS • Text Question: What is a logical reason that the total area under a joint density curve should be equal to 1? Answer: The total area is the probability that some outcome will occur. • Drill Question: If a lamina has a uniform density and an axis of symmetry, what information do we then have about the location of the center of mass? Answer: It is on the axis of symmetry. MATERIALS FOR LECTURE • Describe the general ideas behind continuous density functions, computations of mass, and centers of mass. • Do one interesting mass problem. A good exercise is the mass over the unit disk if ρ (x, y) = |x| + |y|. This reduces to 4 ∫ 1 ∫ √ 1−x 2 0 0 (x + y) dydx which, surprisingly, equals 8 3 . • Describe the general idea of the joint density function of two variables. Similarly, describe the concept of expected value. If time permits, show that f (x, y) = 1 1 ( 2π 1 + x 2 + y 2) describes a joint density 3/2 function. 899
Page 1 and 2: 16 MULTIPLE INTEGRALS 16.1 DOUBLE I
Page 3 and 4: SECTION 16.1 DOUBLE INTEGRALS OVER
Page 5 and 6: GROUP WORK 2, SECTION 16.1 An Odd F
Page 7 and 8: GROUP WORK 2, SECTION 16.1 An Odd F
Page 9 and 10: 16.2 ITERATED INTEGRALS SUGGESTED T
Page 11 and 12: GROUP WORK 1, SECTION 16.2 Regional
Page 13 and 14: GROUP WORK 3, SECTION 16.2 The Shap
Page 15 and 16: SECTION 16.3 DOUBLE INTEGRALS OVER
Page 17 and 18: GROUP WORK 1, SECTION 16.3 TypeIorT
Page 19 and 20: GROUP WORK 3, SECTION 16.3 Bounding
Page 21 and 22: SECTION 16.4 DOUBLE INTEGRALS IN PO
Page 23 and 24: SECTION 16.4 DOUBLE INTEGRALS IN PO
Page 25: GROUP WORK 2, SECTION 16.4 Fun with
Page 29 and 30: SECTION 16.5 APPLICATIONS OF DOUBLE
Page 31 and 32: GROUP WORK 3, SECTION 16.5 A Slick
Page 33 and 34: SECTION 16.6 TRIPLE INTEGRALS • S
Page 35 and 36: ( ∫ 1 ∫ √ 4−x 2 0 1 SECTION
Page 37 and 38: GROUP WORK 2, SECTION 16.6 Setting
Page 39 and 40: DISCOVERY PROJECT Volumes of Hypers
Page 41 and 42: SECTION 16.7 TRIPLE INTEGRALS IN CY
Page 43 and 44: GROUP WORK, SECTION 16.7 A Partiall
Page 45 and 46: 16.8 TRIPLE INTEGRALS IN SPHERICAL
Page 47 and 48: SECTION 16.8 TRIPLE INTEGRALS IN SP
Page 49 and 50: GROUP WORK 1, SECTION 16.8 Describe
Page 51 and 52: GROUP WORK 2, SECTION 16.8 Setting
Page 53 and 54: APPLIED PROJECT Roller Derby This p
Page 55 and 56: SECTION 16.9 CHANGE OF VARIABLES IN
Page 57 and 58: SECTION 16.9 CHANGE OF VARIABLES IN
Page 59 and 60: GROUP WORK 2, SECTION 16.9 Transfor
Page 61 and 62: Compute ∫∫∫ R 10 dV and ∫
Page 63 and 64: (b) Evaluate ∫∫ Pac-Man xdAand
Page 65 and 66: (b) 3. (a) CHAPTER 16 SAMPLE EXAM S
Page 67: CHAPTER 16 SAMPLE EXAM SOLUTIONS (a

16 MULTIPLE INTEGRALS

Create successful ePaper yourself

Delete template?

Save as template?