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Math 22 Spring 2007:
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 | Exam 2 stats are posted here. Solutions to the various versions of the test will be available later this week at electronic reserves. |
| Homework is assigned, submitted and graded on-line at http://west.ilrn.com/ilrn/. |
| The last homework is due Sunday, 6/10, 10pm and covers the remaining sections: Double Integrals: 15.3,15.4,15.6, Triple integrals15.7 and 15.8. The pdf files with similar problems can be found here. |
| Practice problems for multiple integrals as well as few old finals will go to the science library tomorrow. The final will cover Chapters 14 + 15. Spherical coordinates for triple integrals will be covered in class but will not be expected on the final. Cylindrical coordinates for triple integrals will be on the final. 15.9 (Change of variables) will be covered in class but will not be on the final. |
| Review sesions: 1) Part of Friday's lecture will be dedicated to review 2) Saturday, 10am-12 noon, BE 301A, with Wei 3) Saturday, 12-2pm, BE 301A, with Joon 4) Sunday night, 7-10pm, ARC Center with Eva (MSI) 5) Monday, 9-11am, with Frank, Thimann 3 |
| The regular final is in the usual
classroom on Monday, 6/11 from 4-7pm. There is an optional late final
on Wednesday, 6/13, from 12-3pm in Thimann 1. I'll bing a sign-up sheet to
class Wednesday and Friday. The DRC finals for those students with
accommodations are in BE 358, both or the Monday and Wednesday finals. |
| The class is supported by MSI (Modified Supplemental Instruction). Your MSI tutor is Eva Barrientos (ebarrien@ucsc.edu). |
| Links to the vector applets are here: 1) vector sum 2) dot or scalar product 3) vector or cross product 4) What good are dot products? 5) Parallelepiped (its volume is computed by the scalar triple product). Another look at this is here. |
| Graphs of planes, cylinders and quadric surfaces a) The circular cylinder x^2+y^2=1 b) The parabolic cylinder z=x^2 c) Ellipsoid d) Elliptic Paraboloid e) Hyperbolic Paraboloid f) Cone g) Hyperboloid of one sheet h) Hyperboloid of two sheets i) Moving from one sheet through a cone to two two sheets. k) Intersection of the two planes x+4y-3z=1 and -3x+6y+7z=0 ; The picture is here. l)The parametric equation of the line (which is this intersection) is x= 46t+ 1/3, y=2t+1/6, z= 18t ; The picture is here. |
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Polar Coordinates/Polar Curves: a)Flower b)Henri's Butterfly, again c) Oscar's Butterfly d) Lemniscate e) Archimedean Spiral. Cylindrical Coordinates/Spherical Coordinates: a)Sphere in spherical coordinates. b)Vase in spherical coordinates, on table c)Hyperboloid of two sheets, cylindrical coordinates d)Cone in cylindrical coordinates. e)Cylinder with cylindrical coordinates f) Ellipsoid with cylindrical coordinates. Guess What? Guess? |
| Vector functions: a) Twisted Cubic pointwise b) C1, C 2, both c) Twisted Cubic with tangent line. d) Helix r(t)=<cos t, sin t, t> in box. e) Helix r(t)=<cos t, sin t, t> with x,y,z coordinate system f) Semicubical Parabola r(t)=<t^3, t^2> in the box g) Semicubical Parabola r(t)=<t^3, t^2> with x,y,z axis h) Twisted Cubic r(t)=<t, t^2, t^3> in the box i) Twisted Cubic r(t)=<t, t^2, t^3> together with the x,y,z axis (sans labels though) j) Cylinder y=x^2 intersecting the cylinder z=x^3 has the twisted cubic as its intersection. |
| On functions of several variables a) No limit at the origin b) Limit exists at origin. c) Paraboloid with tangent plane. d)Two hills. e) Eggcarton. f) A wiggly surface. |
| The National Map viewer:
http://nmviewogc.cr.usgs.gov/viewer.htm Santa Cruz has coordinates Lat: 36.97417 degrees, Long: -122.02972 degrees More topo-maps at: www.topozone.com |
| Lecture on differentiability: a) Example of a function with partials at (0,0) but that is not differentiable at (0,0). b) Second example of a function with partials at (0,0) but that is not differentiable at (0,0). It's crinkled. c) Example of a function that is differentiable, but it's partials are not continuous. |
| a) Hammock b) #30 (from 14.6) c) A surface with one critical point, a relative max but no absolute max or min. d) The surface z^2=xy+1. e) A surface with only saddle points. f)) Just an absolute minimum. g) A surface with two minima, but no maxima. |
Copyright © 1997-2008 by Frank
Bäuerle, Ph.D., UC Santa Cruz.
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