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Math
22 Winter 2008:
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 | Unbelievable, yet true: Final's week is just
around the corner! Your final will be on Wednesday, 3/19, 4-7pm, in the
regular classroom. DRC final in BE 301B |
| The final will cover everything we studied up to and
including triple integrals. The geometry form Chapter 12 will be covered
indirectly with the material in Chapter 14 and Chapter 15. For instance when
you are finding the equation of a tangent plane, you are using the gradient
to find the normal but then use your knowledge about equations of planes to
find the answer. The distribution is to be expected as follows: Assuming the
final is 200 points, about 20-30 points will be from Chapter 13 material,
about 100 points on Chapter 14 material and about 70-80 points on Chapter 15
material. You will definitely be tested on Max/Min problems, Lagrange
Multipliers, Gradient interpretation, Double integrals including polar
coordinates, Triple integrals. Specifically, there will be one question on
triple integrals, and no question on direct evaluation of Riemann sums or
using integration by parts. |
| Since I will be out of town this Wednesday, there
will be a review session in class this Wednesday. There will be other
review sessions: a) Glenn's MSI final review is on Sunday 3/16 5:00-7:00 at the Oakes Learning Center. b) Tuesday, 9-11am, with Frank, College 8, Room 240 c) with Filix, Saturday, 3/15, 2-4pm, Kresge 321 d) all sections on Monday are open to everybody ==> consider them review sessions |
| Frank's office hours next week are: Monday
9-12noon, Wednesday 9-11am. For TA's office hours, follow the Math 22 link
on the left, and click on TA/Section. |
| The LAST HOMEWORK assignment is due Tuesday, 3/18, 10pm and is posted on ILRN. Pdf's can be found as usual on this web site. |
| Midterm 2 is graded and the stats are posted.
Follow the Math 22 link on the left and click on "Exam Info". The test will
be returned in class or can be picked up from me in office hours. Solutions
to the midterm(s) are posted on eres. |
| Corrections to Practice materials on ERES for the
final: 1) Practice Final 01, (2005 final), #8: There is a sign error after the innermost integral gets evaluated. The integrand should be x(2-x^2-y^2) instead of x(2-x^2+y^2). This sign error precipates through the rest of the problem and changes the final answer to 8/15 sqrt(2), assuming I didn't mess up in the arithmetic of the integral. 2) Practice Final 01, (2005 final), #9: In the subsitution, I wrote du = 2y^2, which is of course incorrect. It should be 3y^2. This changes the answer to 1/12 [1- cos (1)] 3) Practice Final 01, (2005 final), #10: There were two errors: firstly, I dropped a 2 from the doubling of the area, and secondly, cos^2 theta = (1 + cos (2 theta) )/2, which changes the answer a bit: The integral of that part becomes 1/2 sin (2 theta), which then evaluates to 0 instead of 2, and so the final value is 6 Pi instead of 2 + 3 pi. |
| Corrections to Practice materials on ERES for
midterm 1: 1) Midterm 1, 2004, Problem 2: I dropped a sign when computing vector PQ, so the vector PQ= <-2,-1,0> which changes the normal to n=<1,-2,4> and the equation of the plane to x-2y+4z=9 2) Midterm 1, 2007, Problem 4c: Typo: first part: x= sint, y= cost t leads to x^2+y^2=1. 3) There is one small typo on the solutions to practice midterm 2, 2007. On Problem 3a, the equation of the plane should be 4(x-2) + 2 (y-1) -4 (z+2) =0 |
| Here's the link to the pdf from Glenn with the main definitions and theorems so far. And here is the next set, again in pdf format. |
| There will be a review session for MSI attendees (must have come at least once) next Wednesday, 7-10pm, ARC 221. |
| The LSS tutor fo students who want individual tutoring in addition to MSI is Sulimon Sattari. Before tutoring is scheduled, you need to attend MSI. Contact 831-4333 OR visit the ARCenter Room #224 for more details. |
| The first midterm is next week, Friday, February 1st. It will cover the material from Chapter 12.1-13.2. Review materials (such as old midterms) available on Electronic Reserves, http://eres.ucsc.edu. |
| The deadline for the next homework assignments have changed slightly. Check here for details. |
| Homework assignments are based on the lecture and the textbook. Homework will be assigned, submitted and graded on-line at http://west.ilrn.com/ilrn/. You can get them from the class web site or the http://west.ilrn.com/ilrn/ web site. First you need to sign up for an account on Ilrn and use the PIN E-5RQAEU83HTZA4 to get access to the homework for this class. More information about this is on the syllabus and will be given in class. |
| The first homework is due Sunday, January 20th at 10pm and covers sections 12.1-12.3. |
| Hint
about how your on-line homework connects to your hardcopy textbook: the
problems are based directly off the book. To find the corresponding problem
in the book of a given homework problem, use the pdf file of similar
problems. At the end of each problem is a cryptic code that contains the
info: For instance, the first problem in the first assignment has code
stet06.02.01.01ab |
| The class is supported by MSI (Modified Supplemental Instruction). The MSI assistant is Glenn Gray (ggray@ucsc.edu). More about that in class. |
| 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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| You are visitor # | since the beginning of winter quarter 2002 |
