Math 11: Resources - FALL 2010

Practise questions for exams, and the exam solutions

• Midterm 1
  • Fall 2010 midterm 1 with solutions and grading scheme. These are not model solutions, but enable you to check answers and see how we broke down the grading of points.
  • Fall 2008 midterm 1. Notes: solutions are written in, so cover them to test yourself! We will not have as many multiple choice as this. #1a we didn't do; #5 is quite hard.
  • Practise problems from Fall 2007/2008 and their solutions. Notes: #1,2 are thought-provoking and non-standard, so save for after you've done the other ones; #10 uses symmetric form of line equation, we didn't do; #13 we didn't do distance between planes so only try if need amusement; skip #18. #22 the solution is wrong: n should be <6,4,-1> with consequence for plane eqn.
  • Fall 2004 midterm 1 Notes: ours will not be all multiple choice format like this. But we may have True/False questions. (Answers: dddbbccdcc)
  • NYU Spring 2003 practise problems and solutions. Notes: #2 not needed; #4 is a little 2D for us, so don't worry about it.
  • NYU Spring 2003 midterm 1, and solutions. Notes: distance in #3 not needed; #4 not needed.
• Midterm 2
  • Fall 2010 midterm 2 with solutions and grading scheme.
  • Fall 2008 midterm 2 Notes: solutions are written in, so cover them to test yourself! #4 has a hard first step (requires clever reasoning).
  • Practise problems for Fall 2007/2008 and their solutions. Notes: #1b we don't need. #4 is weird so don't worry, but it's interesting.
  • Fall 2004 Midterm 2. Notes: ours will not have as much multiple choice as this. #4 is cute and practises bounds. #7,8 not relevant. #11 you could do but we never did this style of optimization problem. (Answers: bcadbdcaca)
  • NYU Spring 2003 midterm 2, and solutions. Notes: only #3,4,5 relevant.
  • NYU Spring 2003 practise exam and solutions. Notes: only #2,5 relevant.
• Final
  • Fall 2010 final with rough solutions and grading scheme.
  • Practise problems for Fall 2007/2008, and solutions. Notes: 1c and 12 you can ignore. 4 is nice (sketch the surface first).
  • Practise exams from 2005: Midterm 1, Midterm 2, and Final.
  • Fall 2004 final. Notes: Looks like some great questions. We won't have a multiple-choice format like this. For # 3 we'd remind you of the definition of Laplace operator. # 4 can skip since we haven't done constructing f from its grad in 3D. Answers: 1. b, 2. d, 3. d, 4. d, 5. c, 6. b, 7. c, 8. c, 9. c, 10. a, 11. b, 12. d, 13. a, 14. d, 15. d, 16. b, 17. a, 18. c, 19. a, 20. c, 21. d, 22. c, 23. b, 24. a, 25. a
  • Practise NYU Spring 2003 final, and solutions. Notes: skip 7, or maybe find the total mass instead of the center of mass?
  • NYU Spring 2003 final, with solutions.
  • NYU Spring 2002 midterm.
  • NYU Fall 2002 final.
  • NYU Fall 2002 midterm.
  • Another NYU Fall 2002 midterm. Notes: skip the last question on probability.

Review notes

• van Erp's review notes on Ch. 17 (may be expanded).
• Flow chart of whole course showing interconnections and what builds on what (note: from a prior course. You don't need to know any Center of Mass applications).
• Surface integral area growth factors arising in common surface shapes.
• Scott Pauls' complete lecture notes, Fall 2007. Contains useful overviews and example problems.

Graphing / visualization tools

• 2D dot product applet, also shows comp_ba and proj_ba.
• cross product applet (in 3D obviously), lets you adjust a and b in a horizontal plane. Another one with arbitrary variation, showing the plane defined by the two vectors.
• Plot 3D graph of function of two variables: from MIT, and from URI (also does contours)
• 2D and 3D grapher applet, does all manner of parametric surfaces etc, but seems you can't type in your own (really?)
• Directional derivative applet from MIT.
• Lagrange multipliers in 2 variables applet from MIT.
• Vector field flow animations: 2D, and 3D
• Vector field visualization: Fileds, and Matthias Kawski's which lets you flow a rectangle of fluid in the field (is fun).
• Parametric surface visualization applet by Barbara Kaskosz. (On that site you will also find cylindircal and spherical versions.)

MATLAB: entirely optional, but a great plotting/computing package that will serve you well in the future

• Download the software from Dartmouth we have 100 or so on-campus licenses (to work you must be online in dartmouth.edu domain).
• Susan A. Schwarz (email her if you have Mac OS 10.2 or earlier for install CDs) can help with installation issues.
• M. Pilant's Matlab examples
• Bent Petersen's Matlab starter page
• Robert Higdon's nice introductory notes
• My 1-page intro53.m code, and 1-page intro code from Linear Algebra (shows more matrix stuff)
• Guide from Cambridge University Engineering Department.
• Simple intro from Utah, Hany Farid's intro reference, and Gilbert Strang's intro at MIT.
• Self-guided courses from Dartmouth academic computing: Introduction to Matlab, Programming in Matlab, and Introduction to Matlab Graphics
• Matlab codes from our class demos:
  • showplane, plots a plane as a panel in 3D.
  • earlydemos, some simple plots of lines, planes, their intersection, and parametric curves, from Ch. 13-14. [uses showplane.m]