- 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.

- 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.

- 2D dot product applet,
also shows comp
_{b}**a**and proj_{b}**a**. - 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.)

- 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]