**CONTOUR MAPS/GRADIENTS **[text and idea from here]

- Examine contour maps and gradients. There are lots of map materials avaiable on the web (EPA, US Geological Survey). The use of global positioning systems (GPS) is leading to tremedously accurate maps. Examine level sets of various properties (rainfall, temperature, etc.). Calculuate directional derivatives, gradients, draw flow lines, calculate average value of functions all based on these maps.
- Maps of the world and the different projections used to draw them. The problem of how to represent a three dimensional sphere on a two dimensional paper is tricky and has been approached in many different ways. One standard method is the Mercantor projection. This topic relates to different coordinate systems: note that spherical coordinates are closely related to longitude and latitude.

**JOURNAL ARTICLES**

- Larry Riddle, “Individualized Computer Investigations for Multivariable Calculus,” The College Mathematics Journal, Vol. 26, No. 3 (May, 1995), pp. 235-237 [password protected, here]
- Michael E. Frantz, “Interactive Graphics for Multivariable Calculus,” The College Mathematics Journal, Vol. 17, No. 2 (Mar., 1986), pp. 172-181 [password protected, here]
- David E. Bailey and Gerald Kobylski, “Interactive Teaching Aids for Multivariable Calculus,” The College Mathematics Journal, Vol. 32, No. 4 (Sep., 2001), pp. 283-287 [password protected, here]
- Caspar R. Curjel and John Sylvester, “A Computer Lab for Multivariable Calculus,” The College Mathematics Journal, Vol. 24, No. 2 (Mar., 1993), pp. 175-177 [password protected, here]
- Jerry Lodder, “Curvature in the Calculus Curriculum,” The American Mathematical Monthly, Vol. 110, No. 7 (Aug. – Sep., 2003), pp. 593-605 [password protected, here]
- John Nord and Edward Miller, “Mercator’s Rhumb Lines: A Multivariable Application of Arc Length,” The College Mathematics Journal, Vol. 27, No. 5 (Nov., 1996), pp. 384-387 [password protected, here]

Historical Resources involving Multivariable Calculus

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