Calc III projects - part the last (part 5)

The following are some modeling projects that come from textbooks.  They may include topics that are typically covered in a particular multivariable calculus classroom, but for me would be additional topics.


  • The Hall Effect:  This is the end-of-chapter project in Chapter 10 of Sullivan/Miranda's Calculus Early Transcendentals. "The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the current." (from Wikipedia)  The project leads students through calculations that involve force, magnetic field, velocity, and electric field as vectors.
  • Road Safety:  This is the end-of-chapter project in Chapter 11 of Sullivan/Miranda's Calculus Early Transcendentals. The project investigates the forces on a vehicle under various road curve secenarios.  The model is described with vector functions for position, velocity, and acceleration.
  • Searching for Exoplanets:  This is the end-of-chapter project in Chapter 12 of Sullivan/Miranda's Calculus Early Transcendentals. The project considers the perturbations due to atmospheric scintillation and their effect on observations by amateur astronomers searching for exoplanets using relatively low powered telescopes.  The mathematics includes calculating total differentials for multivariate functions.
  • Measuring Ice Thickness:   This is the end-of-chapter project in Chapter 13 of Sullivan/Miranda's Calculus Early Transcendentals.  The project uses a function d(x, y) for the thickness of ice on a lake to investigate changes in ice thickness in various directions.  Murphy's note: this project seems contrived.
  • Parametric surfaces:  Although I had to use parametric surfaces in my graduate-level work, it is not a topic that is covered in our calculus curriculum.  OTOH, it is accessible and provides an extension of an underlying theme I carry through the class:  how to identify an object's local dimension and space in which it live by counting variables and parameters.  Reference:  Section 15.6 of Sullivan/Miranda  Calculus Early Transcendentals.  Related to ruled surfaces.  Can be used to model a torus, Dini's Surface, and other surfaces.
  • Surface and Flux Integrals:   Reference:  Section 15.6 of Sullivan/Miranda  Calculus Early Transcendentals.   Applications to physics, and in particular, to electric flux.  Finding centers of mass of 2D lamina.
  • Divergence Theorem:   Reference:  Section 15.8 of Sullivan/Miranda  Calculus Early Transcendentals.   Applications to physics
  • Stokes' Theorem:   Reference:  Section 15.9 of Sullivan/Miranda  Calculus Early Transcendentals.   Applications to physics

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