Mathematica examples from the LC undergraduate physics curriculum

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Mathematica examples from the LC undergraduate
physics curriculum

• John Eric Goff
• Lynchburg College
• Lynchburg, VA 24501

CS-AAPT Fall 2007 Radford University
Radford, VA 24142
November 3, 2007
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LC Physics

• Small number of physics faculty (2 or 3).
• We need a niche!
• We have a computational emphasis.
• Computational Physics joins theory and experiment
  to form the new triumvirate in physics.
• Some form of computation permeates all our
  courses.

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What do we do?

• Intro Excel (Euler method in second lab), some
  Mathematica, simulations (Kinetic Books and
  Physlets)
• Intermediate Mathematica (especially Classical
  Mechanics in 4th semester)
• Advanced Mathematica and Full Programming
  (Computational Physics Course)

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Intro Example (1st Semester)

• Curtain of Death problem (HRW 4-68)

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What is typically done?
Excel Plot
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Use Mathematica!
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Intro Lab Kirchhoffs Rules
PASCO
Six equations in six unknowns (currents)!
How do students compare with theory
without spending most of lab doing algebra???
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Use Mathematica!

• Make sure students write down the six equations
  in six unknowns. Do not skip the physics!

Students evaluate sol with their own V and R
values.
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Classical Mechanics

• Taken by sophomores in spring semester.
• Mathematica is used throughout course.
• One week of class devoted to Mathematica.
• Homework and exam questions require numerical
  solutions.

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Velocity-Dependent Forces

• Thornton and Marion 2-18 (worked fully in class)
• Softball problem uses quadratic air drag.
• Problem cannot be solved analytically!

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Phase Plots

• Thornton and Marion 3-15
• Underdamped Oscillator

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Noninertial Reference Frames

• Thornton and Marion Example 10.2
• Hockey Puck on a Merry-Go-Round

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Electromagnetism

• Griffiths 3-25
• Cylinder (radius R) with charge density
• s(?) k sin(5?)
• Answer

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Visualize with Mathematica!
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Quantum Mechanics

• Griffiths 2.17 (1st ed.)
• Time evolution of particle in even mixture of
  ground- and first-excited states of harmonic
  oscillator potential.

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Animate with Mathematica!
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Quantum Mechanics - Project
See Stuart Farrells Spring 2005 CS-AAPT talk.
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Optics
Fringe patterns on a holographic plate.
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Optics Final Exam Question
Diffraction intensity for a rectangular aperture.
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Computational Physics

• Giordano and Nakanishi Cream in the Coffee
  Problem
• Animation is a must!

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Cream in the Coffee
Show the entropys progression toward a constant
value.
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Fluid Mechanics Project
Velocity field of fluid moving around rectangular
obstruction.
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Fluid Mechanics Project
Stream function of fluid moving around
rectangular obstruction.
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Fluid Mechanics Project
Vorticity of fluid moving around rectangular
obstruction.