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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 4 th semester) Advanced: Mathematica and Full Programming (Computational Physics Course)

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Intro Example (1 st 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 – Kirchhoff’s Rules Six equations in six unknowns (currents)! How do students compare with theory without spending most of “lab” doing algebra??? PASCO

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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 Griffith’s 3-25 Cylinder (radius R) with charge density σ( ) = k sin(5 ) Answer:

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Visualize with Mathematica!

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Quantum Mechanics Griffiths 2.17 (1 st 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 Farrell’s 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 entropy’s 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.

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