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Mathematica examples from the LC undergraduate physics curriculum

This article provides examples of how the use of Mathematica enhances the LC undergraduate physics curriculum, ranging from introductory labs to advanced computational physics courses. Topics covered include Kirchhoff's Rules, classical mechanics, velocity-dependent forces, phase plots, noninertial reference frames, electromagnetism, quantum mechanics, optics, and fluid mechanics. The article emphasizes the integration of theory, experimentation, and computation in the physics curriculum.

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Mathematica examples from the LC undergraduate physics curriculum

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  1. 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

  2. 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.

  3. 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)

  4. Intro Example (1st Semester) • “Curtain of Death” problem (HRW 4-68)

  5. What is typically done? Excel Plot

  6. Use Mathematica!

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

  8. 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.

  9. 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.

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

  11. Phase Plots • Thornton and Marion 3-15 • Underdamped Oscillator

  12. Noninertial Reference Frames • Thornton and Marion Example 10.2 • Hockey Puck on a Merry-Go-Round

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

  14. Visualize with Mathematica!

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

  16. Animate with Mathematica!

  17. Quantum Mechanics - Project See Stuart Farrell’s Spring 2005 CS-AAPT talk.

  18. Optics Fringe patterns on a holographic plate.

  19. Optics – Final Exam Question Diffraction intensity for a rectangular aperture.

  20. Computational Physics • Giordano and Nakanishi “Cream in the Coffee” Problem • Animation is a must!

  21. Cream in the Coffee Show the entropy’s progression toward a constant value.

  22. Fluid Mechanics Project Velocity field of fluid moving around rectangular obstruction.

  23. Fluid Mechanics Project Stream function of fluid moving around rectangular obstruction.

  24. Fluid Mechanics Project Vorticity of fluid moving around rectangular obstruction.

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