# Computer Algebra Recipes for Mathematical Physics by Richard H. Enns

By Richard H. Enns

* makes use of a pedagogical technique that makes a mathematically not easy topic more uncomplicated and extra enjoyable to learn

* Self-contained and standalone textual content that could be utilized in the school room, for an internet path, for self-study, as a reference

* utilizing MAPLE permits the reader to simply and quick switch the types and parameters

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Additional resources for Computer Algebra Recipes for Mathematical Physics

Example text

I. M. Curious who will discuss in her own words the elegant and thorough computer algebra solution that she generated in solving the following problem involving a familiar nonhomogeneous LODE. A mechanical system (of unit mass) experiences a Stokes’s law drag force FStokes = −2 α x, ˙ a Hooke’s law restoring force FHooke = −ω 2 x, and a driving force FDrive = f cos(Ω t + δ). Here α is a positive constant, ω the natural frequency, f the force amplitude, Ω the driving frequency, and δ a phase angle.

6: Resonance curves for f = 1 (bottom curve) to f = 5 (top). 6 Mr. Dirac’s Famous Function The man with a new idea is a crank until the idea succeeds. Mark Twain, Following the Equator, ch. 32, (1897). Consider a very long uniform horizontal beam glued to an elastic foundation, the foundation exerting a Hooke’s law restoring force. 3) YI dx4 where Y is Young’s modulus, I the moment of inertia of the beam’s crosssection about a horizontal axis, K the spring constant, and δ(x) the Dirac delta function.

Sol1:=dsolve({ode1,v(0)=0},v(t)); ode1 := gt sol1 := v(t) = V1 − e(− V1 ) V1 To compare with the experimental data, we need to calculate the distance that the bird falls in T seconds. For the Stokes model, this distance y1 is obtained by integrating the right-hand side (rhs) of sol1 from t = 0 to T . T); gT V1 (−V1 + g T + V1 e(− V1 ) ) y1 := g Let’s now look at Newton’s model of air resistance. Since the motion is in one direction (down) only, the absolute value sign can be dropped, so that FNewton = −b m v 2 .