Abstract
Chapter 6 is devoted to the study of the Manipulate command. In order to show the utility of this command, we present certain introductory examples on the following topics: the main points of a triangle, Euler’s nine points circle, Frenet–Serret trihedron of a helix, and a hyperboloid of one sheet.
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References
Abell, M.L., Braselton, J.P.: Differential Equations with Mathematica. AP Professional, Boston (1993)
Adamchik, V., Wagon, S.: π A 2000-year search changes direction. Math. Educ. Res. 5 (1), 11–19 (1996).{w}ww.cs.cmu.edu/~adamchik/articles/pi/pi.htm
Adamchik, V., Wagon, S.: A simple formula for π. Am. Math. Mon. 104 (9), 852–855 (1997)
Alexander, R.: Diagonally implicit Runge-Kutta methods for stiff O.D.E’s. SIAM J. Numer. Anal. 14 (6), 1006–1021 (1977)
Backhouse, N.: Pancake functions and approximations to π. Math. Gaz. 79, 371–374 (1995). Note 79.36
Bailey, D.H., Borwein, P.B., Plouffe, S.: On the rapid computation of various polylogarithmic constants. Math. Comput. 66 (218), 903–913 (1997)
Baruah, D.N., Berndt, B.C., Chan, H.H.: Ramanujan’s series for 1∕π: a survey. Am. Math. Mon. 116 (7), 567–587 (2009)
Bellard, F.: Computation of the n’th digit of π in any base in O(n 2) (1997). fabrice.bellard.free.fr/pi/
Borwein, J.M., Borwein, P.B.: The class three Ramanujan type series for 1∕π. J. Comput. Appl. Math. 45 (1–2), 281–290 (1993)
Borwein, J.M., Borwein, P.B., Bailey, D.H.: Ramanujan, modular equations, and approximations to π or how to compute one billion digits of π. Am. Math. Mon. 96 (3), 201–219 (1989)
Borwein, J.M., Skerritt, M.P.: An Introduction to Modern Mathematical Computing with Mathematica. Springer Undergraduate Text in Mathematics and Technology. Springer, New York (2012)
Brun, V.: Carl Störmer in memoriam. Acta Math. 100 (1–2), I–VII (1958)
Bryson, A.E., Ho, Y.C.: Applied Optimal Control: Optimization, Estimation, and Control. Halsted Press, New York (1975)
Burns, R.E., Singleton, L.G.: Ascent from the lunar surface. Technical report TN D-1644, NASA, George C. Marshall Space Flight Center, Huntsville (1965)
Cesari, L.: Optimization–Theory and Applications. Problems with Ordinary Differential Equations. Applications of Mathematics, vol. 17. Springer, New York (1983)
Champion, B.: General Visualization Quick Start. Wolfram Research, Champaign (2013). {w}ww.wolfram.com/training/courses/vis412.html
Chudnovsky, D.V., Chudnovsky, G.V.: The computation of classical constants. Proc. Natl. Acad. Sci. USA 86 (21), 8178–8182 (1989)
Cloitre, B.: A BBP formula for π 2 in golden base (2003). abcloitre@wanadoo.fr
Dennis Lawrence, J.: A Catalog of Special Plane Curves. Dover, New York (1972)
Don, E.: Mathematica. Schaum’s Outlines Series. McGraw Hill, New York (2009)
Ebbinghaus, H.D., Peckhaus, V.: Ernst Zermelo. An Approach to His Life and Work. Springer, Berlin/Heidelberg (2007)
Elkies, N.D.: On a 4 + b 4 + c 4 = d 4. Math. Comput. 51 (184), 825–835 (1988)
Fay, T.H.: The butterfly curve. Am. Math. Mon. 96 (5), 442–443 (1989)
Ferguson, H., Gray, A., Markvorsen, S.: Costa’s minimal surface via Mathematica. Math. Educ. Res. 5 (1), 5–10 (1966)
Finch, S.R.: Zermelo’s navigation problem. In: Mathematical Constants II. Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge (Forthcoming)
Floyd, R.W.: Algorithm 245: treesort. Commun. ACM 7 (12), 701 (1964)
Frye, R.E.: Finding 958004 + 2175194 + 4145604 = 4224814 on the connection machine. In: Proceedings of Supercomputing’88. Science and Applications, vol. 2, pp. 106–116 (1988)
Gourevitch, B., Guillera Goyanes, J.: Construction of binomial sums for π and polylogarithmic constants inspired by BBP formula. Appl. Math. E-Notes 7, 237–246 (2007). www.math.nthu.edu.tw/~amen
Gradshteyn, S.G., Ryzhik, I.M.: Tables of Integrals, Series, and Products, 7th edn. Elsevier, Amsterdam (2007)
Guillera, J., Zudilin, W.: Ramanujan-type for 1∕π: the art of translation. In: Bruce, D.P., Berndt, C. (eds.) The Legacy of Srinivasa Ramanujan. Lecture Notes Series, vol. 20, pp. 181–195. Ramanujan Mathematical Society (2013). arXiv 1302.0548
Hartman, P.: Ordinary Differential Equations, 1st edn. Wiley, Hoboken (1964)
Hastings, C., Mischo, K., Morrison, M.: Hands-On Start to Wolfram Mathematica Ⓡ and Programming with the Wolfram LanguageTM. Wolfram Media, Champaign (2015)
Hazrat, R.: MathematicaⓇ: A Problem-Centered Approach. Springer Undergraduate Mathematics Series, vol. 53. Springer, London (2010)
Hoare, C.A.R.: Algorithm 64: quicksort. Commun. ACM 4 (7), 321 (1961)
Hull, D.G.: Optimal guidance for Lunar ascent. Adv. Astronaut. Sci. 134, 275–285 (2009). Proccedings of the AAS Space Flight Machanics Meeting, Savannach
Hull, D.G.: Optimal guidance for quasi-planar Lunar ascent. J. Optim. Theory Appl. 151 (2), 353–372 (2011)
Hull, D.G., Harris, M.W.: Optimal solutions for quasiplanar ascent over a spherical Moon. J. Guid. Control Dyn. 35 (4), 1218–1224 (2012). doi: 10.2514/1.55443
Knuth, D.E.: The Art of Computer Programming. Sorting and Searching. Computer Science and Information Processing, vol. 3. Addison-Wesley, Reading (1973)
Lander, L.J., Parkin, T.R.: Counterexample to Euler’s conjecture on sums of like powers. Bull. Am. Math. Soc. 72 (6), 1079 (1966)
Lawden, D.F.: Analytical Methods of Optimization. Dover Books on Mathematics. Dover, Mineola (2006)
Lucas, S.K.: Integral proofs that 355∕113 > π. Gaz. Aust. Math. Soc. 32 (4), 263–266 (2005)
Lucas, S.K.: Integral approximations to π with nonnegative integrands (2007). carma.newcastle.edu.au/jon/Preprints/Papers/By%20Others/more-pi.pdf
Mangano, S.: Mathematica Cookbook. O’Reilly, Sebastopol (2010)
Manià, B.: Sopra un problema di navigatione di Zermelo. Math. Ann. 113 (1), 584–589 (1937)
McShane, E.J.: A navigation problem in the calculus of variations. Am. J. Math. 59 (2), 327–334 (1937)
Miele, A.: Flight Mechanics. Theory of Flight Path. Addison-Wesley Series in the Engineering Sciences Space Science and Technology, vol. 1. Addison-Wesley, Reading (1962)
Mureşan, M.: Classical Analysis by Mathematica (Forthcoming)
Mureşan, M.: A Primer on the Calculus of Variations and Optimal Control. Trajectories Optimization (Forthcoming)
Mureşan, M.: On a Runge-Kutta type method. Rev. Anal. Numér. Théorie Approx. 16 (2), 141–147 (1987)
Mureşan, M.: Some computing results of a Runge-Kutta type method. Seminar on Mathematical Analysis Nr. 7, Univ. Babeş-Bolyai, Cluj-Napoca, pp. 101–114 (1987)
Mureşan, M.: A semi-explicit Runge-Kutta method. Seminar on Differential Equations Nr. 8, Univ. Babeş-Bolyai, Cluj-Napoca, pp. 65–70 (1988)
Mureşan, M.: Qualitative Properties of Differential Equations and Inclusions. Ph.D. thesis, Babeş-Bolyai University, Cluj-Napoca (1996)
Mureşan, M.: A Concrete Approach to Classical Analysis. CMS Books in Mathematics. Springer, New York (2009)
Mureşan, M.: Instructor Solution Manual, for A Concrete Approach to Classical Analysis. Springer, New York (2012). {w}ww.springer.com/mathematics/analysis/book/978-0-387-78932-3?changeHeader
Mureşan, M.: Soft landing on Moon with Mathematica. Math.Ⓡ J. 14 (2012). doi: dx.doi.org/doi:10.3888/tmj.14–16
Mureşan, M.: On Zermelo’s navigation problem with Mathematica. J. Appl. Funct. Anal. 9 (3–4), 349–355 (2014)
Mureşan, M.: On the maximal orbit transfer problem. Math.Ⓡ J. 17 (2015). doi: dx.doi.org/10.3888/tmj.17–4
Palais, R.S.: The visualization of mathematics: towards a mathematical exploratorium. Not. Am. Math. Soc. 46 (6), 647–658 (1999)
Rao, K.S.: Ramanujan and important formulas. In: Nagarajan, K.R., Soundararajan, T. (eds.) Srinivasa Ramanujan: 1887–1920: A Tribute, pp. 32–41. MacMillan India, Madras (1988)
Robinson, E.A., Jr.: Man Ray’s human equations. Not. Am. Math. Soc. 62 (10), 1192–1198 (2015)
Sedgewick, R.: Implementing Quicksort programs. Commun. ACM 21 (10), 847–857 (1978)
Strogatz, S.H.: Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering. Perseus, New York (1994)
Takano, K.: Pi no arctangent relation wo motomete [finding the arctangent relation of π]. Bit 15 (4), 83–91 (1983)
Torrence, B., Torrence, E.: The Student’s Introduction to Mathematica Ⓡ. A Handbook for Precalculus, Calculus, and Linear Algebra, 2nd edn. Cambridge University Press, Cambridge, UK (2009)
Trott, M.: The Mathematica GuideBook for Graphics. Springer, New York (2004)
Trott, M.: The Mathematica GuideBook for Programming. Springer, New York (2004)
Trott, M.: The Mathematica GuideBook for Numerics. Springer, New York (2006)
Trott, M.: The Mathematica GuideBook for Symbolics. Springer, New York (2006)
Weisstein, W.E.: BBP-Type formula. Technical report, MathWorld-A Wolfram Web Resources. mathworld.wolfram.com/BBP-TypeFormula.html
Weisstein, W.E.: Machbin-Like formulas. Technical report, MathWorld-A Wolfram Web Resources. mathworld.wolfram.com/Machin-LikeFormulas.html
Weisstein, W.E.: Pi formulas. Technical report, MathWorld-A Wolfram Web Resources. mathworld.wolfram.com/PiFormulas.html
Wolfram, S.: The Mathematica Ⓡ Book, 5th edn. Wolfram Media, Champaign (2003)
Wolfram, S.: An Elementary Introduction to the Wolfram Language. Wolfram Media, Champaign (2015)
Wolfram, S.: Differential Equation Solving with DSOLVE. Wolfram Research, Champaign (2008). Wolfram MathematicaⓇ Tutorial Collection. htpps:/reference.wolfram.com/language/tutorial/DSolveOverview.html
Wolfram, S.: Advanced numerical differential equation solving in Mathematica. In: Wolfram MathematicaⓇ Tutorial Collection. Wolfram Research, Champaign (2008). htpps:/www.scrib.com/doc/122203558/Advanced-Numerical-Differential-Equation-Solving-in-Mathematica
Wolfram, S.: http://numbers.computation.free.fr/Constants/Pi/piclassic.html
Wolfram, S.: http://numbers.computation.free.fr/Constants/Pi/piramanujan.html
Zermelo, E.: Über die Navigation in der Luft als Problem der Variationsrechnung. Jahresbericht der deutschen Mathematiker – Vereinigung, Angelegenheiten 39, 44–48 (1930)
Zermelo, E.: Über das Navigationproblem bei ruhender oder veränderlicher Windverteilung. Z. Angew. Math. Mech. 11 (2), 114–124 (1931)
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Mureşan, M. (2017). Manipulate. In: Introduction to Mathematica® with Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-52003-2_6
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