Bibliography for Computer Graphics for Complex Functions

unabridged

 

  1. Pictures by conformal mapping.  
    Uehara, Masahiro
    Forma  16  (2001),  no. 1, 1--15, MathSciNet.  
  2. P. K. Kythe, Computational Conformal Mapping
    Papamichael N.
    Journal of Approximation Theory, October 2000, vol. 106, no. 2, pp. 292-293(2), Ingenta.  
  3. Numerical Conformal Mapping via the Bergman Kernel Using the Generalized Minimum Residual Method
    Razali M.R.M.; Nashed M.Z.; Murid A.H.M.
    Computers and Mathematics with Applications, July 2000, vol. 40, no. 1, pp. 157-164(8), Ingenta.   
  4. Numerical conformal mapping via the Bergman kernel
    Razali M.R.M.; Nashed M.Z.; Murid A.H.M.
    Journal of Computational and Applied Mathematics, 15 September 1997, vol. 82, no. 1, pp. 333-350(18), Ingenta.    
  5. Numerical conformal mapping methods based on Faber series
    DeLillo T.K.; Elcrat A.R.; Pfaltzgraff J.A.
    Journal of Computational and Applied Mathematics, 7 October 1997, vol. 83, no. 2, pp. 205-236(32), Ingenta.     
  6. Computational Conformal Mapping for Surface Grid Generation
    Khamayseh A.; Mastin C.W.
    Journal of Computational Physics, February 1996, vol. 123, no. 2, pp. 394-401(8), Ingenta.     
  7. Fast conformal mapping of an ellipse to a simply connected region
    Carrere H.; Rene F.; Wegmann R.
    Journal of Computational and Applied Mathematics, 30 July 1996, vol. 72, no. 1, pp. 101-126(26), Ingenta.     
  8. The graphs of complex functions in 4-dimensional space and their projections on the 2-dimensional plane. (Chinese. English, Chinese summary)  
    Xie, Bu Ying  
    Tongji Daxue Xuebao Ziran Kexue Ban 23 (1995), no. 1, 113--116, MathSciNet.  
  9. Handbook of conformal mapping with computer-aided visualization.
    Ivanov, V. I.; Trubetskov, M. K.
    CRC Press, Boca Raton, FL, 1995. vi+360 pp., MathSciNet.  
  10. Some conformal map constructs for numerical grids.
    Carey, G. F.; Muleshkov, A.
    Comm. Numer. Methods Engrg. 11 (1995), no. 2, 127--135, MathSciNet.  
  11. The Accuracy of Numerical Conformal Mapping Methods: A Survey of Examples and Results  
    Thomas K. Delillo  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 3. (Jun., 1994), pp. 788-812, Jstor.  
  12. Complex Power Series-A Vector Field Visualization (in Notes)  
    Alan D. Gluchoff  
    Mathematics Magazine, Vol. 66, No. 3. (Jun., 1993), pp. 189-191, Jstor.  
  13. The Vector Field Approach in Complex Analysis  
    Braden, Bart  
    Visualization in Teaching and Learning Math., Providence, R.I., Math. Assoc. of Amer., (1991), pp. 191-196.  
  14. Bilinear Basics (in Notes)  
    T. Hoy Booker  
    Mathematics Magazine, Vol. 62, No. 4. (Oct., 1989), pp. 262-267, Jstor.  
  15. Numerical conformal mapping  
    Mastin, C. Wayne
    Comp. Meth. in App. Mech. and Eng., (1987), V. 63, pp. 209-211.
  16. Polya's Geometric Picture of Complex Contour Integrals  
    Bart Braden  
    Mathematics Magazine, Vol. 60, No. 5. (Dec., 1987), pp. 321-327, Jstor.  
  17. Plotting Streamlines and Pathlines on a Microcomputer  
    Kranc, S. C.  
    Comp. in Ed. Div. of ASEE, (1986), V. VI, No. 3, pp. 20-21.
  18. On Fornberg's Numerical Method for Conformal Mapping  
    Rudolf Wegmann  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 6. (Dec., 1986), pp. 1199-1213, Jstor.  
  19. Uniform approximation as a numerical tool for constructing conformal maps. Special issue on numerical conformal mapping.
    Hartmann, M.; Opfer, G.
    J. Comput. Appl. Math. 14 (1986), no. 1-2, 193--206, MathSciNet.  
  20. Picturing Functions of a Complex Variable (in Computer Corner)  
    Bart Braden  
    The College Mathematics Journal, Vol. 16, No. 1. (Jan., 1985), pp. 63-72, Jstor.  
  21. Computer simulation of conformal mappings.
    Tozoni, O. V.
    Cybernetics 19 (1983), no. 4, 464--474 (1984); translated from Kibernetika (Kiev) 1983, , no. 4, 24--31(Russian), MathSciNet.  
  22. Geometric Transformations on a Microcomputer  
    Shilgalis, Thomas W.
    The Math. Teacher, (1982), V. 75, No. 1, pp. 16-19.
  23. Conformal mappings onto multiply connected regions with specified boundary shapes: a preliminary discussion of computer implementation. Numerical grid generation (Nashville, Tenn., 1982).
    Harrington, Andrew
    Appl. Math. Comput. 10/11 (1982), 601--618, MathSciNet.  
  24. Numerical Conformal Mapping  
    Sukumar Chakravarthy; Dale Anderson  
    Mathematics of Computation, Vol. 33, No. 147. (Jul., 1979), pp. 953-969, Jstor.  
  25. Applications of Conformal Mapping to Potential Theory Through Computer Graphics  
    Donald T. Piele; Morris W. Firebaugh; Robert Manulik  
    American Mathematical Monthly, Vol. 84, No. 9. (Nov., 1977), pp. 677-692, Jstor.  
  26. Computer-Drawn Field Lines and Potential Surfaces for a Wide Range of Field Configurations  
    Brandt, Siegmund and Hermann Schneider  
    Am. J. Phy., (1976),  V. 44, No. 12, pp. 1160-1171.
  27. A Numerical Comparison of Integral Equations of the First and Second Kind for Conformal Mapping  
    John K. Hayes; David K. Kahaner; Richard G. Kellner  
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 512-521, Jstor.  
  28. The Use of Interactive Computer Graphics in the Conformal Mapping Area  
    Bruch, John C.  
    Computers and Graphics, (1975), V. 1, pp. 361-374.  
  29. An Improved Method for Numerical Conformal Mapping  
    John K. Hayes; David K. Kahaner; Richard G. Kellner  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 327-334+s1-s28, Jstor.  
  30. Teaching Complex Variables with an Interactive Computer System
    Bruch, John C. and Roger C. Wood  
    IEEE Trans. on Ed., (1972), E-15, No. 1, pp. 73-80.  
  31. Vektornye polya na ploskosti. (Russian) [Vector fields in the plane]
    Krasnosel 'skiui, M. A.; Perov, A. I.; Povolockiui, A. I.; Zabreuiko, P. P.  
    Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow 1963 245 pp., MathSciNet.    
  32. On the possibility of the application of electronic digital computers to one of the approximate methods for obtaining conformal maps.
    Kudrjavcev, A. L.
    Prikl. Mat. Meh. 24 390--392 (Russian); translated as J. Appl. Math. Mech. 24 1960 567--571, MathSciNet.  
  33. Analog computer construction of conformal maps in fluid dynamics.
    Tomlinson, N. P.; Horowitz, M.; Reynolds, C. H.
    J. Appl. Phys. 26, (1955), MathSciNet.  

 

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(c) John H. Mathews 2003