J. Héctor Morales
J. Héctor Morales

Temas selectos de matemáticas aplicadas I


Temas selectos de matemáticas aplicadas I

 Doctorado en Ciencias (Matemáticas)

 Trimestre 20-I  Grupo CR12  Clave: 2137052

Prof. José Héctor Morales Bárcenas







  • Anthony J. Devaney, Mathematical of Imaging, Tomography and Wavefield Inversion, Cambridge, 2012.
  • Albert Tarantola, Inverse Problems Theory: and Methods for Model Parameter Estimation, SIAM, 2005.
  • John A. Adam, Rays, Waves, and Scattering, Topics in Classical Mathematical Physics, Princeton, 2017.



Ecuaciones diferenciales parciales y análisis funcional



En este curso se estudian los elementos básicos la teoría de dispersión de ondas, tanto del problema directo como del inverso. Se establece la teoría necesaria para plantear el problema de dispersión inversa en espacios funcionales. Se hace énfasis en el análisis de la ecuación de Helmholtz.



Que el estudiante aprenda la teoría de los problemas inversos funcionales.



  • Teoría de dispersión.
  • Dispersión inversa clásica y tomografía de difracción.
  • Problemas inversos funcionales.
  • Introducción a los mínimos cuadrados: operadores derivada y transpuesta en espacios funcionales.



  1. P. A. Martin, Multiple Scattering Interaction of Time-Harmonic Waves with N Obstacles, Cambridge, 2006.
  2. P. A. Martin, “Multiple scattering and scattering cross sections”, J. Acoust. Soc. Am. 143 (2), February 2018.
  3. S. Bernard, et al., “Ultrasonic computed tomography based on full-waveform inversion for bone quantitative imaging”, Phys. Med. Biol. 62 (2017) 7011-7035.
  4. G. Steiner and D. Watzenig, “A Bayesian filtering approach for inclusion detec- tion with ultrasound reflection tomography”, J. Phys: Conference Series 124 (2008) 012049.
  5. R. Snider, “Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves”, J. Acoust. Soc. Am. 121 (5), May 2007.
  6. J. Chen, K. S. Hunter and R. Shandas, “Wave scattering from encapsulated microbubbles subject to high-frequency ultrasound: Contribution of higher-order scattering models”, J. Acoust. Soc. Am. 126 (4), October 2009.
  7. Akira Ishimaru, Wave Propagation and Scattering in Random Media, Two Volumes, Academic Press, 1978.
  8. Bevan B. Baker and E. T. Copson, The Mathematical Theory of Huygens' Principle, Oxford, 1939.
  9. Erich Zauderer, Partial Differential Equations of Applied Mathematics, 2nd Ed., John Wiley & Sons, Inc., New York, 1998.
  10. A. I. Kozlov, L. P. Lightart and A. I. Logvin, Mathematical and Physical Modelling of Microwave Scattering and Polarimetric Remote Sensing, Kluwer Academic Publishers, 2004.
  11. Luis Tenorio, An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems, SIAM, 2017.
  12. Richard E. Blahut, Theory of Remote Image Formation, Cambridge, 2004.
  13. John G. Harris, Linear Elastic Waves, Cambridge, 2004.
  14. Mario Bertero and Patrizia Boccacci, Introduction to Inverse Problems in Imaging, IOP Publishing Ltd, 1998.
  15. D. N. Ghosh Roy and L. S. Couchman, Inverse Problems and Inverse Scattering of Plane Waves, Academic Press, 2001.
  16. Philip M. Morse and K. Uno Ingard, Theoretical Acoustics, Mc Graw-Hill, 1968.
  17. David Colton and Rainer Kress, Inverse Acoustic and Electromagnetic Scattering Theory, 2nd Ed., Springer, 1998.
  18. Andreas Kirsch, An Introduction to the Mathematical Theoery of Inverse Problems, 2nd Ed., Springer, 2011.
  19. D. Colton and B. D. Sleeman, ``Uniqueness Theorems for the Inverse Problem of Acoustic Scattering'', IMA J. Appl. Math. (1983) 31, 253-259.
  20. B. D. Sleeman, ``The Inverse Problem of Acoustic Scattering'', IMA J. Appl. Math. (1982) 29, 113-142.
  21. G. F. Roach, An Introduction to Echo Analisys: Scattering Theory and Wave Propagation, Springer, 2008.
  22. G. F. Roach, Wave Scattering by Time-Dependent Perturbations: An Introduction, Princeton and Oxford, 2007.