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Teaching

In this page you can find information about the courses I am currently teaching and of those I have lectured in the past, about the students I have mentored, as well as links to didactic material. Use the menu on the right to navigate through.

Current courses

During the 2025-1 term, I am teaching the following course:


Lecture notes and auxiliary material

  1. R. G. Plaza, Introduction to initial-boundary value problems for symmetric hyperbolic systems (in Spanish). Lecture notes of the mini-course at the I School of Mathematical Analysis. Facultad de Ciencias,  University of Colima, September 26 thru 30, 2016. [PDF].
  2. A. Capella, R. G. Plaza, Partial Differential Equations, (in Spanish). In preparation.
  3. R. G. Plaza, Hyperbolic Systems of Conservation Laws, (in Spanish). In preparation
  4. R. G. Plaza, Introduction to Mathematical Biology, (in Spanish). In preparation.

Theses currently under supervision

Ph. D.

M. Sc.


Theses supervised

Ph. D.

  1. Fabio Andrés Vallejo Narváez, Kreiss-Métivier-Lopatinski theory for initial-boundary value hyperbolic problems in several space dimensions and their application to seismic waves. (In Spanish.) Ph. D. in Mathematics, Universidad Nacional Autónoma de México. January, 2023. [PDF]
  2. Enrique Álvarez del Castillo de Pina, Spectral stability analysis of periodic traveling wave solutions for Burgers-Fisher equation and scalar viscous balance laws. Ph. D. in Mathematics, Universidad Nacional Autónoma de México. November, 2021. [PDF]
  3. Felipe Angeles García, Local existence for a partially hyperbolic-parabolic system of quasilinear equations through a non-contractive fixed point argument. Ph. D. in Mathematics, Universidad Nacional Autónoma de México. September, 2021. [PDF]
  4. Juan Francisco Leyva Bonilla, Continuous models for bacterial aggregation with chemotaxis and non-linear degenerate diffusion: modelling, numerical simulations, and analysis of travelling fronts. Ph. D. in Mathematics, Universidad Nacional Autónoma de México. October, 2017. [PDF]

M. Sc.

  1. Luis Eduardo Ibáñez Pérez, Dissipative structure of a one-dimensional quantum hydrodynamics system with nonlinear viscosity through the genuine coupling condition. M.Sc. in Mathematics, Posgrado en Ciencias Matemáticas, UNAM. August, 2023. [PDF]
  2. Ricardo Yadel Murillo Pérez, Bifurcation and dynamics in hyperbolic Burgers-Fisher equation. M.Sc. in Mathematics, Posgrado en Ciencias Matemáticas, UNAM. August, 2021. [PDF]
  3. José Manuel Valdovinos Barrera, Well-posedness and dissipative structure of the one-dimensional system for compressible isothermal fluids of Korteweg type. M.Sc. in Mathematics, Universidad Nacional Autónoma de México. November, 2020. [PDF]
  4. Luis Alejandro Rosas Martínez, Existence of non-negative weak solutions to a reaction-diffusion-chemotaxis system with cross diffusion term. M.Sc. in Mathematics, Universidad Nacional Autónoma de México. September, 2020. [PDF]
  5. Isai Padilla Bello, Mathematical modeling of the tumour growth paradox using cancer stem cells (in Spanish). M. Sc. in Mathematics, Universidad Nacional Autónoma de México. February, 2020. [PDF]
  6. Felipe Angeles García, Dissipative structure of viscous systems of conservation laws (in Spanish). M.Sc. in Mathematics, Universidad Nacional Autónoma de México. November, 2016. [PDF]
  7. José Alejandro Butanda Mejía, Spectral methods in the study of traveling wave fronts for reaction diffusion equations (in Spanish). M.Sc. in Mathematics, Universidad Nacional Autónoma de México. June, 2016. [PDF]
  8. Ignacio Pérez Pérez, Multidimensional stability of phase transitions for first order hyperbolic systems (in Spanish). M. Sc. Thesis (Mathematics), Universidad Nacional Autónoma de México. March, 2012. [PDF]
  9. Juan Francisco Leyva Bonilla, On the admissibility criteria for solutions to Lighthill-Whitham traffic models (in Spanish). M. Sc. in Mathematics, Universidad Nacional Autónoma de México. August, 2010. [PDF]

B. Sc.

  1. Eduardo Parra García, C0-semigroups for hyperbolic port-Hamiltonian systems and applications (in Spanish). Honors B. Sc. Thesis (Mathematics), Universidad Nacional Autónoma de México. September 2018. [PDF]
  2. Edgar Itamar Ávalos Almanza, Existence of stationary planar periodic waves in visco-elastic materials with stress/gradient effect (in Spanish). Honors B. Sc. Thesis (Mathematics), Universidad Nacional Autónoma de México. April 2017. [PDF]
  3. Karina Islas Ríos, Mathematical modeling of chemotaxis and existence of traveling waves (in Spanish). Honors B. Sc. Thesis (Mathematics), Universidad Nacional Autónoma de México. April 2015. [PDF]
  4. Felipe Angeles García, Viscous shock profiles for the Navier-Stokes equations of compressible flow (in Spanish). Honors B. Sc. Thesis (Physics), Universidad Nacional Autónoma de México. November 2014. [PDF]
  5. Mónica Romero López, Mathematical study of an anti-angiogenesis model for secondary tumors (in Spanish). Honors B. Sc. Thesis (Mathematics), Universidad Nacional Autónoma de México. August 2010. [PDF]

Past Courses

Graduate courses

  1. Sobolev Spaces and Elliptic Partial Differential Equations.
    Graduate Program in Mathematical Sciences, UNAM, 2024-2 term.
    Course homepage (in Spanish).
  2. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2024-1 term
    Course homepage (in Spanish)
  3. Stochastic Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2023-1 term
    Course homepage (in Spanish)
  4. Hyperbolic Systems of Conservation Laws
    Graduate Program in Matematical Sciences, UNAM, 2022-2 term
    Course homepage (in Spanish)
  5. Semigroups and Evolution Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2022-1 term
    Course homepage (in Spanish)
  6. Ordinary Differential Equations
    Graduate Program in Mathematical Sciences, UNAM. 2021-2 term
  7. Sobolev Spaces and Elliptic Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2021-2 term
    Course homepage (in Spanish)
  8. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2021-1 term
    Course homepage (in Spanish)
  9. Nonlinear Hyperbolic Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2020-2 term
    Course homepage (in Spanish)
  10. Functional Analysis Methods in Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2020-1 term
    Course homepage (in Spanish)
  11. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM. 2019-2 term
    Course homepage (in Spanish)
  12. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2017-2 term
    Course homepage (in Spanish)
  13. Hilbert Space Methods in Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM. 2017-1 term
    Course homepage (in Spanish)
  14. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2016-2 term
    Course homepage (in Spanish)
  15. Hyperbolic Systems of Conservation Laws
    Graduate Program in Matematical Sciences, UNAM, 2015-2 term
    Course homepage (in Spanish)
  16. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2015-1 term
    Course homepage (in Spanish)
  17. Hyperbolic Systems of Conservation Laws
    Graduate Program in Mathematical Sciences, UNAM, 2014-1 term
    Course homepage (in Spanish).
  18. Partial Differential Equations
    Graduate Program in Mathematical Sciences, UNAM, 2013-2 term
    Course homepage (in Spanish)
  19. Applied Partial Differential Equations
    Erasmus Mundus M. Sc. Programme in Mathematical Modelling and Engineering (MathMods)
    University of L'Aquila, Italy. September-December 2012.
  20. Introduction to Hyperbolic Systems of Conservation Laws
    Graduate Program in Mathematical Sciences, UNAM, 2011-1 term
    Course homepage (in Spanish).
  21. Hyperbolic Systems of Conservation Laws
    Graduate Program in Mathematical Sciences, UNAM, 2010-1 term
    Course homepage (in Spanish).

Undergraduate courses

  1. Mathematical Biology I
    School of Sciences, UNAM, 2024-2 term
    Course homepage (in Spanish).
  2. Ordinary Differential Equations I
    School of Sciences, UNAM, 2022-2 term
    Course homepage (in Spanish)
  3. Mathematical Biology I
    School of Sciences, UNAM, 2019-1 term
    Course homepage (in Spanish)
  4. Linear Algebra I
    School of Sciences, UNAM, 2019-1 term
    Course homepage (in Spanish)
  5. Partial Differential Equations II
    School of Sciences, UNAM, 2015-1 term
    Course Homepage (in Spanish).
  6. Partial Differential Equations I
    School of Sciences, UNAM, 2014-2 term
    Course homepage (in Spanish).
  7. Partial Differential Equations I
    School of Sciences, UNAM, 2012-2 term
    Course homepage (in Spanish).
  8. Ordinary Differential Equations I
    School of Sciences, UNAM, 2012-1 term
    Course Homepage (in Spanish).
  9. Partial Differential Equations I
    School of Sciences, UNAM, 2010-2 term
    Course homepage (in Spanish).
  10. Ordinary Differential Equations I
    School of Sciences, UNAM, 2009-2 term
    Course homepage (in Spanish).
  11. Partial Differential Equations II
    School of Sciences, UNAM, 2008-2 term
    Course homepage (in Spanish).
  12. Complex Analysis (with H. Freistühler) (in English)
    University of Leipzig, Germany, Spring term 2006.
  13. Conservation Laws Seminar (with H. Freistühler) (in English)
    University of Leipzig, Germany, Spring term 2006
  14. Differential and Integral Calculus II (with A. Schüler) (in English)
    University of Leipzig, Germany, Fall term 2005
  15. Ordinary Differential Equations for Physicists (with W. König)
    University of Leipzig, Germany, Spring term 2005
  16. Discrete Mathematics
    New York University, Summer term 2003
  17. Discrete Mathematics
    Fordham University, New York, Fall term 2002
  18. Financial Calculus
    Fordham University, New York, Fall term 2002
  19. Differential and Integral Calculus III
    New York University, Spring term 2001
  20. Business Calculus
    New York University, Spring term 2000