Mathematical Methods Books

Evolution Equations

• Initial-boundary Value Problems and the Navier-Stokes Equations Volumen 136
  by Heinz-Otto Kreiss, Jens Lorenz
  Academic Press, 1989 - 402 páginas

Elliptic Theory (Non-Numerical)

• Elliptic Partial Differential Equations of Second Order
  by David Gilbarg & Neil S. Trudinger
  Springer (Classics in Mathematics series)

Finite Element Methods (FEniCS/Firedrake)

• Solving PDEs in Python: The FEniCS Tutorial I
  by Hans Petter Langtangen & Anders Logg
  Simula Springer Briefs on Computing
• Automated Solution of Differential Equations by the Finite Element Method
  by Andrew Logg, Kent-Andre Mardal, Garth R. Wells (Editors)
  Springer (The FEniCS Book)

Non-Numerical Mathematical Physics

• Mathematical Physics by Robert Geroch

• Mathematical Methods of Physics by Oscar Reula PDF
• Metodos Matemáticos de la Física by Oscar Reula PDF

Reviews

• Continuum and Discrete Initial-Boundary Value Problems and Einstein's Field Equations
  by Oliver Sarbach & Manuel Tiglio
  Living Reviews in Relativity
  Focus: Mathematical and numerical theory for hyperbolic equations with applications to general relativity
• Partial Differential Equations of Physics

  by Robert Geroch

  arXiv:gr-qc/9602055 | General Relativity and Quantum Cosmology (gr-qc) | Submitted 27 February 1996

  Apparently, all partial differential equations that describe physical phenomena in space-time can be cast into a universal quasilinear, first-order form...

  View on arXiv PDF PostScript Other formats

Numerical Methods for Differential Equations

• Introduction to Numerical Methods for Time Dependent Differential Equations
  by Heinz-Otto Kreiss & Omar Eduardo Gritz
  Publisher: Wiley
• A Concise Introduction to Numerical Analysis
  by Douglas N. Arnold
  PDF
• Time-Dependent Problems and Difference Methods Second Edition
  Publisher: Wiley
  by Bertil Gustafsson, Heinz-Otto Kreiss & Joseph Oliger