In this page, you will find a list of essential reading material that is relevant to the kind of work I do. In each section, the books are roughly arranged in the order of increasing complexity.

- D. J. Tritton, Physical Fluid Dynamics
- John D. Anderson Jr., Modern compressible flow: With historical perspective
- L. D. Landau and E. M. Lifschitz, Fluid Mechanics
- G. K. Batchelor, An Introduction to Fluid Dynamics
- P. A. Davidson, Turbulence: An introduction for scientists and engineers
- Stephan B. Pope, Turbulent Flows

- Karl E. Gustafson, Introduction to PDE and Hilbert Space Methods
- Heinz-Otto Kreiss and Jens Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations
- G. B. Whitham, Linear and Non-linear Waves
- L. C. Evans, Partial Differential Equations

- Randall LeVeque, Finite difference methods for ordinary and partial differential equations (Book website)
- Vidar Thomee and Stig Larsson, Partial Differential Equations with Numerical Methods
- J. W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods
- Bertil Gustafsson, Heinz-Otto Kreiss, Joseph Oliger, Time dependent problems and difference methods.

- Randall J. LeVeque, Numerical Methods for Conservation Laws
- Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems
- E. Godlewski and P. Raviart, Hyperbolic Systems of Conservation Laws
- E. F. Toro, Riemann solvers and numerical methods for fluid dynamics
- E. Godlewski and P. Raviart, Numerical Approximation of Hyperbolic Systems of Conservation Laws

- John D. Anderson Jr., Computational Fluid Dynamics: The basics with applications
- Jiri Blazek, Computational Fluid Dynamics: Principles and Applications (Codes from 3'rd edition)
- Charles Hirsch, Numerical Computation of Internal and External Flows, Vol. I & II
- Charles Hirsch, Numerical Computation of Internal and External Flows: The Fundamentals of Computational Fluid Dynamics, 2007

- Claes Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method
- Dietrich Braess, Finite elements: Theory, fast solvers and applications in solid mechanics
- Alfio Quarteroni and Alberto Valli, Numerical Approximation of Partial Differential Equations
- Philippe Ciarlet, The Finite Element Method for Elliptic Problems

- James W. Demmel, Applied Numerical Linear Algebra
- G. H. Golub and C. F. Van Loan, Matrix Computations
- Yousef Saad, Iterative Methods for Sparse Linear Systems (Download)

- Brian W. Kernighan and Dennis M. Ritchie, The C Programming Language
- Bjarne Stroustrup, A Tour of C++
- Peter Gottschling, Discovering Modern C++: An Intensive Course for Scientists, Engineers and Programmers
- Richard J. Hanson and Tim Hopkins, Numerical Computing with Modern Fortran
- Victor Eijkhout, Introduction to High Performance Scientific Computing (Download)
- Victor Eijkhout, Parallel Programming in Science and Engineering (Download)
- Georg Hager and Gerhard Wellein, Introduction to High Performance Computing for Scientists and Engineers

- Christopher M. Bishop, Pattern recognition and machine learning (Download)
- Gilbert Strang, Linear Algebra and Learning from Data
- Steven Brunton and Nathan Kutz, Data-driven science and engineering (Book website)

- Gilbert Strang: Computational Science and Engineering I
- Gilbert Strang: Mathematical Methods for Engineers II
- Randall LeVeque: High performance scientific computing: Course site, Class notes
- Steven Brunton has a nice collection of videos on data science, reduced order models, etc.
- Lorena Barba: Computational Fluid Dynamics
- Krishna Garikipati: Introduction to Finite Element Methods
- Wolfgang Bangerth: Finite element methods in scientific computing (based on deal.II)