Welcome

Welcome to Advanced Numerical Methods: Computational Partial Differential Equations, MATH-693B

Logistics

• Office hours: announced on the course Canvas page or by appointment.

Note

Who am I?

• Assistant Professor in the Department of Mathematics & Statistics and the Computational Science Research Center

• Previously:

  • Research Software Engineer for 3+ years at Caltech, in the CliMA group

  • Postdoctoral Research Associate at CU Boulder, in Jed Brown’s PhyPID group

  • PhD in Applied Math from NJIT

  • some industry experience with CAD/CAM system development and at Pixar in the Research group

Resources

• SIAM Membership is free for students (30% discount on SIAM books)

• Books

  • Thomas (1998), Numerical Partial Differential Equations: Finite Difference Methods

    • available at the SDSU library

  • LeVeque (1998), Finite Difference Methods for Differential Equations

  • Strikwerda, Finite Difference Schemes and Partial Differential Equations

  • Driscoll and Braun, Fundamentals of Numerical Computation

    • free, in Julia with demo notebooks and Julia codes

  • Greenbaum and Chartier (2012), Numerical Methods Design, Analysis, and Computer Implementation of Algorithms

    • an excellent, comprehensive book

    • not free, uses Matlab for limited numerical examples

  • LeVeque (2007) Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems]

    • online available from SIAM

  • Sauer (2012), Numerical Analysis

  • Boyd and Vandenberghe (2018), Introduction to Applied Linear Algebra

    • practical introduction to linear algebra for computer scientists; free PDF

  • 3Blue1Brown, Linear Algebra

    • collection of beautiful videos visualizing linear algebra

  • Trefethen and Bau (1997), Numerical Linear Algebra (available at the library)

    • fantastic, but limited to numerical linear algebra and covers more advanced topics; free PDF via library

  • Myers, Van de Geijn, and Van de Geijn (2020), Linear Algebra: Foundations to Frontiers

    • linear algebra with attention to performance; free PDF and videos

Note

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