Course Information

Day One Handout

The course meets in slot 18, from 10:30-11:45 AM on Tuesdays and Thursdays, in ED 4010. My office hours are Mondays, 9:30-11:30am, Wednesdays 11am-noon, and Thursdays, 3-4pm, or by appointment.

Lecture Notes
The course lectures will closely follow those posted for each section below. These notes come from a book in preparation; students are encouraged to keep track of typos and other necessary corrections.

  • Taylor's Theorem and Differencing
  • Finite Differences
  • Spectral Methods
  • Finite Elements in 1D
  • General Finite Elements
  • Linear Solvers

    Textbook
    No textbooks are required for this course. Relevant e-books from the library's collection (or elsewhere) include the following; library login may be required for access.
  • Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems by Leveque
  • A First Course in the Numerical Analysis of Differential Equations by Iserles
  • Finite elements and fast iterative solvers with applications in incompressible fluid dynamics by Elman, Silvester, and Wathen
  • Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory by Braess
  • Finite Volume Methods by Eymard, Gallouët, and Herbin
  • Iterative methods for sparse linear systems by Saad (full text pdf available here)

    Reference books
    Background material from relevant undergraduate courses includes:
  • A First Course in Numerical Methods by Ascher and Greif
  • Scientific Computing - An Introduction using Maple and MATLAB by Gander, Gander, and Kwok

    Python tutorials
  • The official python tutorial
  • Software Carpentry python tutorial
  • Another Software Carpentry python tutorial (beta)

    Scientific Computing Tools in Python
  • General overview
  • Scientific Python Lectures

    D2L
    This course will not be using D2L; all material online will be posted here.
    • Approximate Schedule

  • 9/5: Introduction; Taylor's theorem and differencing
  • 9/10: Differencing in 1D, Taylor's Theorem in nD, HW1 Distributed, Solutions
  • 9/12: 2D meshes and differencing, approximating DEs
  • 9/17: Convergence Theory, HW2 Distributed, Solutions
  • 9/19: Convergence Theory, continued, HW1 Due
  • 9/24: Boundary conditions, HW3 Distributed, Solutions, Solution code, Solution driver
  • 9/26: Boundary conditions continued, complications, HW2 Due
  • 10/1: Meshless Finite Differences, HW4 Distributed, Solutions, Solution code, Solution driver
  • 10/3: Finite volumes in 1D, HW3 Due
  • 10/8: Finite volumes in 2D and 3D
  • 10/10: Spectral Methods, HW4 Due, HW5 Distributed, Solutions, Solution Code, Solution driver
  • 10/15: Fall Break, no lecture
  • 10/17: Fast Fourier Transform and Fast Poisson Solver, HW6 Distributed, Solutions, Solution code, Solution driver
  • 10/22: Midterm Exam, Solutions, Practice exam, Practice exam solutions
  • 10/24: Weak forms and Ritz-Galerkin
  • 10/29: Approximation Theory
  • 10/31: Piecewise linears, HW5 Due
  • 11/5: Piecewise polynomial approximation, HW7 Distributed, Solutions, Solution Code, Solution driver
  • 11/7: Hilbert Spaces, Lax-Milgram Lemma, Céa's Lemma, HW6 Due
  • 11/12: Poincaré-Friedrichs, Reaction-convection-diffusion equations, HW8 Distributed, Solutions
  • 11/14: Finite elements in 2D and 3D, approximation properties, HW7 Due, HW9 Distributed, Solutions, Solution Code, Solution Driver
  • 11/19: Direct Methods
  • 11/21: Iterative Methods and Matrix Splitting, HW8 Due
  • 11/26: Krylov Methods and GMRES
  • 11/28: MINRES and CG, HW9 Due
  • 12/7: Final Exam, 9:00am - 11:00am, Chemistry 4002, Practice exams, Solutions