Daily Log

Daily topics and PDFs (handouts and worksheets) will appear here as they occur. See also the Schedule. You do not have to turn-in any handout or worksheet! Note that the recorded lectures are in Announcements at the Canvas site.

• Wednesday 23 April: finite difference schemes for advection
  worksheet: von Neumann stability analysis (PDF)
• Monday 21 April: advection equation
  (start Chapter 10)
• Friday 18 April: backward Euler and von Neumann analysis on heat equation
• Wednesday 16 April: maximum principle convergence proof for FTCS on heat equation
• Monday 14 April: local truncation error, refinement paths, stability
• Friday 11 April: RK-Chebyshev, FTCS for heat equation
  (start Chapter 9)
• Wednesday 9 April: A-stable, A(alpha)-stable, L-stable, BDF
• Monday 7 April: stiffness
  (start Chapter 8)
• Friday 4 April: worksheet; Project Proposal really due!
  worksheet: stable time steps for 2nd-order schemes (solutions on Canvas page) (PDF)
• Wednesday 2 April: absolute stability for systems
• Monday 31 March: regions of absolute stability
  (start Chapter 7)
• Friday 28 March: multistep and zero stability
• Wednesday 26 March: one step convergence; project go!
• Monday 24 March: proof of Euler convergence
  (start Chapter 6)
• Friday 21 March: Midterm Exam
• Wednesday 19 March: one step error
• Monday 17 March: local truncation error
• Monday 3/10 to Friday 3/14: SPRING BREAK
• Friday 7 March: explicit midpoint, implicit trapezoid
• Wednesday 5 March: direction fields, forward & backward Euler
• Monday 3 March: Lipschitz condition, well-posedness
• Friday 28 February: eigenvalues/vectors, diagonalization
• Wednesday 26 February: examples, matrix exponential
• Monday 24 February: initial value problems
  (start Chapter 5)
• Friday 21 February: 2D linear advection-diffusion steady state problem
• Wednesday 19 February: 2D Poisson equation
  (start Chapter 3)
• Monday 17 February: advection-diffusion
• Friday 14 February: advection, boundary layer
  worksheet: 1st-order DEs, 2nd-order DEs, singular perturbations (PDF)
• Wednesday 12 February: nonlinear BVP
• Monday 10 February: convergence overview; symmetric (self-adjoint) form
  handout: why FD methods work (PDF)
• Friday 7 February: Neumann boundary conditions, well-posedness
• Wednesday 5 February: stability in 2-norm by eigenvalues
• Monday 3 February: fundamental theorem (Lax equivalence theorem)
• Friday 31 January: definition of convergent, stable
• Wednesday 29 January: definitions of local trucation error, consistent
• Monday 27 January: constructive FD solution of u''=f with b.c.s
• Friday 24 January: solve steady-state heat equation
  (start Chapter 2)
• Wednesday 22 January: FD intro done
• Friday 17 January: basic finite differences (FD)
  (start Chapter 1)
• Wednesday 15 January: examples; Taylor's theorem; linear ODEs
• Monday 13 January: examples to get us started