Tentative Schedule of Lectures: EECS 219A, Fall 2010
August 2010
2010/08/30 (Mon):
- 1-2:30: Class syllabus and logistics (grading/HWs/midterm/final). Introduction.
September 2010
2010/09/01 (Wed):
- 1-2:30 and 4-5: Introduction continued. Modelling basic circuit elements: linear resistor, capacitor, inductor, controlled sources, independent sources. Linearity and memorylessness. Nonlinear devices: diode, BJT.
- HW1 assigned: see HWs page
2010/09/08 (Wed): NO CLASSES (instructor out of town). Make-up lectures page.
2010/09/13 (Mon):
- 1-2:30: Circuit element modelling (contd.): MOS (Schichman-Hodges) models. Glimpses of BSIM, Antoniadis models. Nonlinear capacitors and inductors. Derivatives, continuity concepts.
2010/09/15 (Wed):
- 1-2:30 and 4-5: Circuit element modelling (contd.): smoothing functions, numerical evaluation problems, memristors. Circuit equation formulations: sparse tableau, nodal analysis and modified nodal analysis by example.
- 1-2:30: Circuit equation formulations (contd.). Mechanical equation system example. SPICE netlist syntax; parsing and equation setup.
2010/09/22 (Wed):
- 1-2:30 and 4-5: DAEAPI introduction and demo. Quiescent steady state algorithms and NR. Newton-Raphson: convergence properties.
- HW2 assigned: see HWs page
- 1-2:30: Newton-Raphson: convergence criteria. Failure mechanisms of NR. Limiting and initialization. Jacobian sparsity.
2010/09/29 (Wed):
- 1-2:30 and 4-5: Numerical solution of linear equation systems. Gaussian Elimination. LU factorization. Algebra of GE and LU.
October 2010
2010/10/04 (Mon):
- 1-2:30: Matrix conditioning. LU error propapation. Simple iterative techniques for linear solution. Basic data structures for sparse matrices; sparse matrix packages.
2010/10/06 (Wed):
- 1-2:30 and 4-5: Biochemical reaction pathways. Rate equations for unimolecular and bimolecular reactions. Conservation.
- 1-2:30: Rate equations for multi-molecular reactions. Stoichiometry.
- HW3 assigned: see HWs page
2010/10/13 (Wed):
- 1-2:30 and 4-5: ))Michaelis-Menten(( approximations of enzyme-catalyzed reactions. Identifying conservation laws numerically for systems of reactions. Numerical solution of ODEs. Existence and uniqueness conditions.
- 1-2:30: Existence and uniqueness conditions, contd.. FE, BE and TRAP methods. LMS methods. Application of ODE methods to DAEs. Stability.
2010/10/20 (Wed):
- 1-2:30 and 4-5: Stability of FE, BE and TRAP. Small-timestep errors of FE, BE and TRAP. Starting higher-order LMS methods. Exactness constraints for LMS methods. Highest-accuracy p=2 LMS method.
- 1-2:30: MIDTERM exam.
2010/10/27 (Wed): CLASSES CANCELLED (instructor travel disruption). Make-up lectures page.
November 2010
2010/11/01 (Mon):
- 1-2:30: Stability of general LMS methods. The stability polynomial. Best p=2 method unstable for any h>0. Roots at sigma=0. Power-series method for estimating root behavior for small sigma. Principal and parasitic roots of the stability polynomial.
- HW4 to be assigned
2010/11/03 (Wed):
- 1-2:30 and 4-5: Condition for existence of simple principal root. Sufficient conditions for stability for small sigma. Notions of convergence and zero-stability of LMS methods. The root condition and its equivalence to zero-stability. General notion of consistency. Limit on accuracy for zero-stable LMS methods (Dahlquist's First Barrier). The converence theorem: zero-stability+consistency=convergence. Large-sigma behaviour: stiff systems. Relative and weak stability; the strong root condition for relative stability. Absolute stability and A-stability. There are no p>1 LMS methods that are A-stable (Dahlquist's Second Barrier).
- 1-2:30: Stiff stability properties: regions in the sigma plane, rationale. Gear's approach to designing stiffly stable LMS methods: all roots of stability polynomial -> as sigma -> \infty. BDF and Gear's methods.
2010/11/10 (Wed): NO CLASSES (instructor out of town). Make-up lectures page.
2010/11/15 (Mon):
- 1-2:30: Large-timestep stability of TRAP. Consistent initial conditions for DAEs. Linearization about quiescent steady states.
2010/11/17 (Wed):
- 1-2:30 and 4-5: Periodic steady state analysis of LTI systems. LTI transfer functions from DAEs.
2010/11/22 (Mon):
- 1-2:30: Eigenanalysis of transfer functions. Parameter sensitivity analysis around quiescent steady states.
2010/11/24 (Wed):
- 1-2:30 and 4-5: Direct and adjoint sensitivity computation. White and coloured noise. Thermal, shot and flicker noise. Vector stochastic processes. Stationary noise computation for LTI systems: direct and adjoint methods.
- 1-2:30: Stochastic modelling of biochemical systems. Basic reactions and their propensities. State probabilities. The Chemical Master Equation.
December 2010
2010/12/01 (Wed):
- 1-2:30 and 4-5: CME for ))Michaelis-Menten(( example. Gillespie's Stochastic Simulation Algorithm.
- HW5 to be assigned
2010/12/15 (Wed): FINAL EXAM (7-10 pm, 299 Cory).