Tentative Schedule of Lectures: EECS 219A, Fall 2013
September 2013
2013/09/04 (Wed):
- 1-2:30 and 4-5: Syllabus and logistics. Introduction. Modelling basic circuit elements: linear resistor, capacitor, inductor, controlled sources, independent sources. Linearity and memorylessness.
2013/09/09 (Mon):
- 1-2:30: Time invariance. Nonlinear devices: diode, BJT.
2013/09/11 (Wed):
- 1-2:30 and 4-5: Modelling ckt elements (contd.): BJT contd.. MOS ())Schichman-Hodges(( model). Glimpse of BSIM model. Nonlinear capacitors and inductors. Derivatives, continuity concepts. Smoothing nonsmooth functions. Domain and finite-precision issues.
- 1-2:30: Memristors. Circuit equation formulations: sparse tableau by example, nodal analysis and modified nodal analysis by example. Standard DAE form.
2013/09/18 (Wed):
- 1-2:30 and 4-5: KVL and KCL using incidence matrices. Formulating Sparse Tableau, NA in general. Formulating MNA in general. Mechanical equation system example. Aadithya on describing DAEs in DAEAPI and SPICE netlist syntax (with demos).
- 1-2:30: DAEs with inputs and outputs. SPICE netlist syntax; parsing and equation setup. Glimpse of mechanical and biological "netlists". Quiescent steady state and NR: introduction. NR: graphical interpretation. Failure of NR.
2013/09/25 (Wed):
- 1-2:30 and 4-5: NR contd: Quadratic and linear convergence properties. Convergence criteria — deltax and residual, reltol-abstol. NR failure: ))Vsrc-R-diode(( example. Initialization for NR.
- 1-2:30: Limiting. Tradeoffs between init/limiting algorithms, equation formulations and code modularity. Jacobian sparsity. Numerical solution of linear equation systems.
October 2013
2013/10/02 (Wed): NO CLASSES (instructor out of town)
2013/10/07 (Mon):
- 1-2:30: Gaussian Elimination. LU factorization; forward and backward substitution. Matrix ordering for sparsity.
2013/10/09 (Wed):
- 1-2:30 and 4-5: Algebra of GE and LU. Matrix conditioning; error amplification in Ax=b solution. Ax=b error growth in LU factorization. Pivoting for controlling error growth. Simple iterative techniques for linear solution.
- 1-2:30: Basic data structures for sparse matrices; sparse matrix packages. Biochemical reaction pathways. Rate equations, conservation, equilibrium for unimolecular reactions. Eigenanalysis of unimolecular reactions.
2013/10/16 (Wed):
- 1-2:30 and 4-5: Bimolecular reactions. Rate equations for multi-molecular reactions. Stoichiometry. Enzyme-catalyzed reactions and their ))Michaelis-Menten(( approximations. Using SVDs to identify conservation laws of reaction chains.
- 1-2:30: Numerical solution of ODEs. Existence and uniqueness conditions. Time-axis discretization. Towards numerical methods for ODEs: approximating solutions using piecewise polynomials.
2013/10/23 (Wed): MIDTERM EXAM
- 1-2:30 and 4-5: MIDTERM exam. Midterm solution/discussion.
- 1-2:30: FE, BE and TRAP methods. LMS methods. Adapting LMS methods for solving DAEs. Stability. Stiff systems and the need for "large" timesteps. Stability regions of FE, BE and TRAP.
2013/10/30 (Wed):
- 1-2:30 and 4-5: Small-timestep errors of FE, BE and TRAP. Accuracy and truncation error. Starting higher-order LMS methods. Exactness constraints for LMS methods.Highest-accuracy p=2 LMS method. Stability of general LMS methods. The stability polynomial. Best p=2 method unstable for any h>0. Large-sigma behaviour of the trapezoidal method; TRAP and DAEs. Notions of timestep control. Periodic steady state analysis of LTI systems.
November 2013
2013/11/04 (Mon):
- 1-2:30: LTI DAEs. Linearization of nonlinear systems about quiescent steady states. Small-signal sinusoidal (SSS, aka "AC") analysis. Connection with Laplace-domain analysis.
2013/11/06 (Wed):
- 1-2:30 and 4-5: AC sweeps. Transfer function eigenanalysis. Parameter sensitivity analysis of QSS/DC operating points. Linearization of parameter dependence. Direct and adjoint methods for computing sensitivities. Introduction to noise analysis. Intuitive notions of noise.
2013/11/11 (Mon): Academic holiday
2013/11/13 (Wed):
- 1-2:30 and 4-5: Stochastic processes primer: random variables as functions of time. Point-by-point and waveform ensemble views. Stationarity. Ergodicity. Stationary variance as average noise power. Autocorrelation function of a stationary stochastic process. Power spectral density. White noise. Thermal, shot and flicker noise. Propagation of stationary noise through LTI systems.
2013/11/18 (Mon):
- 1-2:30: Vector stochastic processes. Stationary noise computation for LTI systems: direct and adjoint methods.
2013/11/20 (Wed):
- 1-2:30 and 4-5: Stochastic modelling of biochemical systems. Well stirred systems. The concept of propensity. Basic reactions and their propensities.
2013/11/25 (Mon):
- 1-2:30: State probabilities. The Chemical Master Equation. Example: CME for enzyme-catalyzed reaction system.
2013/11/27 (Wed):
- 1-2:30 and 4-5: Infeasibility of the CME for realistic problems. Waiting time probability to the next reaction. Propensity of the jth reaction after time tau. Next Reaction Index (NRI) and Time to Next Reaction (TtNR) as independent random variables, and their distributions. Gillespie's Stochastic Simulation Algorithm (SSA). Sampling NRI and TtNR. Example: SSA on enzyme-catalyzed reaction system.
December 2013
2013/12/02 (Mon):
- 1-2:30: Computational macromodelling. The model reduction problem. Algorithmic macromodelling. Model reduction for LTI systems. The concept of moments and its importance. LTI MOR via moment matching. Efficient moment computation using a single LU factorization of G. Pade approximants.
2013/12/04 (Wed):
- 1-2:30 and 4-5: Pade approximation. Computing the coefficients of the denominator and the numerator of the Pade rational function. Numerical conditioning issues. Why Pade approximants are better suited to DAE transfer functions than power series. From rational functions to companion form ODEs. Asymptotic Waveform Evaluation. Preview of Krylov subspace MOR methods.
2013/12/11 (Wed): FINAL EXAM 9:00AM to 12:00noon at the Hogan room (521 Cory).