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Tentative Schedule of Lectures: EECS 219A, Fall 2015


August 2015

2015/08/26 (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. Nonlinear elements.

2015/08/31 (Mon): (class given by Tianshi)
  • 1-2:30: Time invariance. Affineness. Nonlinear devices: diode, BJT. MOS ())Schichman-Hodges(( model). Glimpse of BSIM model. Nonlinear capacitors and inductors. Derivatives, continuity concepts.
September 2015

2015/09/02 (Wed):
2015/09/07 (Mon): NO CLASS (academic holiday)
2015/09/09 (Wed):
2015/09/14 (Mon):
2015/09/16 (Wed):
  • 1-2:30 and 4-5: Circuit equation formulations (contd.): Mechanical equation system example. DAEs with inputs and outputs. SPICE netlist syntax; parsing and equation setup. Glimpse of mechanical and biological "netlists". Quiescent steady state and NR: introduction. Tianshi on DAEAPI (with demos).


2015/09/21 (Mon):
  • 1-2:30: NR continued: the algorithm and its graphical interpretation. Failure of NR. NR convergence rate.

2015/09/23 (Wed):
  • 1-2:30 and 4-5: NR continued: Quadratic and linear convergence properties. Convergence criteria — deltax and residual, relto-abstol. NR failure: ))Vsrc-R-diode(( example. Initialization for NR. Limiting.


2015/09/28 (Mon):
2015/09/30 (Wed):
  • 1-2:30 and 4-5: Jacobian sparsity. Gaussian Elimination. LU factorization; forward and backward substitution. Matrix ordering for sparsity.


October 2015

2015/10/05 (Mon):

2015/10/07 (Wed):
  • 1-2:30 and 4-5: Simple iterative techniques for linear solution. Summary of pitfalls in Ax=b solution. Sparse matrix packages. Biochemical reaction pathways. Rate equations, conservation, equilibrium for unimolecular reactions. Eigenanalysis of unimolecular reactions.

2015/10/12 (Mon):
  • 1-2:30: Rate equations for multi-molecular reactions. Stoichiometry. Enzyme-catalyzed reactions and their ))Michaelis-Menten(( approximations. Using SVDs to identify conservation laws of reaction chains.

2015/10/14 (Wed):
  • 1-2:30 and 4-5: Using SVDs to identify conservation laws of reaction chains. Introduction to transient simulation. Numerical solution of ODEs. Existence and uniqueness conditions. Time-axis discretization.

2015/10/19 (Mon):
  • 1-2:30: Towards numerical methods for ODEs: approximating solutions using piecewise polynomials. FE, BE and TRAP methods. LMS methods and GEAR2. Small-timestep errors of FE, BE and TRAP.

2015/10/21 (Wed):MIDTERM EXAM
  • 1-2:30 and 4-5:MIDTERM exam. Midterm solution/discussion.
2015/10/26 (Mon):
  • 1-2:30: Cont: small-timestep errors of FE, BE and TRAP. Adapting LMS methods for solving DAEs. The DAE initial condition consistency problem. Stability properties (oscillatory tendencies) of TRAP for DAEs; workarounds. ODE/DAE packages. Periodic steady state analysis of LTI systems.

2015/10/28 (Wed):

November 2015

2015/11/02 (Mon):
  • 1-2:30: Finishing AC analysis. Connection with Laplace-domain analysis. Transfer function eigenanalysis.

2015/11/04 (Wed):
  • 1-2:30 and 4-5: Parameter sensitivity analysis of QSS/DC operating points. Linearization of parameter dependence. Expression for the DC sensitivity matrix. Density of the DC sensitivity matrix. Computing the sensitivity matrix directly via LU factorization and its cost. Adjoint sensitivity computation. Introduction to noise analysis. Intuitive notions of noise. Probability and random variables primer: Sampling a random variable. Histograms.

2015/11/09 (Mon):
  • 1-2:30: Noise analysis continued. Random variable. Histograms. From histograms to probability density functions. Gaussian and uniform distributions. Mean and variance derived from PDFs. PDFs of functions of RVs.

2015/11/11 (Wed): NO CLASSES (academic holiday)
2015/11/16 (Mon):
  • 1-2:30: Simultaneous sampling of several RVs - joint probabilities. Independence and correlation. Jointly Gaussian PDF. 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.

2015/11/18 (Wed):
  • 1-2:30 and 4-5: Autocorrelation function continued. Power spectral density. White noise. Thermal, shot and flicker noise.


2015/11/23 (Mon):
  • 1-2:30: Propagation of stationary noise through LTI systems. Vector stochastic processes. Stationary noise computation for LTI systems: direct and adjoint methods.

2015/11/25 (Wed): NO CLASSES (day before Thanksgiving)
2015/11/30 (Mon):
  • 1-2:30: Stochastic modelling of biochemical systems. Well stirred systems. The concept of propensity. Basic reactions and their propensities. State probabilities. The Chemical Master Equation. Example: CME for enzyme-catalyzed reaction system.

December 2015

2015/12/02 (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. 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. 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. Conclusions and review.

2015/12/10 (Thu): FINAL EXAM 4-7pm in 299 Cory.