Tentative Schedule of Lectures: EECS 219A, Fall 2014
September 2014
2014/09/03 (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.
2014/09/08 (Mon):
- 1-2:30: Time invariance. Affineness. Nonlinear devices: diode, BJT.
2014/09/10 (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.
- 1-2:30: Smoothing nonsmooth functions (contd.). Domain issues. Finite-precision issues: floating point overflow.
2014/09/17 (Wed):
- 1-2:30 and 4-5: Finite-precision issues: catastrophic cancellation. limexp(). Memristors. Circuit equation formulations: sparse tableau by example.
- 1-2:30: Circuit equation formulations (contd.): nodal analysis and modified nodal analysis by example. Standard DAE form. KVL and KCL using incidence matrices. Formulating Sparse Tableau in general.
2014/09/24 (Wed):
- 1-2:30 and 4-5: Circuit equation formulations (contd.): Formulating and NA and MNA in general. Mechanical equation system example. Aadithya on DAEAPI (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.
October 2014
2014/10/01 (Wed):
- 1-2:30 and 4-5: NR continued: the algorithm and its graphical interpretation. Failure of NR. Quadratic and linear convergence properties.
- 1-2:30: Convergence criteria — deltax and residual, reltol-abstol. NR failure: ))Vsrc-R-diode(( example.
2014/10/08 (Wed):
- 1-2:30 and 4-5: Initialization for NR. Limiting. Tradeoffs between init/limiting algorithms, equation formulations and code modularity. Jacobians and sparsity.
- 1-2:30: Jacobian sparsity continued: how sparse graph structure translates to sparse Jacobians for STA and MNA equations. Numerical solution of linear equation systems: Gaussian Elimination.
2014/10/15 (Wed):
- 1-2:30 and 4-5: LU factorization; forward and backward substitution. Matrix ordering for sparsity. Algebra of GE and LU. Matrix conditioning; error amplification in Ax=b solution.
- 1-2:30: Matrix conditioning and error amplification in Ax=b solution (contd.). Ax=b error growth in LU factorization. Pivoting for controlling error growth. Simple iterative techniques for linear solution.
2014/10/22 (Wed):
- 1-2:30 and 4-5: When to use iterative linear methods over direct. Basic data structures for sparse matrices. Summary of pitfalls in Ax=b solution. Sparse matrix packages. Biochemical reaction pathways. Rate equations, conservation, equilibrium for unimolecular reactions. Eigenanalysis of unimolecular reactions.
- 1-2:30: Bimolecular reactions. Rate equations for multi-molecular reactions. Stoichiometry. Enzyme-catalyzed reactions and their ))Michaelis-Menten(( approximations.
2014/10/29 (Wed):MIDTERM EXAM
- 1-2:30 and 4-5: MIDTERM exam. Midterm solution/discussion.
November 2014
2014/11/03 (Mon):
- 1-2:30: Using SVDs to identify conservation laws of reaction chains. Introduction to transient simulation.
2014/11/05 (Wed): (lectures by Aadithya)
- 1-2:30 and 4-5: Numerical solution of ODEs. Existence and uniqueness conditions. Time-axis discretization. Towards numerical methods for ODEs: approximating solutions using piecewise polynomials. FE, BE and TRAP methods.
- video of 1-2:30pm lecture.
- [https://draco.eecs.berkeley.edu/videos/2014-Fall-219A/2014-Nov-05
EE219A-introducing-FE-BE-TRAPcontinued.html|video of 4-5pm lecture].
2014/11/10 (Mon):
- 1-2:30: Stability. Stiff systems and the need for "large" timesteps. Stability regions of FE, BE and TRAP.
- 1-2:30 and 4-5: LMS methods and GEAR2. 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.
- 1-2:30: Periodic steady state analysis of LTI systems. LTI DAEs. Linearization of nonlinear systems about quiescent steady states. Small-signal sinusoidal (SSS, aka "AC") analysis. Connection with Laplace-domain analysis. AC frequency sweeps.
2014/11/19 (Wed):
- 1-2:30 and 4-5: Transfer function eigenanalysis: numerical-analytical procedure for obtaining the transfer function of LTI DAE systems in the Laplace domain. Poles and residues. Parameter sensitivity analysis of QSS/DC operating points. Linearization of parameter dependence. Expression for the DC sensitivity matrix.
- 1-2:30: 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.
2014/11/26 (Wed):
- 1-2:30 and 4-5: From histograms to probability density functions. Gaussian and uniform distributions. Mean and variance derived from PDFs. PDFs of functions of RVs. Simultaneous sampling of several RVs - joint probabilities. Independence and correlation. Jointly Gaussian PDF.
December 2014
2014/12/01 (Mon):
- 1-2:30: 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.
2014/12/03 (Wed):
- 1-2:30: Thermal, shot and flicker noise. Propagation of stationary noise through LTI systems. Vector stochastic processes. Stationary noise computation for LTI systems: direct and adjoint methods.
- video of 1-2:30pm lecture. (The first half of the lecture was lost - file corrupted)
- class scribbles (PDF)