### Numerical Methods for Partial Differential Equations: A Simplified Unravelling

Liebmann Method

This is simply the Gauss-Seidel method applied for elliptic PDEs (i.e. B^2-4*A*C<0, usually steady-state).

A good example would be applications of the Laplace PDE to heat conduction.

(Working with Maths symbols is hard with a keyboard so I'll just do it on paper)

General steps in using numerical methods for solving PDEs:

Step 1: Transform the continuous PDE into a discrete representation.

Step 2: Isolate the present state variable (or the variable asked by the problem).

Step 3: Use overrelaxation if necessary to fasten convergence.

Explicit Method

This method is used for parabolic PDEs with a little problem in stability. (i.e. B^2-4*A*C=0).

A good example would be applications of the Fourier's Law of Heat Conduction.

The problem above differs from the plate problem due to the fact that we are dealing with unbounded sides. Also, the explicit method is only stable when the "constant" (that is, 0.02087 we've used in the problem) is less than 1/2.

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors