Studying EECS

[trying2eecs-blog]

Electrical Circuits Crib Sheet

We get three full pages front and back for crib sheets.

\(\tau_L = \frac{L}{R_T}\) \(\tau_R = R_T C\) To find \(R_T\) turn all current sources into opens and voltage sources to shorts and open the energy-storing component, then simplify the resistors.

Powers of Ten Prefixes \(T = 10^{12} \) \(G = 10^9 \) \(M = 10^6  \) \(k = 10^3\) \(1 = 10^0\) \(m = 10^{-3} \) \(\mu = 10^{-6} \) \(n = 10^{-9} \) \(p = 10^{-12} \)

Things about transient circuits \(i_L\) can’t jump. \(v_C\) can’t jump. \(L \frac{di}{dt} = v_L\) \(C \frac{dv}{dt} = i_L\) \(CV^2/2\) Energy stored in capacitor Initial conditions are the following: \(i_L(0^-), v_C(0^-)\). \(u(t) = 1, \)for\( t>0 \lor 0,\) for \(t<0\) look up the characteristic equations for series and parallel

Things about any RLC circuits R or L in parallel \(\frac{product}{sum}\) R or L in series just sum C is backwards VDP \(v_x = v_s \frac{R_x}{\Sigma R}\) CDP \(i_x = i_s \frac{R_{other(s)}}{\Sigma R}\)

Nortons and Thevenins Norton | current source and resistor in parallel Thevenin | voltage source and resistor in series \(v_T = i_N R \land R_T = R_N\) Note: transformations change inner voltage, current, and power values, but not outside To transform ANY circuit between two nodes: \(R_T\) is equal to the simplified version of all resistors after voltage sources are replaced with shorts and current sources are replaced with opens. \(V_T\) then becomes the voltage between the two nodes. Max Power occurs when \(R_T = R_N = R \)

General Equations \(V = IR\) \(P = IV\)

General Solution for First-Order Switching Transient DC Circuits: Don’t forget, current can’t jump for inductors and voltage can’t jump for capacitors. \(y(t) = y(0)e^{-{t}/{\tau}}+y(\infty)(1- e^{-{t}/{\tau}})\) Transforming cos to sin:

30 60 90 triangles too 45 45 triangles

Second-order Switching Transient DC Circuits: NEED QUADRATIC EQUATION NEED DERIVATIVE RULEs FOR PRODUCTS

Choose Characteristic EQ

Parallel: \(s^2+\frac{1}{RC}s+\frac{1}{LC} = 0\)

Series:  \(s^2+\frac{R}{L}s+\frac{1}{LC} = 0\)

Solve for s

Only 1 real \(s\) \(v(t) = A_1e^{st}+A_2te^{st}+A_3\)

Real and distinct \(s_1, s_2\) \(v(t) = B_1e^{s_1t}+B_2e^{s_2t}+B_3\)

Complex \(\alpha \pm \hat \jmath \beta\) \(v(t) = C_1e^{\alpha t}sin(\beta t)+C_2e^{\alpha t}cos(\beta t)+C_3\)

[trying2eecs-blog]

Next Finals: Electrical Circuits and Logic Design

Both these classes are entry-level EE courses. They’re pretty straight forward especially Logic Design. I ditched one too many Electrical Circuits courses and didn’t do some homework assignments, so I’ll be focusing primarily on Op-amps, DC and AC RLC Circuits of First and Second-order. Logic Design, on the other hand, is really, really easy. The amount of binary with which I deal in all of my classes (e.g. Computer Science, Mathematical Logic) relaxes any difficulties of any digital systems. Anyway, hit the bump for a few details on Electrical Circuits and Logic Design.

EE 261 Electrical Circuits

There are only three or four topics worth mentioning here because I suck at going to classes. Op amp circuits deal with amplification in inverting and non-inverting signals. The other three are all resistor, inductor, capacitor (RLC) circuits of various types. First-order RLC circuits are very simple as they only involve one energy-storing component - either an inductor or capacitor. Second-order RLC circuits are a little more complicated as they involve both kinds of energy-storing components. However, in this course, we only need to solve for two situations: all the components in parallel or all the components in series. The last RLC circuit is AC circuits. These are actually pretty straightforward as you can just change everything into phasor form and everything just solves itself. 

EE 231 Logic Design

I don’t actually have anything to say about this course. Uhh...

[trying2eecs-blog]

Week 2 of Data Structures

I posted week 1 just a second ago, but I guess it just got lost. Huh. Weird right?

Here are the topics:

Strings Functions: scanf(), putchar(), atoi() C preprocessor Structs Memory Management: malloc() and free()

Also fuck this right now, I’m just going to go over some algorithms for graphs instead. lol.

[trying2eecs-blog]

If you can draw boxes, you can write code.

Shit Professors Say

[trying2eecs-blog]

Data Structures Summary

This class was a bit disjointed and not structured too well, but so am I, so it works out well. Hit the jump for an unorganized, unstructured summary of the course. 

Differences between C and Java

Actually, this was a decent portion on the test, but I always forget. Both are high-level coding languages (meaning it needs a translator of some sort to mess with the 1s and 0s down below). Anyway, one of the main differences is that Java is object oriented, so it can create instances and structures REAALLLLLYY easily. Another one is that Java is a lot more secure because it has security built into it; you can break your machine really easily if you’re coding purely in C. Especially when you start coding in memory and you access things out of bounds. C is more portable, that’s kind of important too, because you can run C on nearly any computer. It’s a very direct workstation. Java, on the other hand, requires a Java environment to run, and because of that, is much more secure. That’s all I remember, but maybe I’ll read up on it more.

Alright, the rest of this will just be links to other topics because that was a lot more text than I wanted.

Learning Basic C

Header and Source Files Command-Line Build Types Functions and printf(); atoi() Preprocessor Constants Expressions: arithmetic, logical, conditional Statements: conditional and looping Arrays Pointers, memory architecture Command line arguments User-defined functions Strings Functions: scanf(), putchar() +  C preprocessor Structs Memory management: malloc() and free() Dynamically allocated arrays Addressing and manipulating arrays C debugging techniques, hunting down segfaults Passing pointers as function arguments File I/O

Basic Data Structures

Intermediate Data Structures

Or maybe not? this is a lot of info. Damn. I’ll just go through the powerpoints I guess.

[trying2eecs-blog]

Balls and Boxes

Just killed my discrete structures final. (First one this semester, by the way.) But I messed up on one of the simplest of questions.

True or False? There are 45 ways to sort 8 identical balls into 3 boxes.

I answered false, stating that there are about several powers of ten above it, but that’s due to very, very incorrect miscalculation.

The correct answer is true, and can be answered using binomial coefficients.

 Binomial coefficients take the form of \(\binom {m}{n}\) and can be used to count the number of ways to choose \(n\) distinct things from \(m\) distinct objects. Although the eight balls are identical (read: not distinct), the possibilities of sorting these balls into three distinct boxes can be counted with the Balls and Boxes Theorem (or more accurately Balls and Separators).

Sorting 8 identical balls into 3 distinct boxes creates a Diophantine equation of the form \(x_1+x_2+x_3=8, x_n \ge 0\). The number of solutions to this equation is equivalent to the answer of the original equation. (Yes, 45, but how?) The \(x_n\)’s in the equation are the boxes, and their value represents the number of balls in that box. There are certain limitations: the total of these number cannot exceed 8 because there are only 8 balls total and the \(x_n\) values cannot be negative because anti-balls are not of our concern.

Now binomials. I’m just going to cut to the chase. \(\binom{10}{2}\) is the answer. Where does this come from? Well, it comes from \(\binom{8+2}{2}\). It’s easiest to draw a picture.

_ _ _ _ _ _ _ _ _ _

Each space represents either a possible ball or separator. There are ten spaces, and you’d need to choose 2 places put separators. (That’s where \(\binom{10}{2}\) comes from.) Choosing these separators leaves 8 empty spaces. Each empty space is representative of a ball. These separators also leave 3 groups of balls each representative of the \(x_n\)’s. Using |’s as separators, here is one example of a distribution:

_ _ _ | _ _ | _ _ _ 

In this example, \(x_1 = 3, x_2 = 2, x_3 = 3\). But how do you evaluate \(\binom{10}{2} = 45\)?

[trying2eecs-blog]

6 Relations and Functions

6.1 Relations Relations occur between elements from two sets (different or the same). The set of all possible relations from set S to itself can be described as S x S. Elements of this relation set, R, take the form of (a,b) is an element of R such that  a and b are elements of S. My professor likes to denote this as a~b (a is related to b) rather than having an ordered pair an element of the relation set R.

6.2 Equivalence Relations Equivalence relations occur when multiple elements are related to the same thing. I think. I need to study this one a little harder. I’m assuming that equivalence relations are kind of  like a~c and b~c so a and b are kind of equivalent. I’m not sure at all actually, but finals are next week.

Oh! I just remembered, they have to have three specific characteristics to be an equivalence relations. Reflective, something, and something. 

6.3 Functions Functions are special relations. For a relation to be a function there should be two defined sets - a domain and codomain - and a subset of the codomain - range. I forgot if images and preimages apply to relations too, but the image of an element in the domain is its corresponding element of the range. The preimage is that backwards. Forgot something important, any element in the range can only have one preimage in the domain (but multiple elements in the codomain can have the empty set as its preimage.)

Attributes! Alright, so there are three basic attributes of functions. It can be, monic, epic, and/or bijective. 

Monic, one-to-one, or injective functions are those with the following condition: for each element in the domain there exists a unique image in the range. In other words, it passes the horizontal line test.

Epic, onto, or surjective functions are those that satisfy the following condition: the range and codomain are equivalent. In otherwords, when you pump the entirety of the domain into the function, it pumps out the entire codomain set.

Bijective functions are both monic and epic. 

6.4 Compositions

6.5 Pigeonhole Principle