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### Latest Posts

Let’s take a trip down to thought-experiment-lane, where the examples truly are interesting, the questions are truly too hard to be on the test, and maybe—just maybe—they could legitimately transform the way you think about your classwork. Here is today’s question:

Find the value of the voltage *v *in the circuit below.

The first thing you should notice is the two different types of sources (current sources are the ones with arrows in the middle of them, voltage sources are the ones with the plus and minus). The 5 ampere current source (the arrow with a circle around it) and the 16 volt voltage source (the circle with a plus and minus in it), are independent sources.

When a reaction is allowed to ‘run’ for some time, at some point it will no longer be favorable to continue forward or reverse and it will be at equilibrium

It is important to remember that equilibrium does not mean that the reactant concentrations and the product concentrations are equal, but that the

*rate of the forward reaction is equal to the rate of the reverse reaction*until something were to change (add more reactants/products, temperature, etc.)

A pointer is simply a variable that stores the address of another variable.

An address of a variable is where the variable is located in memory. For example, if you declare int n = 8; in your program, then your computer’s memory would look something like this…

My favorite metaphor for a math and science education is the toolbox metaphor: every technique you learn is like a tool, which can be used to solve a number of problems in the future. Some tools are very niche, and are used only in rare circumstances; others are so frequently applicable that you don’t even think about them anymore. You can think of multiplication as your trusty hammer, while derivatives are more like a… um… a pickaxe. Don’t think too hard about it.

The best way to approach why we use infinity instead of does not exist (DNE for short), even though they are technically the same thing, is to first define what infinity means.

Infinity is not a real number. It's a mathematical concept meant to represent a really large value that can’t actually be reached. In terms of solutions of limits, it means that the equation you are taking the limit of will go in that direction forever.

When I took MAT 22B, one of the topics I heard the most complaints about was Qualitative Analysis. But I thought Qualitative Analysis was one of the easier—or at least more fun—parts of the course. Let’s take a look at one such problem now, and you’ll see what I mean.

The electrochemistry unit at CU begins with redox reactions. Make sure you understand the basics of this before continuing through this article.

A **voltaic cell**, a.k.a. a galvanic cell, requires several parts. In official terms, you’ll need a cathode, an anode, and a conductive substance (usually wire) and salt bridge connecting the two. Less formally, you’ll need

Whenever you start a related rates problem (or most word problems) it's a good idea to:

Define a coordinate system: For this we can use the usual: it’s positive if it’s moving to the right or up. This is to make sure we don’t miss a negative sign somewhere.

Draw out the system in question:

When I was in high school, my chemistry teacher presented me with a radioactive decay problem, and a formula that read Q=Q_0 * e^(-rt) where 𝑄 represented the current amount of radioactive material, 𝑄0 represented the starting amount of material, and 𝑟 was some unknown “decay rate”.

This article will cover unsigned addition and subtraction, and 2’s complement addition and subtraction in base 16 (hexadecimal). This article will also cover the topic of overflow in relation to these operations.

A very important data structure, that is often confusing to beginning CS students, is the linked list. Linked lists are a linear data structure, just like basic arrays. However, unlike an array, the linked list is not one large, continuous block in memory. Instead, each element in a linked list contains a pointer to the next element. Each element is “linked” to the next, hence the term “linked list.”

Optimization refers to the maximums or minimums of a function in calculus.

Common types of optimization problems include:

Optimization Area & Perimeter

Optimization Volume & Surface Area

Optimization of the Distance Between a Point on a Curve

This article will cover:

The basic method of computing the determinant of any square size matrix

How row operations affect the determinant and how they can be used in your favor

Upper triangular form

A buffer, by definition, is a solution that resist change in pH. In a buffered solution, adding acid will only result in a small decrease in pH whereas adding the same volume and concentration of acid to a non-buffered solution will cause a much larger change in pH.

Voltage

Voltage from a

**point particle**Voltage from an

**electric field**- The only distance Δd that matters is the distance that is**parallel to the electric field**

If you need to find a particle’s speed from its voltage or energy, use the work-energy theorem from Physics 1

Each element in a chemical equation has an oxidation state, and you will have to assign these oxidation states to each element in order to determine the correct redox reaction stoichiometry. These states can be fairly easily determined just by looking at the periodic table.

Quick recap of Force Problems

1. Write down knowns + unknowns

2. Draw a picture

3. Choose a coordinate system

+ Usually x is horizontal, y is vertical

+ For ramps choose x to be down the ramp and y to be perpendicular to the ramp

While meeting with students in beginner level CSCI courses I have noticed a fairly common theme, many students are just typing code into a file with little to no organization. By the end of the project their code is so messy that the flow is almost impossible to follow. Because of this I have put together a simple set of rules for keeping your functions ordered.

The following will be covered in this article:

General notes

Definitions

Strong vs. weak acids and bases

Major species

Conjugate acids and conjugate bases

Basic pH calculations

Computer science is a complex subject that requires a thorough understanding of concepts. It doesn’t matter how smart or prepared you think you are, there is going to be a point in your career where you stare at your screen and think “what the heck is going on here?”.

Elimination reactions are helpful in many situations, especially in synthesis when you have an alkane and need an alkene. Similar to substitution reactions, eliminations produce similar products but depend on different factors. Most notably, E1 reactions have a carbocation intermediate while E2 reactions do not (for more information on E1 reactions, see “SN1/E1 Reactions”).

SN1 and E1 Reactions have very similar mechanisms, the final result just depends on whether the nucleophile or the base is attacks first. Compared to second order SN2 and E2 reactions (see “SN2 Reactions” and “E2 Reactions”), SN1/E1 are first order, the rate of the reaction depends only on the substrate.

Graphs in computer science are different than what most people consider a graph to be. Graphs are a data type consisting of connected nodes (much like a linked list), only, with graphs, nodes have no limit to how many connections to other nodes they have.

Consider the following mechanism for the overall reaction A+B→C

How do we find the overall rate law for this reaction?

First of all, we need to know the **Rate Determining Step (RDS)** to write the rate law. Note that this is the **slow** step, as the part of the overall mechanism that proceeds the slowest will ultimately determine the overall rate of the reaction.

A *vector* is just an arrow from the origin to a point. It has *magnitude* (how big it is) and *direction* (which way it’s pointing). A variable will have an arrow above it if it’s a vector!

Vectors can be in any number of dimensions

Method for Solving Kinematic Equations

Draw a picture!

Write down every variable you

*know*, and every variable you*don’t know / want to find*. Sometimes known variables are super obvious (e.g. if a ball is launched horizontally, then you know that its starting y-velocity, v_y0 = 0)

When I was first taught integrals, I was told they are like area. More specifically, the integral of f(x) dx from 0 to 1 represents the infinite sum of the area of rectangles given by height (f(x)) times width (dx), taken on the interval from 0 to 1. Double and triple integrals are an extension of this same concept, but now we have multiple parameters that can vary.