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.Read More
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:Read More
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.Read More
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…Read More
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.Read More
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.Read More
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.Read More
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”.Read More
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.Read More
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.”Read More
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