Posts tagged UC Davis
Double and Triple Integrals

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
Nodal Analysis

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
Your Integral Calculus Toolbox

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
Infinity and DNE in Limits

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
Linked Lists

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