What would you do if I asked you to solve a linear system with 100 variables or 100 equations? Scream? Cry? Perhaps. Or maybe you just need a new tool in your toolbelt. What new tool? Matrices! Why Matrices are Useful for Larger Linear Systems While the graphing method, substitution method, elimination method, or even…
Markov Chain Applications
What if I told you that it had been mathematically proven that the orange and red properties in Monopoly by Hasbro are the most profitable (i.e., they are the most landed-on properties)? And when playing the game of RISK, the best strategy for world domination is to attack when you have twice as many armies…
Newton’s Method
Suppose you are asked to approximate a root of an equation. What do you do? Well, you know that a root is synonymous with x-intercept, so you are being asked to find where the function crosses the x-axis. This means you need to set your equation equal to zero and solve for x. That seems…
Curl And Divergence
What if I told you that washing the dishes will help you better to understand curl and divergence on a vector field? Hang with me… Imagine you have just finished your meal and you’re bringing all of your dishes to the sink. What do you do? You turn on the faucet to let water pour…
Double Integral
What is a double integral? For starters, it’s the path to calculate the volume of a region in three-space. Definite Integral Review Recall how in single variable calculus we learned how to subdivide the area of a region into simple geometric shapes, namely rectangles. By summing the area of each of these subdivided rectangles we…
Inverse Trig Derivatives
Did you know that inverse trig derivatives are sometimes referred to as the derivatives of arc-functions? For example, arcsin is the same thing as sin^(-1). Just as there are synonyms for different words in the English language, there are synonyms in math. Inverse Trig Functions And if we recall from our study of precalculus, we…
Moments and Center of Mass
Picture a seesaw and two children are placed at opposite ends, an equal distance from the fulcrum. Now if one child is bigger than the other than the seesaw will tip, but if the distance and mass of both children are equal than the seesaw will balance. Why? Because the mass is concentrated about one…
Calculus Tutor
Online Calculus Tutoring Free Resources In this weeks update of our online calculus tutoring, we’re exploring limits. Limits are critical in our study and understanding of how we find and evaluate such things as derivatives and integrals. By having a strong foundation in limits, you’ll be ready to head into and tackle derivatives. Limits Video…
L’Hopital’s Rule
Wouldn’t it be nice to be able to find the limit of an indeterminate form quickly and easily without having to use the conjugate or trig identities? Great news! Because that’s exactly what L’Hopital’s Rule is for. Our foundational rule for taking limits is not difficult – plug the number into the function and simplify.…
Vector Valued Function
What type of function has a range that does not consist of numbers? A function whose domain is a set of real numbers and whose range is a set of vectors is considered a vector function, sometimes called a vector valued function. Terminology But before we can talk about vector functions and space curves, we…