While you are learning statistics, you will often have to focus on a sample rather than the entire population. This is because it is extremely costly, difficult and time-consuming to study the entire population. The best you can do is to take a random sample from the population – a sample that is a ‘true’ representative of it.

Here, in particular, you would be learning about confidence intervals – what is a confidence interval, what is the process of constructing confidence intervals, the difference between one-sided confidence interval and two-sided confidence interval and most importantly, how to interpret confidence intervals?

Stokes’ Theorem is about tiny spirals of circulation that occurs within a vector field (F). The vector field is on a surface (S) that is piecewise-smooth. Additionally, the surface is bounded by a curve (C). The curve must be simple, closed, and also piecewise-smooth.

In this calculus crash course, we will demonstrate different techniques for performing the alternating series test. We’ll apply the test using several examples to make the concepts clearer. Finally, we will consider the quality of the test using the estimate of the remainder term.

The goal of this article is to introduce the gradient theorem of line integrals and to explain several of its important properties. In the first section, we will present a short interpretation of vector fields and conservative vector fields, a particular type of vector field. Here, we will consider the essential role of conservative vector fields.

In this article, we will describe the two various types of functions, the explicit and the implicit functions. We will provide several examples to show the importance of the implicit form of a function. Afterward, we will explain the role of implicit differentiation and look at how it can simplify the derivative-finding problems.

In this article, you will learn about some of the useful concepts in statistics like quartiles and the Interquartile Range (IQR). These concepts allow graphical representation of several probability distributions and also help create box and whisker plots, which are an effective way to represent and compare data.

In your multi-variable calculus course, you have likely encountered double integrals over a planar region and line integrals along the curve on a plane. But did you know that a double integral of some arbitrary function over a planar region is equal to a line integral around the boundary of that region? Green’s theorem, which relates double integrals and line integrals, is the subject of this review.