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Edit: At 00:22:40 I said "imagine you are a fixed particle". That's wrong. You can't be a fixed particle. There are no fixed particles in ...

Real analysis is the foundation of many important areas of maths, with practical applications from the Fourier series to complex ...

support the channel: https://ko-fi.com/thegraycuber previous video: https://youtu.be/AGh5LM7Jmfk my other projects: ...

One of the most important concepts in probability is that of a function of a random variable. For example, the mean and variance ...

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: ...

In this video, you'll learn how to determine whether a graph is continuous on a given interval--whether it's open or closed.

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: ...

Intermediate Value Theorem – proving that a continuous function takes on every value between its endpoints. This is our ...

... 29:33 Theorems and Examples 38:25 Left and Right Continuity 38:45 Continuity on Intervals 44:52 Continuous Functions 47:07 ...

The moment generating function is an important advanced concept in probability. Much like functions can be expanded in a Taylor ...

In this lecture, we focus on one exercise: proving that if f is a continuous scalar-valued function on a nice rectangle S in R^n, then f ...

Timeline TOC Introduction, Defn of Continuity - 0:00 Example 1 - 1:43 Continuity of Some Types of Functions - 9:27 Defns of Right ...

This is a strong version of continuity but we will see that all continuous functions on a closed and bounded interval have this ...

In this video, we introduce continuity for functions of several variables and build the foundation for everything that follows in ...

Piecewise functions can be differentiated easily using Calculus 1 derivative techniques. Continuity and differentiability of functions ...

We will examine the derivative of the function f(x)=x*abs(x) at x=0. We know the derivative of abs(x) is NOT defined at x=0, ...

So remember that we can determine a function is continuous at a point. If the function is not continuous at that point, they fall, ...

In this video, you will use the Mean Value Theorem to show that a positive derivative on an interval means a function is increasing ...

The joint probability distribution quantifies the joint dependence between two random variables, X and Y. If these random ...