In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability. Real analysis is distinguished from complex analysis, which deals with the study of complex numbers and their functions. (Wikipedia).
RA1.1. Real Analysis: Introduction
Real Analysis: We introduce some notions important to real analysis, in particular, the relationship between the rational and real numbers. Prerequisites may be found in the Math Major Basics playlist.
From playlist Real Analysis
Real Analysis - Part 1 - Numbers
Here, I present the first video in my Real Analysis series. It is all about numbers by showing the path to the real numbers, which we will need in this course. I explain the natural numbers, the integers and the rational numbers. I apologise for my pronunciation. The focus is on the math
From playlist Real Analysis (English)
Real Analysis Chapter 0: Preliminaries
Awwwww yeaaaaa...finally, we are starting our deep dive in to the wonderful work of Analysis! Naturally, we start with just the real numbers, and will slowly (but steadily) lumber through the complex numbers and beyond. But there is no time for that now! In this introductory video, we w
From playlist Real Analysis
Real Analysis Chapter 1: The Axiom of Completeness
Welcome to the next part of my series on Real Analysis! Today we're covering the Axiom of Completeness, which is what opens the door for us to explore the wonderful world of the real number line, as it distinguishes the set of real numbers from that of the rational numbers. It allows us
From playlist Real Analysis
Real Analysis | Compact set of real numbers.
We provide a definition of a (sequentially) compact subset of the real numbers and prove a classic theorem that says this definition is equivalent to the set being closed and bounded. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.co
From playlist Real Analysis
Real Analysis Course #1 - Ordered Sets
Here's the first video in a series of many on the topic of mathematical real analysis. This course is fundamental and usually required for all math majors. Let's dive in with ordered sets and the study of Real Analysis! **Note** that in definition i) exactly 1 and only 1 of the three case
From playlist Real Analysis Course
Neighborhood of a Point in Real Analysis | Real Analysis
What is an epsilon neighborhood of a point in real analysis? We introduce the definition of the neighborhood of a point and show how the definition of the limit of a sequence can be rewritten in terms of neighborhoods. The concept of a neighborhood is important, so it's handy to have this
From playlist Real Analysis
Real Analysis | The countability of the rational numbers.
We present a proof of the countability of the rational numbers. Our approach is to represent the set of rational numbers as a countable union of disjoint finite sets. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.ne
From playlist Real Analysis
6 Things I Wish I Knew Before Taking Real Analysis (Math Major)
Real Analysis can be a tough class. Real Analysis can be a tougher class when you don't know these six things. Here's the top six things I wish I knew before taking Real Analysis. Enjoy! Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases.
From playlist Math Talk
Complex Analysis - Part 1 - Introduction
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From playlist Complex Analysis
Complex analysis: Introduction
This lecture is part of an online undergraduate course on complex analysis. This is the first lecture, and gives a quick overview of some of the topics that might be covered, such as Cauchy's theorem, analytic continuation, the Riemann zeta function, and the Mandelbrot set. For the oth
From playlist Complex analysis
Complex Analysis - Part 1 - Introduction [dark version]
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From playlist Complex Analysis [dark version]
History of Mathematics - Complex Analysis Part 2: functions of a complex variable. 3rd Yr Lecture
Complex numbers pervade modern mathematics, but have not always been well understood. They first emerged in the sixteenth century from the study of polynomial equations, and were quickly recognised as useful – if slightly weird – mathematical tools. In these lectures (this is the second
From playlist Oxford Mathematics 3rd Year Student Lectures
Learn Real Analysis with This Book
In this video I go over a book on real analysis that I read a long time ago. It wasn't until someone left a comment about it that I ordered it and discovered it once more. This is a fairly decent book on real analysis and it is good for beginners. The book is called Introduction to Real A
From playlist Book Reviews
Real Analysis - Part 51 - Riemann Integral - Definition
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From playlist Real Analysis
A Classic Book on Real Analysis from the 1960s
Real analysis is very hard to learn so it helps to have as many resources as possible. This is one of the classics and is one of the better books on the subject. The book is called Real Analysis and it was written by Royden. This is the book on amazon: https://amzn.to/3li078c (Note this
From playlist Book Reviews
Math Major Guide | Warning: Nonstandard advice.
A guide for how to navigate the math major and how to learn the main subjects. Recommendations for courses and books. Comment below to tell me what you think. And check out my channel for conversation videos with guests on math and other topics: https://www.youtube.com/channel/UCYLOc-m8Wu
From playlist Math
Real Analysis - Part 1 - Introduction
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From playlist Real Analysis
The Best Math Textbook for Everyone
I discuss one of my favorite math textbooks, Fourier Analysis: An Introduction by Elias Stein and Rami Shakarchi. I recommend this book to everyone in a STEM field who knows multivariable calculus and has some familiarity with ODE and linear algebra. This book is excellent for initiating
From playlist Math