Introduction to Real Analysis Course, Lecture 1: Overview, Mean Value Theorem, Sqrt(2) is Irrational

   • Real Analysis Exam 1 Review Problems and S...  . Introduction to Real Analysis Course Lecture 1: an Introduction and Overview. Textbook: Russell Gordon's "Real Analysis, a First Course": https://amzn.to/3421w9I. Introduction to Real Analysis, Lecture 1. Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. #realanalysis #realanalysislecture #realanalysiscourse 🔴 Real Analysis Exam 1 Review Problems and Solutions:    • Real Analysis Exam 1 Review Problems and S...   (0:00) Introduction and Moodle page. (4:41) Study Guide for Chapter 1. (9:52) What is Real Analysis about? (16:02) The Mean Value Theorem (MVT): geometric interpretation and example. (27:17) Idea of the proof of the Increasing Function Theorem with the MVT. (33:20) Example emphasizing the need for the derivative to be positive on the entire interval, and not just at a point. (36:45) Corollaries and an outline of the proof, working backwards toward more basic principles. (40:24) Introduction to the completeness axiom. (43:22) Proof by contradiction that sqrt(2) is irrational. (53:25) A Harder Question: How do we know sqrt(2) exists? Bill Kinney, Bethel University Math Department. "Hands On Start to Mathematica": https://amzn.to/2MycspH Check out my blog at: https://infinityisreallybig.com/ Follow me on Twitter:   / billkinneymath   Bill Kinney, Bethel University Department of Mathematics and Computer Science. St. Paul, MN. AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.