Real Analysis Courses and Certifications

Topos Institute

The Fundamental Theorem of Calculus: Point-Free Analysis

Explore point-free topology's innovative approach to calculus fundamentals through geometric logic, examining how spaces and continuity can be defined without traditional point-set methods.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Michael Penn

The Ruler Function is Nowhere Differentiable

Explore the fascinating mathematical concept of the ruler function, which exhibits the unusual property of being nowhere differentiable, in this engaging analysis.

• YouTube
• 14 minutes
• On-Demand
• Free Video

Data Analysis | SQL,Tableau,Power BI & Excel | Real Projects

5819 ratings at Udemy

4-in-1 bundle: Practical learning of the essential tools used in Data Science with hands on examples and projects

• Udemy
• 13 hours 23 minutes
• On-Demand
• Paid Course

SQL for Data Analysis: Solving real-world problems with data

2092 ratings at Udemy

A simple & concise mySQL course (applicable to any SQL), perfect for data analysis, data science, business intelligence.

• Udemy
• 1 hour 57 minutes
• On-Demand
• Free Online Course

Convergence Tests for Series and Power Series - Lecture 8

Master convergence tests for infinite series and explore power series fundamentals, including limsup, liminf concepts, and radius of convergence in this MIT real analysis lecture.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Extreme and Intermediate Value Theorem - Metric Spaces - Lecture 11

Explore extreme and intermediate value theorems using sequences, then discover metric spaces and their properties including convergence and Cauchy sequences with examples.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Limsup and Liminf - Power Series - Continuous Functions - Exponential Function - Lecture 9

Explore limsup, liminf concepts, power series convergence, and the exponential function's definition while advancing your understanding of continuous functions in real analysis.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Integrable Functions - Lecture 18

Explore uniform continuity and prove that continuous functions on compact intervals are integrable, establishing well-defined areas under their graphs.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Existence and Uniqueness for ODEs - Picard-Lindelöf Theorem - Lecture 23

Explore the Picard-Lindelöf theorem proving existence and uniqueness of solutions for first-order ODEs using metric spaces and contracting mapping principles.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Sequential Compactness - Bolzano-Weierstrass Theorem in a Metric Space - Lecture 14

Explore sequential compactness and the Bolzano-Weierstrass theorem in metric spaces, proving that sequences in compact subsets have convergent subsequences.

• YouTube
• 1 hour 24 minutes
• On-Demand
• Free Video

Integrals and Derivatives under Uniform Convergence - Lecture 21

Explore uniform convergence properties using Weierstrass M-test for power series continuity and prove completeness of C([a,b]) with supremum norm for differential equations.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Continuous Functions and Exponential Function Properties - Lecture 10

Explore continuous functions and complete the proof of exponential function properties, including series product results in this advanced real analysis lecture.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

Rolle's Theorem - Mean Value Theorem - L'Hôpital's Rule - Taylor Expansion - Lecture 16

Explore Rolle's Theorem, Cauchy Mean Value Theorem, L'Hôpital's rule for evaluating limits, and Taylor expansion fundamentals in this MIT real analysis lecture.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Fundamental Theorem of Calculus - Lecture 19

Explore the essential connection between differentiation and integration through two versions of the fundamental theorem, plus improper integrals and unbounded functions.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video

Pointwise Convergence and Uniform Convergence - Lecture 20

Explore pointwise vs uniform convergence, arc length of curves via integrals, and master the Weierstrass M-test for determining uniform convergence in real analysis.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video