Real Analysis Courses and Certifications

Derivatives - Laws for Differentiation - Lecture 15

Master differentiation fundamentals including continuity proofs, Leibniz rule, quotient rule, chain rule, Rolle's lemma, and mean value theorem in real analysis.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Sequences and Convergence - Lecture 4

Explore sequences and convergence in real analysis, covering fundamental properties of converging sequences and the concept of subsequences in this MIT lecture.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

How to Write a Proof - Archimedean Property - Lecture 3

Master mathematical proof techniques through the Archimedean property and explore why √2 is irrational in this MIT Real Analysis lecture.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Taylor Polynomials - Remainder Term - Riemann Integrals - Lecture 17

Explore Taylor polynomial approximations and remainder term estimation, then delve into Riemann integral construction for calculating areas of complex figures.

• YouTube
• 1 hour 22 minutes
• Self-Paced
• Free Video

Cauchy Convergence Theorem - Lecture 6

Explore the Cauchy Convergence Theorem to determine sequence convergence without explicitly finding limits, plus discover its wide-ranging mathematical applications.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Convergence in Metric Spaces - Operations on Sets - Lecture 12

Explore convergence, Cauchy sequences, balls, bounded sets, and open/closed subsets in metric spaces, extending real line concepts to more general mathematical structures.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Sam Sanders - Uniformity in Mathematics

Explore uniformity in mathematics, from historical examples to modern applications. Examine how uniform theorems challenge traditional logical systems and impact proof methods across various mathematical domains.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

On the Group of Real-Analytic Diffeomorphisms - Lecture 2

Delve into advanced mathematical concepts of real-analytic diffeomorphisms, focusing on regimentation lemma and its applications to manifolds with nontrivial circle actions in topology.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Serrano.Academy

The Stone-Weierstrass Theorem - How to Approximate Functions

Explore the fascinating Stone-Weierstrass Theorem through engaging analogies, learning how continuous functions can be approximated using polynomials in compact spaces.

• YouTube
• 37 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

The Bolzano-Weierstrass Property

Explore the Bolzano-Weierstrass Property, a fundamental concept in mathematical analysis, and its implications for understanding convergence in real number sequences.

• YouTube
• 10 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Factorization of the Calderón Problem Through the Born Approximation

Explore analytic techniques in dynamics and geometry, focusing on the Calderón problem and its factorization through the Born approximation.

• YouTube
• 58 minutes
• Self-Paced
• Free Video

Michael Penn

Real Analysis - The Fundamental Theorem of Calculus

Comprehensive proof of both parts of the Fundamental Theorem of Calculus, demonstrating the relationship between differentiation and integration in real analysis.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

Michael Penn

Real Analysis - L'Hospital's Rule - Infinity-Infinity Case

Rigorous proof of L'Hospital's rule for infinity/infinity case, demonstrating its application in calculating limits of indeterminate forms in real analysis.

• YouTube
• 20 minutes
• Self-Paced
• 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
• Self-Paced
• Paid Course

Wrath of Math

Proving All the Sequence Limit Laws - Real Analysis

Comprehensive proof of five fundamental sequence limit laws in real analysis, covering sum, difference, constant multiple, product, and quotient of convergent sequences with practical applications.

• YouTube
• 54 minutes
• Self-Paced
• Free Video