Michael Penn Courses

Finding a Taylor Series Using Differential Equations

Explore an innovative approach to deriving Taylor series using differential equations, offering a fresh perspective on this fundamental mathematical concept.

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

A Physicist's Favorite Function

Explore a physicist's perspective on mathematical functions, blending humor and science to illuminate key concepts in continuity and piecewise functions.

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

The Dilogarithm - A Favorite Special Function

Explore the dilogarithm function, its properties, and applications in mathematics. Gain insights into this intriguing special function and its significance in various mathematical contexts.

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

The Quantum Derivative

Explore the concept of quantum derivative, its applications, and mathematical foundations in this concise tutorial on advanced calculus and quantum mechanics.

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

An Amazing and Mysterious Approximation for Pi

Explore a fascinating and enigmatic approximation of pi, uncovering its mathematical significance and the intriguing properties that make it remarkable.

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

How Archimedes Inspired Me to Approximate Cube Roots

Explore Archimedes' influence on cube root approximation methods, blending historical insights with practical mathematical techniques for modern problem-solving.

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

A Much More Friendly Approach to the Cubic Formula

Explore a user-friendly approach to understanding and applying the cubic formula, making complex mathematical concepts more accessible and manageable.

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

Clever Tricks with the Alternating Harmonic Series - Rearrangement Strategies

Explore clever rearrangement strategies for the alternating harmonic series, uncovering mathematical insights and surprising results in this engaging video lecture.

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

Convoluted Fibonacci Numbers

Explore the intriguing concept of convoluted Fibonacci numbers, delving into their mathematical properties and unique characteristics in number theory.

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

Can You Define Trig Functions via a Differential Equation

Explore an unconventional approach to defining trigonometric functions using differential equations, offering a fresh perspective on these fundamental mathematical concepts.

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

Why 1 Is Never Prime, and Sometimes Neither Are Some of Your Favorites

Explore the concept of prime numbers, focusing on why 1 is not considered prime and examining other surprising non-prime numbers in mathematics.

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

A Nice Product From Ramanujan - Featuring 3 Important Constants

Explore Ramanujan's fascinating product involving three crucial mathematical constants, uncovering its significance and implications in number theory.

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

Beyond Real Numbers - Solving X + 1 = 0 in Different Number Systems

Explore solutions to x² + 1 = 0 in various number systems, expanding mathematical understanding beyond real numbers and into complex realms.

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

A Wallis-Type Product for E

Explore a Wallis-type product representation for the mathematical constant e, delving into its derivation and significance in number theory and analysis.

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

Gamma Reflection via Double and Contour Integration

Explore gamma function reflection using double and contour integration techniques, enhancing understanding of complex analysis and special functions in mathematics.

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