About This Track
Most people think calculus is hard because of how it's taught — as a parade of formulas with no intuition behind them. The best calculus podcast episodes flip that script. Instead of memorizing rules, you build genuine understanding: why the derivative measures the rate of change, what the integral is actually computing, and how these two ideas are secretly the same thing (the Fundamental Theorem of Calculus).
This track curates the clearest explanations of calculus from educators who have spent decades finding the right mental models. Sal Khan breaks down limits and continuity with the patience and precision that made Khan Academy famous. Grant Sanderson (3Blue1Brown) uses visual intuition to make derivatives and integrals feel obvious rather than arbitrary. Steven Strogatz connects calculus to the real world — from how Newton invented it to explain planetary motion, to how it governs everything from population growth to the spread of disease.
You don't need to be a math prodigy to understand calculus deeply. You need the right explanations in the right order — and these episodes provide exactly that. Whether you're a high school student preparing for the CLEP Calculus exam, a self-directed learner who gave up on textbooks, or a professional who uses calculus every day but wants to finally understand *why* it works, this track meets you where you are.
Each episode is sequenced so concepts build on each other: intuition first, formal definitions second, applications third. By the end, you won't just be able to use calculus — you'll understand it at a level most graduates never reach.
Curriculum
What you'll learn in this track
- Mathematical intuition behind limits and derivatives
- Integration and the geometry of change
- Differential equations applied to real-world problems
- Why calculus underlies physics, economics, and machine learning
All 10 Episodes
Every episode in this track
What IS a Number, Really?
Before calculus can make sense, you need to understand what numbers actually are—not as symbols on paper, but as abstract representations of quantity, measurement, and relationship. This episode dismantles the assumption that numbers are obvious and …
▶ Watch on YouTube — freeThe Essence of Limits
Limits are where arithmetic ends and calculus begins. This episode uses visual animations to show how the concept of "approaching but never reaching" transforms from a frustrating abstraction into an elegant tool. You'll see why limits aren't a techn…
▶ Watch on YouTube — freeLimits: The Analyst's Perspective
Where the visual approach to limits uses geometry, this episode takes the analyst's route: epsilon-delta definitions, squeeze theorems, and the formal machinery that makes calculus rigorous. It's less intuitive but more powerful—the version you need …
▶ Watch on YouTube — freeDerivatives Step by Step
A methodical, example-driven walkthrough of derivatives that prioritizes computation over theory. This episode is for learners who want to be able to solve derivative problems confidently before worrying about why the rules work. Practice first, intu…
▶ Watch on YouTube — freeDerivatives: The Geometry of Change
What does it mean for something to change at a single instant? This episode reframes derivatives not as formulas to memorize but as slopes of tangent lines—a geometric idea you can see and feel. The visual approach makes the chain rule, product rule,…
▶ Watch on YouTube — freeIntegration: Adding Up Infinity
Integration is the art of adding up infinitely many infinitely small things—and somehow getting a finite, meaningful answer. This episode builds integration visually as the area under a curve, connecting it to derivatives through the Fundamental Theo…
▶ Watch on YouTube — freeCalculus in the Wild
Calculus isn't a classroom exercise—it's the hidden language of motion, growth, and optimization running beneath everyday reality. This episode connects derivatives and integrals to population growth, GPS navigation, medical imaging, and climate mode…
▶ Watch on YouTube — freeDifferential Equations: Where Calculus Gets Serious
Differential equations are where calculus stops being a subject and starts being a tool. This episode introduces ODEs through physical intuition—springs, pendulums, and population models—showing how equations that describe rates of change can predict…
▶ Watch on YouTube — freeCategory Theory: The Mathematics of Mathematics
What if there were a branch of math that studied the patterns common to all other branches? Category theory abstracts away from numbers, shapes, and equations to focus on relationships and transformations themselves. This episode shows how thinking c…
▶ Watch on YouTube — freeStatistics Meets Calculus: The Central Limit Theorem
The central limit theorem is one of the most surprising results in all of mathematics: add up enough random things, and you always get the same bell curve, no matter what you started with. This episode connects calculus, probability, and statistics t…
▶ Watch on YouTube — freeGo Deeper
Explore Further
Recommended books to go beyond the podcast — handpicked for this track.
Calculus Made Easy
The classic 1910 text that demystifies calculus with plain English and wit. Gardner's edition adds modern context. If you can read, you can learn calculus.
Learn More →
The Joy of X
A guided tour through the hidden wonders of math — from calculus to chaos theory. Strogatz is the voice you hear in this track. This book is his love letter to math.
Learn More →
Infinite Powers
The story of calculus — how it was invented, what it revealed, and why it still runs the modern world. Science, history, and math in one deeply readable book.
Learn More →📎 Amazon affiliate links. Purchasing through them supports University of Podcasts at no extra cost to you.
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