3Blue1Brown
What does area have to do with slope? | Chapter 9, Essence of calculus
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
The paradox of the derivative | Essence of calculus, chapter 2
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
What they won't teach you in calculus
A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.
3Blue1Brown
e^(iπ) in 3.14 minutes, using dynamics | DE5
A quick explanation of e^(pi i) in terms of motion and differential equations
3Blue1Brown
What's so special about Euler's number e? | Essence of calculus, chapter 5
What is the derivative of a^x? Why is e^x its own derivative? This video shows how to think about the rule for differentiating exponential functions.
3Blue1Brown
Backpropagation calculus | Deep learning, chapter 4
The math of backpropagation, the algorithm by which neural networks learn.
3Blue1Brown
The paradox of the derivative: Essence of Calculus - Part 2 of 11
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
Backpropagation calculus | Appendix to deep learning chapter 3
The math of backpropagation, the algorithm by which neural networks learn.
3Blue1Brown
Higher order derivatives | Footnote, Essence of calculus
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Understanding e to the i pi: Differential Equations - Part 5 of 5
A quick explanation of e^(pi i) in terms of motion and differential equations
3Blue1Brown
Higher order derivatives: Essence of Calculus - Part 10 of 11
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Backpropagation calculus: Deep learning - Part 4 of 4
The math of backpropagation, the algorithm by which neural networks learn.
3Blue1Brown
Higher order derivatives | Essence of calculus, chapter 10
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
What does area have to do with slope? Essence of Calculus - Part 9 of 11
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
Limits, L'Hopital's rule, and epsilon delta definitions: Essence of Calculus - Part 7 of 11
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
The paradox of the derivative | Chapter 2, Essence of calculus
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
Limits | Chapter 7, Essence of calculus
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
Professor Dave Explains
Power Series Solutions Part 1: Leibniz Method
New ReviewOne technique for solving differential equations is to use power series. Hopefully we remember Maclaurin series and Taylor series from our study of calculus. These will actually have an important application here, as we can use infinite...
Curated Video
𝑮𝒊𝒗𝒆𝒏 𝒕𝒉𝒂𝒕 𝒚=𝟑𝒔𝒊𝒏𝟑𝒙+𝒄𝒐𝒔𝟑𝒙, 𝒑𝒓𝒐𝒗𝒆 𝒕𝒉𝒂𝒕 (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )=−𝟗𝒚
Welcome to our comprehensive series of Advanced High School Mathematics Tutorials! This series is perfect for students, teachers, and anyone looking to deepen their understanding of higher-level mathematics. Each video breaks down...
Curated Video
Learn how to use the Newton-Raphson method to find the root of an expression.
Welcome to our comprehensive series of Advanced High School Mathematics Tutorials! This series is perfect for students, teachers, and anyone looking to deepen their understanding of higher-level mathematics. Each video breaks down...
Professor Dave Explains
Classification of Differential Equations
Now that we know what differential equations are, we have to learn how to classify them. We have to know whether a DE is ordinary or partial, linear or nonlinear, homogenous or nonhomogenous, autonomous or nonautonomous. We have to be...
Professor Dave Explains
Linear Second-Order Differential Equations Part 1: Homogeneous Case
After a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these,...
Professor Dave Explains
Linear First-Order Differential Equations
We just got our feet wet with separable differential equations, so now let's look at something slightly trickier. Solving linear first-order differential equations will require a little bit more effort, involving something called an...