3Blue1Brown
Solving the heat equation: Differential Equations - Part 3 of 5
Solving the heat equation.
3Blue1Brown
The Brachistochrone, with Steven Strogatz: Brachistochrone - Part 1 of 2
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
The Brachistochrone, with Steven Strogatz
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
Differential equations, studying the unsolvable | DE1
What is a differential equation, the pendulum equation, and some basic numerical methods
3Blue1Brown
Differential equations, studying the unsolvable: Differential Equations - Part 1 of 5
What is a differential equation, the pendulum equation, and some basic numerical methods
3Blue1Brown
But what is a partial differential equation? Differential Equations - Part 2 of 5
The heat equation, as an introductory PDE.
Professor Dave Explains
Numerical Methods for Solving Differential Equations
Solving differential equations can get pretty tricky, but in this modern age we have some tools that can be very useful. We can use computers to carry out sophisticated numerical methods that can solve any differential equation, no...
Professor Dave Explains
Power Series Solutions Part 1: Leibniz Method
One 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...
Professor Dave Explains
Power Series Solutions Part 2: Frobenius Method
We just learned how to solve differential equations using power series. However the simpler approached we used assumed that all the functions involved are infinitely differentiable at the point we are expanding about. This will not...
Curated Video
First Order Differential Equations - Simplified!
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
Exact First-Order Differential Equations
We've looked at a few simple examples of first-order differential equations and how to solve them. Now let's take a look at exact first-order differential equations.
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
Homogeneous Differential Equations and Bernoulli Differential Equations
We have covered three classes of first-order differential equations, those being separable, linear, and exact. There are just two more to go over, those being homogenous and Bernoulli differential equations. What are these, how do we...
Professor Dave Explains
Separable First-Order Differential Equations
Now that we know how to classify differential equations, we have to learn how to solve them. Let's start with the easiest ones to solve, separable first-order differential equations. This will involve some simple algebra and then basic...
Professor Dave Explains
Introduction to Differential Equations
After learning calculus and linear algebra, it's time for differential equations! This is one of the most important topics in mathematics, especially for those who are interested in physics and engineering, as these equations show up...
Flipping Physics
Charge and Current vs. Time in an RC Circuit
Explore the dynamics of RC circuits in this informative lesson. Unveil the charge and current as functions of time within an RC circuit. We dive into the Kirchhoff’s Loop Rule and differential equations to derive key insights. Witness...
Curated Video
How Do Physics-Informed Neural Networks Work?
Can physics help up develop better neural networks?
Virtually Passed
5.0 A better way to understand Differential Equations | Nonlinear Dynamics | Bendixson's Criterion
Bendixson's criterion is another method used to disprove the existence of closed orbits. A periodic solution is a type of closed orbit. This theorem only holds for simply connected regions in 2D. The statement is that if on a simply...
Virtually Passed
3.0 A better way to understand Differential Equations | Nonlinear Dynamics | Linearization
These second-order nonlinear differential equations can be written in the form: dx/dt = f(x,y) dy/dt = g(x,y) Got a nonlinear differential equation? No problem, just linearize it! This method approximates the vector field as a linear...
Virtually Passed
1.0 A better way to understand Differential Equations | Nonlinear Dynamics | 1D Linear Diff Eqns
Here we show another way to graphically interpret first order ordinary differential equations (ODE's) in the form dx/dt = f(x). Rather than solve the differential equation by integrating, which is often impractical, it's useful to graph...
Virtually Passed
3.1 Linearization PROOF | Nonlinear Dynamics
Nonlinear Dynamics mini-series Part 1: • 1.0 A better way ... Part 2: • 2.0 A better way ... Part 3: • 3.0 A better way ... This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find...
Virtually Passed
1.1 Stability of Fixed Points PROOF | Nonlinear Dynamics
This video deals with nonlinear differential equations in the form: dx/dt = f(x) To find out whether a fixed point is stable or not, a linear stability analysis is done whereby the function is approximated as a line. If the slope of that...
Zach Star
The applications of hyperbolic trig | Why do we even care about these things?
The applications of hyperbolic trig | Why do we even care about these things?
Flipping Physics
Electricity and Magnetism #2 Free Response Question Solutions - AP Physics C 1998 Released Exam
This Free Response Question includes the following concepts: Circuit Diagram, Voltmeter, Resistance, Capacitance, Inductance, Potential Difference, Charge, and Electric Potential Energy