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MADifferentiation formula sheet #differentiation #viralreels #maths #simplify
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#Finite Difference Method
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UMThe simulation models the two-dimensional propagation of waves on a square grid using the classical finite-difference method. The physical field is updated in time using previous and current states, producing a stable approximation of the wave dynamics. The initial condition is a Gaussian pulse placed at the center of the domain, which naturally expands and forms a circular wavefront. The code is written in traditional Fortran 77 using fixed-format style and simple array loops for performance and clarity. At each output step, the program writes a data file containing x, y, and amplitude values arranged in blocks compatible with gnuplot. These files can be visualized using gnuplot’s pm3d mode to create smooth color maps or surface plots. A sequence of frames is produced and saved as frame0001.dat, frame0002.dat, and so on. Gnuplot can then load these frames to generate individual images. Finally, the images can be combined into an mp4 animation using ffmpeg, creating a clear visualization of the evolving wave.
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WIFEA (Finite Element Analysis) series coming soon!
In this series we’ll go over how we use @simscale_ to check the structural integrity of each component - to ensure our final design is road worthy. 🏎️ 🔥
Next, we’ll use the results to slim down parts of the vehicle where needed and optimize our final build.
It’s a super fun, and slightly nerdy, process. But it makes all the difference before starting a build.
Follow along if you want to learn more!
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MENodal analysis breaks complex heat transfer into solvable temperature nodes using thermal circuits. Stan explains how this technique helps engineers model conduction, convection, and more.
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MA✨️video’s Manim code Link in bio- easy, fully explained & customizable.
Differentiation Made Simple! ✨️
In mathematics, differentiation is the process of finding the derivative of a function — the measure of how fast something changes. 🚀 It’s the foundation of calculus, showing us the instantaneous rate of change and the slope of a curve at a point. From velocity in physics to growth rates in economics, differentiation is everywhere. 🌍
👉 Why it matters:
✅ Understand how curves behave at every point.
✅ Learn why derivatives = slopes of tangents.
✅ See how the limit definition connects secant lines to tangents.
✅ Build stronger intuition for solving real-world problems.
🌟 Whether you’re studying for AP Calculus (US), A-Level Maths (UK), IB Math, or university-level engineering & science courses, mastering differentiation will unlock higher-level math and problem-solving. Perfect for exam prep, competitive exams, and self-study.
💡 Differentiation is not just for exams — it’s the language of physics, engineering, computer science, data science, economics, and AI. Once you understand it, you see change everywhere!
🚀 If you’ve ever wondered “how fast is this changing right now?” — that’s differentiation in action.
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UK✅️ Follow us ✅️ Comment your thoughts!
FDTD (Finite-Difference Time-Domain) is a powerful numerical method used to simulate the behavior of electromagnetic fields. By dividing the simulation space into a grid and updating the fields at each time step, FDTD can accurately model various phenomena, including antenna design, microwave circuits, and optical devices. While computationally demanding for large-scale simulations, FDTD's versatility and accuracy make it an indispensable tool in fields such as engineering and physics.
#FDTD #simulation #electromagnetic #fields #Maxwell #equations #numerical #technique #antenna #design #microwave #circuits #EMC #biomedical #engineering #optical #devices #software #visualization #computational #cost #numerical #dispersion
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AL2D FINITE-DIFFERENCE 📈
In the previous post, the approach of 1-Dimensional Finite-Difference was discussed. Can this be extended to 2-Dimensions? YES!
As discussed Finite-Difference is a technique of solving Differential Equations, that interprets derivatives as telling the solution how to change from one point to the next. If you chop up the region you are solving into a grid, you can get equations at every point, of how the solution at *this* point, depends on the solution at the points around it. These look like linear equations, and so you can solve all of these equations together, and get an approximate solution to the equation! In 2-dimensional finite-difference, these linear equations don't only depend on the point ahead and behind, but also the points to the left and right of the point you care about!
Notice how as the number of dots increases, the FD solution (in the wireframe) approaches the exact solution (the transparent overlay).
Music (🎶): "Ajar" - Mike Lazarev ( @lazarevplays)
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STDeterminant in linear algebra #familyguy #computerscience #maths
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EQ➡️ Day-90/500 of Visual Interpretations of Mathematics: 🇮🇳 🌟
➡️ Experience India's 1st-ever visualization of differentiation as a limit! Witness the fundamental derivation come to life with unparalleled clarity and understanding. See how the concept unfolds visually, making it simpler than ever to grasp. Unlock a whole new perspective on differentiation! 🚀📈
➡️ Follow @equationacademy for more
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#python #pythonprogramming#viralvideos #viralreels #trendingreels #trending #differentiation#calculus#exponential#limit
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THDerivative Explained
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❤️ Follow @thevisualmaths for more Cool Math animation
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ME🔹 Negative Determinant in 3D
In linear algebra, a linear transformation f: V → V between vector spaces can be represented by a matrix once we fix an input basis B1 and an output basis B2.
The notation M(f, B1, B2) denotes the matrix of f with respect to these bases.
How is it built?
Take each vector of the input basis B1 = {v1, v2, v3}.
Compute its image: f(v1), f(v2), f(v3).
Express each image in coordinates with respect to the output basis B2.
Place these coordinate vectors as the columns of the matrix.
So M(f, B1, B2) encodes, column by column, the coordinates of the images of the basis vectors of B1.
If we use the same basis for both input and output (for example, the canonical basis B of R³), then M(f, B, B) directly tells us the transformed vectors in the same coordinate system.
In the example we are visualizing:
The vector e1 (the x-axis unit vector) remains unchanged.
The vector e3 (the z-axis unit vector) also remains unchanged.
The vector e2 (the y-axis unit vector) flips direction: from (0,1,0) to (0,−1,0).
This creates a very typical situation:
The parallelepiped generated by {f(e1), f(e2), f(e3)} has the same volume as that generated by {e1, e2, e3}.
But the orientation changes: the cyclic order of the vectors no longer follows the right-hand rule, but instead the left-hand rule.
👉 The determinant captures exactly this:
If det > 0, the orientation of the basis is preserved.
If det < 0, the orientation is reversed.
In this case, det(M(f,B,B)) < 0, which tells us the transformation preserves volume but flips orientation, just like a reflection in a mirror.
#math #maths #physics #merlinomath
@merlinomaths
✨ Руководство по #Finite Difference Method
Instagram содержит 250+ публикаций под #Finite Difference Method, создавая одну из самых ярких визуальных экосистем платформы.
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