#calculus — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #calculus, aggregated by home.social.
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Alright, future engineers!
**Mean Value Theorem:** For continuous, differentiable `f` on `[a,b]`, there's a `c` where `f'(c)` equals the avg rate of change.
Ex: `f'(c) = (f(b)-f(a))/(b-a)`
Pro-Tip: Guarantees a tangent line parallel to the secant line!
#Calculus #MVT #STEM #StudyNotes -
Alright, future engineers!
**Derivative:** The instantaneous rate of change of a function, or the slope of the tangent line at any point.
Ex: If `f(x)=x^2`, then `f'(x)=2x`.
Pro-Tip: Always think slope! It reveals how fast something is changing *right now*.
#Calculus #Derivatives #STEM #StudyNotes -
Alright, future engineers!
**Limit:** The value a function *approaches* as its input gets infinitely close to a point.
Ex: `lim (x->2) (x+1) = 3`.
Pro-Tip: It's about the value *near* the point, not necessarily *at* it! Crucial for derivatives.
#Calculus #Limits #STEM #StudyNotes -
Alright, future engineers!
**Indefinite Integral:** The reverse of differentiation; finding the function whose derivative is given.
Ex: `int(2x dx) = x^2 + C`
Pro-Tip: Don't forget the `+C`! It represents any constant that vanished during differentiation.
#Calculus #Integration #STEM #StudyNotes -
Alright, future engineers!
**Derivative (f'(x)):** Instantaneous rate of change of `f(x)` or slope of its tangent line.
Ex: `d/dx(x^n) = nx^(n-1)` (Power Rule!)
Pro-Tip: Essential for analyzing motion, optimization, and system responses.
#Calculus #MathSkills #STEM #StudyNotes -
Alright, future engineers!
**FTC:** The link between differentiation & integration.
Ex: `int[a,b] f'(x)dx = f(b) - f(a)`.
Pro-Tip: It's the bridge from rates of change to total accumulation. Crucial for definite integrals!
#Calculus #Integrals #STEM #StudyNotes -
Alright, future engineers!
**Numerical Integration:** Approximates definite integrals (area under curve) when exact solutions are tough.
Ex: Trapezoidal Rule for `[a,b]` is `h/2 * (f(a) + f(b))` for one segment.
Pro-Tip: Smaller step size `h` = greater accuracy (but more computation)!
#NumMethods #Calculus #STEM #StudyNotes -
Alright, future engineers!
**Fundamental Theorem of Calculus:** The foundational link between differentiation and integration.
Ex: `∫_a^b f'(x) dx = f(b) - f(a)`
Pro-Tip: It's why we can use antiderivatives to easily solve definite integrals! Super powerful!
#Calculus #FTC #STEM #StudyNotes -
**Limit:** The value a function approaches as its input gets arbitrarily close to a specific number.
Ex: `lim x->0 (sin(x)/x) = 1`.
Pro-Tip: Limits allow us to define instantaneous change & area – they are the foundation that makes all of calculus possible!
#Calculus #LimitsFoundations #STEM #StudyNotes -
**Optimization:** Finding max/min values of a function to solve problems.
Ex: Maximize structural strength or minimize material cost. Set `f'(x)=0`.
Pro-Tip: Always check domain endpoints & critical points for global extrema!
#Calculus #EngrHacks #STEM #StudyNotes -
Alright, future engineers!
**Definite Integral:** The net accumulation of a quantity, or the signed area under a curve between two points.
Ex: `int_a^b f(x) dx`
Pro-Tip: Think 'total change' of a rate. Crucial for finding displacement from velocity!
#Calculus #Maths #STEM #StudyNotes -
Alright, future engineers!
**Definite Integral:** The net accumulation of a quantity, or the signed area under a curve between two points.
Ex: `int_a^b f(x) dx`
Pro-Tip: Think 'total change' of a rate. Crucial for finding displacement from velocity!
#Calculus #Maths #STEM #StudyNotes -
Grazie a Mr. Bundus è stato creato un nuovo software per Commodore 128: addirittura un Computer Algebra System con cui calcolare derivate, integrali, disegnare grafici (con il Webge80 di Graham , risolvere equazioni ordinarie e differenziali. Ed ora anche trasformate di Laplace e antitrasformate. #commodore128 #calculus #basic https://www.youtube.com/watch?v=Pn0-I941iMc
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Alright, future engineers!
**Limit:** What a function's output *approaches* as its input gets infinitesimally close to a specific value.
Ex: `lim (x->0) (sin x)/x = 1`
Pro-Tip: A limit can exist even if the function isn't defined at that exact point. It's about the *tendency*!
#Calculus #Maths #STEM #StudyNotes -
Alright, future engineers!
**Limit:** What a function's output *approaches* as its input gets infinitesimally close to a specific value.
Ex: `lim (x->0) (sin x)/x = 1`
Pro-Tip: A limit can exist even if the function isn't defined at that exact point. It's about the *tendency*!
#Calculus #Maths #STEM #StudyNotes -
Alright, future engineers!
**Trapezoidal Rule:** Approximates definite integrals by summing areas of trapezoids under the curve.
Ex: Integral approx `h/2 * (f(x0)+2f(x1)+...+f(xn))`
Pro-Tip: Simple, but accuracy improves with more intervals (smaller 'h')!
#NumericalIntegration #Calculus #STEM #StudyNotes -
Alright, future engineers!
**Limit:** The value a function approaches as its input gets arbitrarily close to a specific point.
Ex: `lim x->0 (sin(x)/x) = 1`
Pro-Tip: The function doesn't even need to be defined *at* that point for the limit to exist!
#Calculus #Limits #STEM #StudyNotes -
Alright, future engineers!
**Derivative:** The instantaneous rate of change of a function. It's the slope of the tangent line at any point.
Ex: `d/dx(x^2) = 2x`
Pro-Tip: Essential for finding max/min values, velocity from position, and understanding sensitivity!
#Calculus #Derivatives #STEM #StudyNotes -
Alright, future engineers!
**Definite Integral:** Calculates the *net area* under a curve over a specific interval [a,b].
Ex: `∫[a,b] f(x) dx`
Pro-Tip: Think of it as summing infinitely many tiny rectangles! Great for total accumulation.
#Calculus #Integration #STEM #StudyNotes -
Grazie a Mr.Bundus è stato creato un nuovo software per Commodore 128: addirittura un Computer Algebra System con cui calcolare derivate, integrali, disegnare grafici (con il Webge80 di Francesco Gramignani), risolvere equazioni ordinarie e differenziali. Ed ora anche limiti e sviluppi in serie. #commodore128 #calculus #basic https://www.youtube.com/watch?v=zYNKIQ-rg6U
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Grazie a Mr.Bundus è stato creato un nuovo software per Commodore 128: addirittura un Computer Algebra System con cui calcolare derivate, integrali, disegnare grafici (con il Webge80 di Francesco Gramignani), risolvere equazioni ordinarie e differenziali. Ed ora anche limiti e sviluppi in serie. #commodore128 #calculus #basic https://www.youtube.com/watch?v=zYNKIQ-rg6U
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Alright, future engineers!
**Derivative:** The instantaneous rate of change of a function. It's the slope of the tangent line at any point.
Ex: If `f(x)=x^2`, then `f'(x)=2x`.
Pro-Tip: It's how fast something is changing *at that exact moment*. Crucial for optimization!
#Calculus #RatesOfChange #STEM #StudyNotes -
Alright, future engineers!
**Limit:** What a function's output *approaches* as its input gets closer to a specific point.
Ex: `lim x->2 (x+1) = 3`.
Pro-Tip: It's about what it *wants* to be, not always what it *is* at that exact point. -
Alright, future engineers!
**Integral:** The total accumulation or 'area under the curve' of a function.
Ex: `int x dx = x^2/2 + C`.
Pro-Tip: Essential for finding total quantities or total change from a rate!
#Calculus #Integration #STEM #StudyNotes -
Alright, future engineers!
**Derivative:** The instantaneous rate of change of a function. It's the slope of the tangent line!
Ex: `f(x)=x^2`, then `f'(x)=2x`. At `x=3`, slope is `6`.
Pro-Tip: Think how fast is it changing *right now*?
#Calculus #Derivatives #STEM #StudyNotes -
📰 Hacker News
📢 LLM-Integrated Multivariable Calculus Course
🔗 https://calculus.academa.ai/
#Llm-integrated #Multivariable #Calculus #Course #GlobalFeed #News #EN
Automatically posted by Global Feed Bot
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📰 Hacker News
📢 LLM-Integrated Multivariable Calculus Course
🔗 https://calculus.academa.ai/
#Llm-integrated #Multivariable #Calculus #Course #GlobalFeed #News #EN
Automatically posted by Global Feed Bot
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🎓🚀 Oh look, another #calculus #lecture series with fancy acronyms and more numbers than a phone book! Because clearly, the world needs another complex way to say "math is hard" and "let's add #AI to make it confusing" 🤖📚.
https://calculus.academa.ai/ #math #education #complexity #HackerNews #ngated -
🎓🚀 Oh look, another #calculus #lecture series with fancy acronyms and more numbers than a phone book! Because clearly, the world needs another complex way to say "math is hard" and "let's add #AI to make it confusing" 🤖📚.
https://calculus.academa.ai/ #math #education #complexity #HackerNews #ngated -
Grazie a Mr. Bundus è stato creato un nuovo software per Commodore 128: addirittura un Computer Algebra System con cui calcolare derivate, integrali, disegnare grafici (con il Webge80 di Graham), risolvere equazioni ordinarie e differenziali. #commodore128 #calculus #basic https://www.youtube.com/watch?v=GiPwJTzjAgI
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Find the area under the curve of the hippopotamus defined by the equations...
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Alright, future engineers!
**Newton-Raphson:** Iteratively finds roots by using tangent lines to refine guesses.
Ex: `x_new = x_old - f(x_old) / f'(x_old)`.
Pro-Tip: A good initial guess is CRUCIAL for convergence. Bad ones can lead to divergence!
#NumMethods #Calculus #STEM #StudyNotes -
Alright, future engineers!
**Trapezoidal Rule:** Approximates definite integrals by summing areas of trapezoids under the curve.
Ex: Area of one segment `0.5 * h * (f(a) + f(b))`.
Pro-Tip: Smaller step size 'h' dramatically boosts accuracy! More segments = better estimate.
#NumMethods #Calculus #STEM #StudyNotes -
Alright, future engineers!
**Derivative:** Instantaneous rate of change of a function at a point (slope of its tangent line).
Ex: For `f(x)=x^2`, `f'(x)=2x`.
Pro-Tip: It's *how fast* something is changing at that exact moment! Think velocity.
#Calculus #Derivatives #STEM #StudyNotes -
🚀 Ah, the noble quest for Differentiable Fortran, because someone thought, "Why not bring #calculus to Fortran in 2023?" ⚗️ Meanwhile, #Tesseract keeps vomiting out buzzwords like an overzealous tech bro at a crypto convention. 🌐
https://docs.pasteurlabs.ai/projects/tesseract-core/latest/blog/2026-07-09-enzyme-lfortran-autodiff.html #DifferentiableFortran #TechBuzzwords #Fortran2023 #HackerNews #ngated -
🚀 Ah, the noble quest for Differentiable Fortran, because someone thought, "Why not bring #calculus to Fortran in 2023?" ⚗️ Meanwhile, #Tesseract keeps vomiting out buzzwords like an overzealous tech bro at a crypto convention. 🌐
https://docs.pasteurlabs.ai/projects/tesseract-core/latest/blog/2026-07-09-enzyme-lfortran-autodiff.html #DifferentiableFortran #TechBuzzwords #Fortran2023 #HackerNews #ngated -
Alright, future engineers!
**Mean Value Theorem (MVT):** For a smooth, continuous curve, there's a point where instantaneous slope equals average slope over an interval.
Ex: `f'(c) = (f(b) - f(a)) / (b - a)`
Pro-Tip: Tangent at `c` is parallel to the secant line connecting the endpoints!
#Calculus #MVT #STEM #StudyNotes -
Find the Taylor series around x=1 for f(x)=2-x. Simplify your answer.
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🚁🧠 Ah yes, the thrilling world of drone physics, where you too can transform your weekend hobby into an endless maze of equations and jargon! 🤓✨ Perfect for those who've always dreamed of mixing #calculus with their drone flying, because who wouldn't want to spend their free time reconciling inertial frames? 📉😂
https://iahmed.me/post/drone-physics/ #dronephysics #hobbyist #physicsfun #aerialdrones #weekendprojects #HackerNews #ngated -
🤡 Oh, look! Yet another tech blog trying to dazzle us with the groundbreaking revelation that #synthesis is hard! 🚀 Thanks for the newsflash, Captain Obvious! Meanwhile, back in reality, mathematicians and #computer scientists have been wrestling with this since before you could say "lambda calculus"! 🧐
https://surfingcomplexity.blog/2026/07/03/synthesis-is-harder-than-analysis/ #techblog #science #lambda #calculus #math #humor #HackerNews #ngated -
Not a calculus 1 tutor. No, no, no.
Not a calculus 2 tutor. No, no, no.
A calculus 3 tutor.
At $12/h.
:why:
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Frenet–Serret Formula ✍️
It explains how a curve reveals its hidden geometry by tracking the way it bends and twists through space. Imagine tracing the path of a roller coaster, a winding river, or the spiral of a DNA strand. At every point along the path, the curve is constantly changing direction, and the Frenet–Serret formulas provide a precise way to describe that change.
They do this by attaching a moving frame of three special directions to each point on the curve. The first points forward along the path, showing where the curve is heading. The second points inward, toward the direction of bending. The third stands perpendicular to both, capturing how the curve twists out of its plane. Together, they form a local coordinate system that travels with the curve itself.
As you move along the curve, these three directions rotate and evolve. The formulas measure this evolution using two key quantities: curvature and torsion. Curvature tells how sharply the path bends, while torsion tells how strongly it twists into three dimensions. If curvature vanishes, the path becomes straight; if torsion vanishes, the curve lies flat in a plane.
Mathematicians and physicists use the Frenet–Serret formulas to study motion, design smooth paths in engineering, understand particle trajectories, and analyze natural shapes. They transform a simple line into a rich geometric story, revealing exactly how space is being navigated at every step.
#FrenetSerretFormula #DifferentialGeometry #Geometry #Mathematics #Math #PureMathematics #AppliedMathematics #MathematicalPhysics #Physics #STEM #ScienceEducation #MathEducation #Curvature #Torsion #SpaceCurves #VectorCalculus #Calculus #LinearAlgebra #GeometricAnalysis
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Grazie ad Andrea, proviamo un aggiornamento del programma in BASIC v7 del Commodore 128 che ora calcola anche derivate e integrali di funzioni elementari in modo simbolico. #commodore128 #basic #calculus https://www.youtube.com/watch?v=Z0id4ClG07E
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Alright, future engineers!
**Limit:** The value a function *approaches* as its input gets closer to a specific point.
Ex: `lim x->0 of sin(x)/x = 1`.
Pro-Tip: Even if the function isn't defined *at* the point, the limit can still exist! It's fundamental for understanding continuity.
#Calculus #Limits #STEM #StudyNotes -
Alright, future engineers!
**Derivative:** Measures a function's instantaneous rate of change—the slope of its tangent line at any point.
Ex: If `f(x) = x^2`, its derivative `f'(x) = 2x`.
Pro-Tip: It's vital for finding maximum/minimum values & understanding how sensitive systems are to input changes!
#Calculus #Derivatives #STEM #StudyNotes -
Alright, future engineers!
**Product Rule:** Differentiates the product of two functions.
Formula: `(uv)' = u'v + uv'`
Pro-Tip: It's NOT just `u'v'`! Each function gets a turn being differentiated while the other stays put. -
Alright, future engineers!
**Chain Rule:** Differentiates composite functions (function within a function).
Ex: `d/dx sin(x^2) = cos(x^2) * 2x`.
Pro-Tip: Always differentiate outside in!
#Calculus #Differentiation #STEM #StudyNotes -
Alright, future engineers!
The **Intermediate Value Theorem (IVT)** says a continuous function `f` on `[a,b]` takes every value between `f(a)` & `f(b)`.
Ex: If `f(0)=1, f(2)=5`, then some `x` in `[0,2]` has `f(x)=3`.
Pro-Tip: Use it to prove a root *exists*!
#Calculus #Theorem #STEM #StudyNotes -
Alright, future engineers!
**Optimization:** Using derivatives to find the max or min value of a function (e.g., max volume, min cost).
Ex: Set `f'(x) = 0` to find critical points.
Pro-Tip: Don't forget to check *endpoints* of your interval too, not just critical points!
#Calculus #Optimization #STEM #StudyNotes