#calculus — Public Fediverse posts

You know you've reached peak academia when someone writes 1811 pages on how to make #calculus "simple" 😂. Spoiler: It's still calculus, and no amount of "refactoring" is gonna change that 📚🔢.
https://arxiv.org/abs/1811.03459 #peakacademia #humor #education #funnywriting #HackerNews #ngated

You know you've reached peak academia when someone writes 1811 pages on how to make #calculus "simple" 😂. Spoiler: It's still calculus, and no amount of "refactoring" is gonna change that 📚🔢.
https://arxiv.org/abs/1811.03459 #peakacademia #humor #education #funnywriting #HackerNews #ngated

You know you've reached peak academia when someone writes 1811 pages on how to make #calculus "simple" 😂. Spoiler: It's still calculus, and no amount of "refactoring" is gonna change that 📚🔢.
https://arxiv.org/abs/1811.03459 #peakacademia #humor #education #funnywriting #HackerNews #ngated

You know you've reached peak academia when someone writes 1811 pages on how to make #calculus "simple" 😂. Spoiler: It's still calculus, and no amount of "refactoring" is gonna change that 📚🔢.
https://arxiv.org/abs/1811.03459 #peakacademia #humor #education #funnywriting #HackerNews #ngated

You know you've reached peak academia when someone writes 1811 pages on how to make #calculus "simple" 😂. Spoiler: It's still calculus, and no amount of "refactoring" is gonna change that 📚🔢.
https://arxiv.org/abs/1811.03459 #peakacademia #humor #education #funnywriting #HackerNews #ngated

Simplifying and Refactoring Introductory Calculus

https://arxiv.org/abs/1811.03459

Comments: https://news.ycombinator.com/item?id=49306196

#HackerNews #calculus #education #refactoring #math #simplification #arxiv

Simplifying and Refactoring Introductory Calculus

https://arxiv.org/abs/1811.03459

Comments: https://news.ycombinator.com/item?id=49306196

#HackerNews #calculus #education #refactoring #math #simplification #arxiv

Simplifying and Refactoring Introductory Calculus

https://arxiv.org/abs/1811.03459

Comments: https://news.ycombinator.com/item?id=49306196

#HackerNews #calculus #education #refactoring #math #simplification #arxiv

Simplifying and Refactoring Introductory Calculus

https://arxiv.org/abs/1811.03459

Comments: https://news.ycombinator.com/item?id=49306196

#HackerNews #calculus #education #refactoring #math #simplification #arxiv

Simplifying and Refactoring Introductory Calculus

https://arxiv.org/abs/1811.03459

Comments: https://news.ycombinator.com/item?id=49306196

#HackerNews #calculus #education #refactoring #math #simplification #arxiv

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

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

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

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

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

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!
**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!
**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

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

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

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

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

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.

#Calculus #Limits #STEM #StudyNotes

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

📰 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

📰 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

📰 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

🎓🚀 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

🎓🚀 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

🎓🚀 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

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

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

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

Of course... that's so obvious!

#math #calculus