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What’s the Calculus
Whats-the-Calculus-Best-Of.mp3
Whats-the-Calculus-Best-Of.mp4
Whats-the-Calculus.mp3
Whats-the-Calculus.mp4
Whats-the-Calculus-Pt-2.mp3
Whats-the-Calculus-Pt-2.mp4
Whats-the-Calculus-Unplugged-Underground-XXVIII.mp3
Whats-the-Calculus-Unplugged-Underground-XXVIII.mp4
Whats-the-Calculus-intro.mp3
[Intro]
What is your calculus
(For the rest of us)
[Verse 1]
Why not put your dot
(… on a plot)
Does the point of view
(… start to skew)
[Bridge]
What is your calculus
(For the rest of us)
[Chorus]
Is it in a straight line
(“Everything will be fine”)
Or does it swerve and curve
(Equaling a mayday heyday)
[Verse 2]
Do your figures align
(… with reality)
There’s no straight line
(… to normality)
[Bridge]
What is your calculus
(For the rest of us)
[Chorus]
Is it in a straight line
(“Everything will be fine”)
Or does it swerve and curve
(Equaling a mayday heyday)
[Outro]
Quick!
(Watch that hockey stick)
Growth
(Intensity, Frequency — both)
This ain’t no straight line
(No, not at any time)
[Instrumental, Whistle Solo]
No, not a straight line
(Not aligned with fine)
Hey!
(It’s a mayday heyday)
ABOUT THE SONG AND THE SCIENCE
What is nonlinear calculus?
Nonlinear calculus refers to the branch of calculus that deals with nonlinear relationships — equations or systems where the output is not directly proportional to the input.
Examples of nonlinear behavior include:
Exponential growth/decay
Logistic curves
Chaos and strange attractors
Nonlinear differential equations
Climate feedback loops
Anything with powers, products, or functions of functions
In nonlinear systems, small changes in input can produce big, disproportionate changes in output, or vice versa. These systems often show:
feedback loops
tipping points
instability
multiple equilibria
exponential or polynomial scaling
chaotic behavior
This is why nonlinear calculus is central to climate science, economics, biology, engineering, and many real-world dynamic systems.
Is all calculus nonlinear?
No — but most of the natural world is.
Mathematically, calculus can be applied to:
1. Linear functions and linear systems
These obey strict proportionality
Derivatives and integrals behave predictably and additively.
Linear calculus is much simpler, and many early models in physics and economics relied on it.
2. Nonlinear functions and nonlinear systems
Anything that isn’t strictly linear is nonlinear Most real systems — weather, population growth, climate dynamics, biological systems, markets — are fundamentally nonlinear.
So what exactly is nonlinear calculus?
It’s not a separate field, but rather:
“The application of calculus to nonlinear functions and nonlinear differential equations.”
This includes:
Nonlinear differential equations
Nonlinear dynamical systems
Bifurcation theory
Chaos theory
Nonlinear optimization
Nonlinear PDEs (Navier–Stokes, climate models, etc.)
Multivariate nonlinear functions and Jacobians
In practice, nonlinear = complex, sensitive, coupled, and often unstable — which is why nonlinear calculus is the basis for modern climate modeling, turbulence, economics, ecosystems, etc.
Growth Curve
The shape that resembles a “hockey stick”—a curve that starts relatively flat and then suddenly turns upward very steeply—is typically referred to mathematically as an exponential curve or an exponential growth curve. In calculus, this shape is characteristic of an exponential function where the rate of growth accelerates over time. “Hockey stick” is an informal, descriptive nickname used in climate science to highlight the sudden and dramatic change observed.
From the album “Nonlinear“
View all episodes
By Whats-the-Calculus-Best-Of.mp3
Whats-the-Calculus-Best-Of.mp4
Whats-the-Calculus.mp3
Whats-the-Calculus.mp4
Whats-the-Calculus-Pt-2.mp3
Whats-the-Calculus-Pt-2.mp4
Whats-the-Calculus-Unplugged-Underground-XXVIII.mp3
Whats-the-Calculus-Unplugged-Underground-XXVIII.mp4
Whats-the-Calculus-intro.mp3
[Intro]
What is your calculus
(For the rest of us)
[Verse 1]
Why not put your dot
(… on a plot)
Does the point of view
(… start to skew)
[Bridge]
What is your calculus
(For the rest of us)
[Chorus]
Is it in a straight line
(“Everything will be fine”)
Or does it swerve and curve
(Equaling a mayday heyday)
[Verse 2]
Do your figures align
(… with reality)
There’s no straight line
(… to normality)
[Bridge]
What is your calculus
(For the rest of us)
[Chorus]
Is it in a straight line
(“Everything will be fine”)
Or does it swerve and curve
(Equaling a mayday heyday)
[Outro]
Quick!
(Watch that hockey stick)
Growth
(Intensity, Frequency — both)
This ain’t no straight line
(No, not at any time)
[Instrumental, Whistle Solo]
No, not a straight line
(Not aligned with fine)
Hey!
(It’s a mayday heyday)
ABOUT THE SONG AND THE SCIENCE
What is nonlinear calculus?
Nonlinear calculus refers to the branch of calculus that deals with nonlinear relationships — equations or systems where the output is not directly proportional to the input.
Examples of nonlinear behavior include:
Exponential growth/decay
Logistic curves
Chaos and strange attractors
Nonlinear differential equations
Climate feedback loops
Anything with powers, products, or functions of functions
In nonlinear systems, small changes in input can produce big, disproportionate changes in output, or vice versa. These systems often show:
feedback loops
tipping points
instability
multiple equilibria
exponential or polynomial scaling
chaotic behavior
This is why nonlinear calculus is central to climate science, economics, biology, engineering, and many real-world dynamic systems.
Is all calculus nonlinear?
No — but most of the natural world is.
Mathematically, calculus can be applied to:
1. Linear functions and linear systems
These obey strict proportionality
Derivatives and integrals behave predictably and additively.
Linear calculus is much simpler, and many early models in physics and economics relied on it.
2. Nonlinear functions and nonlinear systems
Anything that isn’t strictly linear is nonlinear Most real systems — weather, population growth, climate dynamics, biological systems, markets — are fundamentally nonlinear.
So what exactly is nonlinear calculus?
It’s not a separate field, but rather:
“The application of calculus to nonlinear functions and nonlinear differential equations.”
This includes:
Nonlinear differential equations
Nonlinear dynamical systems
Bifurcation theory
Chaos theory
Nonlinear optimization
Nonlinear PDEs (Navier–Stokes, climate models, etc.)
Multivariate nonlinear functions and Jacobians
In practice, nonlinear = complex, sensitive, coupled, and often unstable — which is why nonlinear calculus is the basis for modern climate modeling, turbulence, economics, ecosystems, etc.
Growth Curve
The shape that resembles a “hockey stick”—a curve that starts relatively flat and then suddenly turns upward very steeply—is typically referred to mathematically as an exponential curve or an exponential growth curve. In calculus, this shape is characteristic of an exponential function where the rate of growth accelerates over time. “Hockey stick” is an informal, descriptive nickname used in climate science to highlight the sudden and dramatic change observed.
From the album “Nonlinear“