Financial analysis & decision-making tools Investment Optimization app📈 1:1 math tutoring (all levels) Optimization Tools LLC🎸✌️
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📐The Calculus of Falling Bodies
How can math explain motion under gravity?
This week's newsletter explores velocity, displacement, quadratic equations, and the domain of a falling body's height function.
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#Calculus #Physics #Mathematics
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Old friends are the best friends. Jensen rocks.
The Star Mind computer being co-engineered by SpaceX and Nvidia is far better than almost anyone expects and will reach volume production next year.
Working with the incredibly talented Nvidia engineering team is pure joy!
Jensen Huang says he loves working with Elon Musk, and reveals their engineering teams are designing a new type of server to put data centers in space
“I’m delighted that I love working with Elon. He’s using our technology for his own AI in training models and such, deploying models, of course."
"Grok Bot is super cool. The demand for Grok Bot, the consumption for Grok Bot is really skyrocketing. And then, of course, he rents it."
"And so the combination of these three things, he’s fairly unique in doing that. I guess Google does that. That would be yet another example."
"And so I think he also has the advantage that he loves the intersection between computing and the physical buildouts. He loves that whole area. Nobody knows more about energy than he does."
"One particular new market that we’re going to go explore together is putting data centers out in space. Our two engineering teams are working super closely together to create a new type of server, a new type of architecture that might be super good in space and on Earth.”
Bookkeeping can take up a lot of an accountant’s time.
At Optimization Tools, we’re building Investment Optimization to make it easier. Our AI helps individuals and businesses classify each financial entry, giving accountants more time to focus on their clients.
News today:
Sending warm prayers to Pope Leo XIV as he recovers from surgery for lung adenocarcinoma. Encouraging to hear he’s walking, eating, and celebrating Mass.🙏💜
Medical progress keeps bringing hope to once-daunting diagnoses. Wishing him strength and a speedy recovery.
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Remember this: The pain is all in your head.
If you want to evolve, you need to go where the problems and the pain are. By confronting the pain, you will see more clearly the paradoxes and problems you face. Reflecting on them and resolving them will give you wisdom.
The harder the pain and the challenge, the better. #principleoftheday
This week:
Finding a function’s domain and range. I use a square-root example to identify the allowed inputs, bound the outputs, and prove every value in the range is reached. One step closer to calculus.♾️
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How do you compute the derivative of x^x?
We use logarithms. Specifically, the natural logarithm.
Notice in the image that the domain is x∈(0, ∞), due to the properties of ln(x).♾️
News today:
In Athens, Rubio invoked the fierce individuality, ambition and spirit of discovery that helped shape the West. Greece’s democracy reminds us that power belongs with the people, not just a few. Greece and America are true allies.
World peace, not world terror.✌️🇺🇸🇬🇷
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THE FUTURE IS FUNDED. 🇺🇸
Trump Accounts are giving America's next generation a real stake in the American dream, & auto enrollment makes it happen.
70M accounts. $4.5B+ already deposited since July 4th. Claim your Trump Account to unlock the one-time $1,000 contribution. 💸
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Formation of conic sections ✍️
Circle: When the cutting plane is perpendicular to the axis of the cone, the cross-section is a circle.
Ellipse: When the plane is angled, but still cuts through only one cone (without being parallel to the side of the cone), the result is an ellipse.
Parabola: If the plane is parallel to the side (slant) of the cone, it creates a parabola.
Hyperbola: If the plane cuts both halves of the double cone, it forms a hyperbola - two separate curves.
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The curve y = ∛(x²) + 0.9 sin(kx)√(3 − x²) is a sine wave on |x| ≤ √3, carried by the cusp ∛(x²) and scaled by a semicircle.
Since |sin(kx)| ≤ 1, it never leaves the band between ∛(x²) − 0.9√(3 − x²) and ∛(x²) + 0.9√(3 − x²). Those two envelopes are the heart: lobes peaking at 2.27 near x = ±1.03, a point at −0.9√3 ≈ −1.56 on the axis.
Raising k only packs the wave tighter. At k = 100 it crosses the band about 110 times.
How do you find the highest and lowest values of a nonlinear function? This week’s newsletter walks through critical points, the second derivative test, and endpoint checks with a worked example.
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#Calculus #Math
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A real professor makes a simple problem look complicated, just to impress the students.😄
News today:
Protests over school conditions in France have included fires and clashes with police. We’ve seen protests turn destructive in the U.S. too. Peaceful protest is a right. Arson, looting and violence are unacceptable. Demand change without harming people.
Reliability is a valuable quality you can bring to a job.
Show up. Work hard. Follow through. Support your team. Take pride in what you do.
Most importantly, pair reliability with ethics.
Be someone others can trust and count on.
What does reliability mean to you?
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Today, with over 100 industry partners, we introduced the NVIDIA Open Agent Safety Platform, bringing together OpenShell and Sentry.
Artificial intelligence is extraordinary technology that will advance discovery, productivity, security, health, and prosperity for generations to come.
But its full promise can only be realized when people have confidence that AI is being built to be safe and deployed with wisdom and responsibility.
This is bigger than a single product. It's the beginning of an open ecosystem to build the trust layer for safe agent systems.
Together, we are building the foundation of the AI economy.
Trust and innovation are not in conflict. Safety is how trust is earned. We must build not only the most capable AI, but the most trusted AI, so that this extraordinary technology can realize its enormous promise for the world. nvda.ws/4hcoq7m
New newsletter:
Finding the Basis of the Null Space
We’ll go from Ax=0 to a basis for the null space, using RREF, parametrization, and linear combinations along the way.
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A twist is a rotation whose angle grows along its own axis: Tₓ(s) turns the point (x, y, z) about the x axis through the angle sx.
The face x = 0 stays put, each slice x = c turns rigidly through sc, and edges along the axis bend into helices. With s = cos θ and side 2, the far face swings through ±2 radians, about ±115°.
The map is not linear, yet its Jacobian has determinant 1 everywhere, so the twist keeps volume.