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TA

Team Aquin

Ash, Paul, Sambhav

A
Ash

Yo sup ppl, did you guys try out cursor follow in production?

3:00 AM
P
Paul

Yeah! It's working amazing. We should make more posts about it!!!

3:02 AM
S
Sambhav

Lets make a list of posts, they better be 🔥

3:03 AM
A
Ash

Let's schedule a call to discuss implementation

10:28 AM
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Write Aquin's Context

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Context Window2m ago
Research Notes1h ago

Write Aquin's Context

What if you yourself could write complete context for AI?
Instead of uploading and attaching files, tabs etc again and again and again.
Think of it as notes but with purpose of providing plenty of accurate relevant or maybe not relevant context to AI.
Now obviously you cant just write so much (that would be kind of lame)
Ergo, we have all kinds of integrations from google services, maps, X, spotify, youtube, code files, browser tabs, urls and so much more!
We like to call these notes as "Context Windows"
Continue to scroll to view applications and all features!

Calculus Research & Study Materials

Differential Calculus - Fundamental Concepts

Starting with the foundational definition of limits and continuity. This textbook chapter covers epsilon-delta proofs:
Limits-and-Continuity-Chapter3.pdf
Found an excellent article explaining the historical development of calculus from Newton and Leibniz:
The History and Development of Calculus
MIT OpenCourseWare lecture notes on derivatives are incredibly detailed:
MIT 18.01 Single Variable Calculus

Derivative Rules & Applications

Visual representation of the derivative as the slope of tangent line. This diagram really helps illustrate the concept:
tangent-line-derivative.png
My notes on chain rule, product rule, and quotient rule derivations:
Derivative-Rules-Notes.pdf

Code Implementations - Differentiation

Python implementation for numerical differentiation using finite differences:
Code
python
1def numerical_derivative(f, x, h=1e-5):
2    """Calculate derivative using central difference method"""
3    return (f(x + h) - f(x - h)) / (2 * h)
4
5# Example: derivative of x^2 at x=3
6result = numerical_derivative(lambda x: x**2, 3)
7print(f"Derivative at x=3: {result}")  # Should be ~6
3Blue1Brown has the best visual explanation of derivatives I've ever seen:
Wolfram MathWorld reference on derivative definitions and properties:
Derivative - Wolfram MathWorld
Symbolic differentiation implementation using sympy:
Code
python
1from sympy import symbols, diff, sin, cos, exp
2
3x = symbols('x')
4# Define function
5f = x**3 + 2*x**2 - 5*x + 1
6# Calculate derivative
7f_prime = diff(f, x)
8print(f"f'(x) = {f_prime}")  # 3x^2 + 4x - 5
Paul's Online Math Notes - comprehensive calculus resource:
Calculus I - Paul's Online Math Notes

Integral Calculus - Integration Fundamentals

The Fundamental Theorem of Calculus connects differentiation and integration. This paper provides rigorous proofs:
Fundamental-Theorem-Proof.pdf
Collection of integration techniques - substitution, parts, partial fractions:
Integration-Techniques-Guide.pdf

Study Resources

This lo-fi study playlist helps me focus while working through integration problems:
Saw this fascinating thread about the beauty of calculus and its real-world applications:
Interactive Desmos graph showing Riemann sums and definite integrals:
Riemann Sums Visualization

Real-World Applications

Physics problem set using integration for kinematics and dynamics:
Physics-Calculus-Problems.pdf
Research paper on using calculus to model population growth and decay:
Population-Models-Calculus.pdf
Numerical integration code using Simpson's rule:
Code
python
1def simpsons_rule(f, a, b, n=100):
2    """Approximate integral using Simpson's Rule"""
3    if n % 2 == 1:
4        n += 1  # Must be even
5    h = (b - a) / n
6    x = [a + i*h for i in range(n+1)]
7    y = [f(xi) for xi in x]
8    
9    integral = y[0] + y[-1]
10    integral += 4 * sum(y[i] for i in range(1, n, 2))
11    integral += 2 * sum(y[i] for i in range(2, n-1, 2))
12    integral *= h / 3
13    
14    return integral

Multivariable Calculus & Advanced Topics

Lecture notes on partial derivatives and gradient vectors from Calc III:
Partial-Derivatives-Notes.pdf
Vector calculus textbook covering divergence, curl, and line integrals:
Vector-Calculus-Textbook.pdf

Study Location & Resources

Planning to visit San Francisco for a mathematics conference. Location saved here:
Interactive 3D graphing calculator for multivariable functions:
Research paper on applications of calculus in computer graphics and physics engines:
Calculus-in-Computer-Graphics.pdf
Implementing gradient descent optimization in Python:
Code
python
1import numpy as np
2
3def gradient_descent(f, grad_f, x0, learning_rate=0.01, iterations=1000):
4    """Minimize function using gradient descent"""
5    x = x0
6    history = [x]
7    
8    for i in range(iterations):
9        gradient = grad_f(x)
10        x = x - learning_rate * gradient
11        history.append(x)
12    
13    return x, history
14
15# Example: minimize f(x) = x^2
16result, path = gradient_descent(
17    lambda x: x**2,
18    lambda x: 2*x,
19    x0=5.0
20)
21print(f"Minimum found at x = {result}")
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