Random Thoughts 8/n 💭

07.04.24

Well hello Tumblr,

Currently trying to do research for the summer as a student who has never done research before. Here I’m just attempting to dissect some code while writing down key points of the project and what steps I want to take.

I feel filming Timelapses on my iPhone is the only way for me to stop scrolling endlessly yknow?

Real-Life Uses of Calculus

Calculus isn’t just an abstract, ivory tower concept relegated to textbooks—it’s a powerful tool woven deeply into the fabric of our daily lives, from the precision of medical dosage to the unpredictability of the stock market.

1. Medicine: Optimizing Drug Dosage

Calculus plays a key role in pharmacokinetics, the branch of science that deals with the absorption, distribution, metabolism, and excretion of drugs in the body. When doctors prescribe medication, they need to ensure that drug levels remain within therapeutic bounds, not too high to cause toxicity and not too low to be ineffective. This is where differential equations, a core part of calculus, come into play. The rate of change of drug concentration over time is modeled with calculus to determine optimal dosage and scheduling for sustained, effective drug levels.

Take antibiotics, for example: they must be administered at specific intervals to maintain an effective concentration in the bloodstream while preventing bacterial resistance. Calculus allows for the continuous monitoring of drug levels and the adjustment of dosages based on individual metabolism rates, ensuring maximum therapeutic benefit.

2. Physics and Engineering: Motion and Forces

In classical mechanics, calculus is used to describe motion. Newton's laws of motion and universal gravitation are based on derivatives and integrals, the foundational elements of calculus. The change in velocity (acceleration) is the derivative of position with respect to time, while the area under the velocity-time graph gives us the distance traveled.

For instance, when designing cars, engineers use calculus to model the forces acting on the vehicle, such as friction, air resistance, and engine power. Calculus helps optimize everything from fuel efficiency to safety features, ensuring that a car can handle various conditions without exceeding performance thresholds.

3. Economics and Finance: Predicting Stock Market Trends

In economics, calculus is used to understand and predict market behavior. The concept of marginal analysis—examining the effects of small changes in variables—relies heavily on calculus. For example, marginal cost is the derivative of total cost with respect to quantity, and marginal revenue is the derivative of total revenue with respect to the quantity of goods sold.

In the stock market, calculus is utilized in quantitative finance to model stock prices using stochastic differential equations. Techniques like Black-Scholes for options pricing rely on calculus to determine the fair price of financial derivatives by analyzing how small fluctuations in stock prices impact their expected value. The concept of risk management—how much risk is worth taking for a given return—also uses derivatives to evaluate the rate of change of potential outcomes over time.

4. Environmental Science: Climate Modeling

Climate change models are inherently tied to calculus. Calculus is used to model the flow of energy through the Earth's atmosphere, oceans, and land, and how this energy affects global temperatures. The change in temperature over time is governed by differential equations, accounting for factors like greenhouse gas emissions, solar radiation, and ocean currents. As a result, climate scientists use calculus to predict future climate scenarios under various emission levels, helping inform policy decisions on global warming and sustainability.

5. Computer Science and Machine Learning: Optimization Algorithms

In machine learning, algorithms are designed to optimize a given function—whether it's minimizing the error in predictions or maximizing efficiency in a task. These algorithms often rely on derivatives to find the minimum or maximum of a function. For example, gradient descent, a popular optimization algorithm, uses the derivative of a function to iteratively adjust parameters and reach the optimal solution.

In computer graphics, calculus is essential for creating smooth curves and realistic animations. The mathematical process of curvature, which is the rate of change of direction along a curve, is vital for rendering images in 3D modeling and augmented reality.

6. Astronomy and Space Exploration: Orbital Mechanics

In space travel, calculus is crucial in calculating orbits, trajectories, and spaceship velocity. The path a spacecraft takes through space is influenced by gravitational forces, which can be modeled using calculus. For example, NASA’s mission to Mars relied on calculus to calculate the optimal launch window by accounting for the positions and motions of both Earth and Mars, ensuring the spacecraft would reach its destination efficiently.

/ Harry Gruyaert, Ireland, 1983-84

DO YOU LIKE BRAHMS? (2020) dir. Jo Young Min

ah yes, my favorite genre…yearning.

“I stopped explaining myself when I realized people only understand from their level of perception.”

— Unknown

Middle Term Diaries 1/n 💊🏫

house at midnight

02 July 2024

After finishing the laboratory reports that I assigned to myself, I reviewed for my midterm exam in Medicinal Organic Chemistry even though I felt lazy to review.

“But I love you like I love my homeland, I don't want to belong somewhere else.

But you love me exactly like you love your homeland,

You wish to fly away and never look back.”

— Ale

You're not grown until you know how to communicate, apologize, be truthful and accept accountability without blaming someone else.