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Why is the Lorentz Transformation Linear, and How is its Linearity Derived?
Have you ever wondered why can the physicists make the assumption that Lorentz transformation must be linear?
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Why are Phasors Introduced in Circuit Analysis, and What is the Physical Significance of Their Components?
Algebra, Circuit Analysis, Circuits, Differential Equation, Electromagnetism, Linear Algebra, Linear Time-Invariant, Mathematics, Phasor, Physics, ProofWhy are there imaginary numbers in current and voltage for circuit analysis??? Why phasor? Because the phasor method elegantly transforms the complex systems of differential equations that govern circuit behavior into much simpler systems of algebraic equations.
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My Fall 2025 U.S. Transfer Admissions Decisions (Undergraduate)
With no SAT score, no competition awards, and a dismal high school record, the rejections from top universities felt justifiable…. This is the story of how I overcame that past, found my academic purpose, and ultimately earned a place at my top-choice university.
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Intro to Generalized Coordinates
Ever wondered why we bother introducing “generalized coordinates” in analytical mechanics when Cartesian coordinates can also describe every state of a system under constraints?
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A Mathematical Exploration of the Virial Theorem
Ever wondered how a deep mathematical principle can govern the motion of stars and the behavior of gases? The Virial Theorem is a hidden gem that reveals these connections with an elegant identity equation!
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Recommendations for Rigorous Classical Mechanics Textbooks
As a student of pure mathematics, I have always sought rigor in my studies, especially in natural sciences like classical mechanics. If you’re like me, unsatisfied with textbooks that gloss over crucial foundational concepts, this post might resonate with you.
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Why Aren’t Generalized Coordinates in the Lagrangian Equation Considered Functions of Time?
Ever wondered why generalized coordinates in the Lagrangian formulation are treated as independent of time, despite their obvious connection?
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A Mathematical Exploration of Norton’s Dome and Determinism in Classical Mechanics
Chinese, Classical Mechanics, Differential Equation, Introduction, Latex, Mathematics, Paradox, PhysicsIn classical mechanics, the principle of determinism states that the motion of a system is fully predictable given its initial conditions. However, does this principle always hold?
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Why Use L2 Norm Instead of L1 Norm in Loss Functions?
Algebra, Computer Science, Deep Learning, Latex, Likelihood, Machine Learning, Mathematics, Optimization, Probability, Probability Theory, Regression Analysis, StatisticsHave you guys noticed that, in machine learning, MSE is often the preferred choice…
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Intro to Git, Github and VSCode
Hi, this is Louis Liu. In this tutorial, I will guide you through some basic operations in Git, GitHub, and VSCode.
