Hardware and Systems Engineering Essentials: From Circuit to Machine Learning 


Basic principles in electrical and systems engineering are essential for understanding a broad spectrum of technologies, from electrical system design to signals and linear system processing, probabilistic modeling, and machine learning systems. Rooted in foundational concepts from physics, mathematics, probability and statistics, and computer science, these principles find applications in traditional domains like digital and analog signal processing in consumer electronics. They are also increasingly relevant in emerging fields such as hardware-software systems and modern data science. The purpose of this overview is not just to introduce these key theories and principles, but to foster a deeper engineering intuition. By exploring these fundamental concepts, we aim to enhance first-principles thinking, equipping engineers and practitioners with the insights needed to analyze component behavior, system analysis techniques, and the underlying logic that governs complex systems. Whether the focus is on electronic circuits, signal processing, data science, or machine learning models, a first-principles understanding will be invaluable in tackling real-world engineering challenges 


Scalar vs. Vector Value 

Positive vs. Negative Feedback 

System Response & Stability 

Dot Product vs Cross Product 

Transformer Dot Convention  

Maxwell Equation Teardown 

Proximity Effect 

Skin Effect 

Fourier Transform vs. Lapace Transform 

Linear Time Invariant System 

Linearity vs. Flatness 

Lorentz force 

Lenz's Law 


Negative Resistance 


I/V Curve 

Regulated vs Unregulated Output 

Common Mode vs Differential Mode Signals 

Transmission Line Effect 

Transformer vs. Coupled Inductor 

Independent and Identically Distributed Random Variables (i.i.d) 

FIR vs IIR Digital Filter  

Signal Processing 

Foundation of the Study of Linear Algebra and Functional Analysis 

Machine Learning and Data Science