Last revised on April 2023
Problems, Notes and Articles
Transduction and Element Synthesis Demo
This is a brief demo to short how transduction across domains can be used to create mechanical behavior using electric circuits. This idea, across various domains, along with the necessary mathematical rigor and empirical results, is the essence of the Modeling and Control course.
The Professional Education Policy Committee (PEPC) at MIT proposed various aspects of this course while I served as member along with Prof. Gill Pratt, who later designed the version that served as the basis of my own.
Changing Basis to Solve Problems in Engineering
This one-hour lecture directed to practicing engineers tries to both demystify and emphasize the importance of transformations to find solutions.
Electric Field from a Strip
I created this problem to illustrate the relationship between the dimension of the charge source and the field dependence on distance. This is an example of an added layer of abstraction in the solution where the student not only finds several solutions, but also finds the relationship between them.
Refrigerator in a Room Discussion
This is a typical interview problem used as an excuse to provide a thermodynamics refresher. The importance of the format and discussion is to understand the difference between empirical and analytical thinking.
Thermal Dynamics
This problem was motivated by a real-world application, and I wanted to illustrate the utility of simplifying a problem to more easily link the mathematical result with intuition.
Continued Fraction Approximations
Python script to find the closest rational approximations to any float, with examples for the Golden ratio φ ≈ 1.618, π ≈ 3.14159, √2 ≈ 1.4142, and Euler's constant e ≈ 2.718.
Afterwards, I found a similar post from the blog of Dr. John D. Cook—I highly recommend it! No doubt, there are likely many others that have solved this problem; I just couldn't find an complete solution when I needed it.
Weakly Quadratic Roots
A quadratic equation where the quadratic term is small is almost a line. What does the transition between a first and second order algebraic equation look like?
Smart Systems as a Catalyst for Local Innovation
This short talk makes the case for the introduction of microcontrollers in development to bridge the gap between information processing and the physical world. This is part of my efforts within IDDS and IDIN. I am also part of IDIN's introductory video, where we explain the philosophy of these programs.
I created this website in early 2023; if you spot errors, please feel free to let me know via email.