Johan’s Theoretical Math

I love math. Math proves the theorems about sciences such as physics and helps solve difficult problems. I envision problems in mathematical terms, and like to talk about it until I fall asleep. I love learning about math, because it is intuitive and forms the basis for many of my favorite sciences.

Learning

Mathcounts
AMC 10/12

Learning at home

I jumped ahead of the school curriculum, and spent much of the summer with my dad and learned about applications of calculus.

Euler’s Formula
Proof of Euler’s formula, identify and relation to trigonometry. «read more»
Laplace Transforms
Proof of Laplace transforms as used in my Electronics article «read more»
own work
Laplace in Mechanical Systems
Using Laplace transforms to solve mechanical ordinary differential equations «read more»
own work
Impedance
Introduces the formulas for Capacitor and Inductor impedance. «read more»
Evaluating Transfer Functions.
Evaluating transfer functions with impulse, unit step and sinusoidal input signals «read more»
own work
RC Low-pass Filter
Low-pass filters remove high frequency components from a signal. A single-pole passive RC filter consists of a resistor and capacitor in series. «read more»
own work
RLC Low-pass Filter
Filters can remove low and/or high frequencies from an electronic signal. They can be used to suppress unwanted frequencies such as background noise. This article shows the math and visualizes the poles in the
s-place, examines and visualizes the the step and frequency response. «read more»
own work
RLC Resonator
RLC circuits are resonant circuits, as the energy in the system “resonates” between the inductor and capacitor. We will examine the properties of a resonator consisting of series circuit of an inductor (L), capacitor
(C) and resistor (R), where the output is taken across the resistor. «read more»

Mandelbrot


This is a zoomable Mandelbrot sequence using Node JS. Zoom in on an interesting area by dragging your cursor and go back to the previous view by pressing the “space” key. The program uses imaginary numbers to generate the sequence. These numbers have separate real and imaginary pieces. The different coordinates in the Mandelbrot set must pass a test. The set is white and the rest is another color. 

My code for this project is at github.com or at khanacademy.org.

Johan’s Software

Software that I wrote

Mandelbrot
Mandelbrot calculations that I wrote in Node JS «read more»
Countdown
Countdown to Christmas animation that I wrote in Node JS «read more»

Learning at home

Getting started with Arduino
Breakout and shields. Development environment. «read more»
Web browser accessing Arduino data
Shows how an external web site can change i/o values on your Arduino. «read more»
Lego Mindstorms Graphical Programming
Bridges the gap between C programming and Lego NXT [2012] «read more»
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