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

## 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.

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**Laplace Transforms**

Proof of Laplace transforms as used in my Electronics article

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**Laplace in Mechanical Systems**

Using Laplace transforms to solve mechanical ordinary differential equations

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**Impedance**

Introduces the formulas for Capacitor and Inductor impedance.

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**Evaluating Transfer Functions.**

Evaluating transfer functions with impulse, unit step and sinusoidal input signals

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**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.

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**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.

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**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.

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