Gain insights into Python for scientific computing. Explore arrays, plotting, linear equations, and algorithms using NumPy, Matplotlib, SciPy. Delve into applying tools with practical exercises.

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Python3

If you're a scientist or an engineer interested in learning scientific computing, this is the place to start.

In this course, you'll learn to write your own useful code to perform impactful scientific computations. Along the way, your understanding will be tested with periodic quizzes and exercises.

Topics covered in this course include arrays, plotting, linear equations, symbolic computation, scientific algorithms, and random variables. You’ll also be exposed to popular Python packages like NumPy, Matplotlib, SciPy, and others. In the last part of the course, the application section will test your ability to recall and apply the tools you have studied into newly learned scientific concepts.

At the end of this course, you'll be equipped with the tools necessary for everyday scientific computation.

Python for Scientists and Engineers

# Harmonographs

A **harmonograph** is a mechanical apparatus that employs multiple coupled pendulums to create geometric images. As you can see below, the images are complex, yet beautiful.

<center>
<img src="/api/collection/10370001/5898593854554112/page/5381384441954304/image/5322432224165888" width="350">

</center>

These images can be created by attaching a pencil to the bottom of the pendulum. So, as the pendulum moves, these patterns are drawn.


<center>
<img src="https://media.giphy.com/media/ggNi4abEG5r1u/giphy.gif" width="450">

</center>

## A harmonograph on a single axis 
A harmonograph creates its figures using the movements of damped pendulums. The movement of a damped pendulum along the $x-axis$ is described by the equation:

$$x(t) =Asin(2\pi ft+p)e^{dt}$$
where 
* $A$ is the amplitude, 
* $f$ is the frequency of the pendulum, 
* $t$ is the time, 
* $p$ is the phase, 
* and $d$ is the damping factor.

If we have two independent pendulums oscillating along the x-axis, the principle of superposition says that both contribute to the overall motion of our pencil. The total motion along the x-axis is given by:

$$x(t) = A_1sin(2\pi f_1t+p_1)e^{d_1t} + A_2sin(2\pi f_2t+p_2)e^{d_2t}$$




Preview of harmonographs and how they work.

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Preview: Harmonographs

Harmonographs #

A harmonograph on a single axis