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

# Preview

In optical physics, light can be described using **Jones calculus**. 

Light polarization is represented by a **Jones vector**, with dimensions $2 \times1$:
> <img src="/api/collection/10370001/6066104977850368/page/4580102618742784/image/6441996354846720" width="35"> Each light polarization has its distinct Jones vector.

$$\begin{bmatrix}x \\y \end{bmatrix}$$

and all optical elements are represented by **Jones matrices**, with dimensions $2 \times2$:
$$\begin{bmatrix}a & b \\c & d \end{bmatrix}$$



> <img src="/api/collection/10370001/6066104977850368/page/4580102618742784/image/6441996354846720" width="35"> Each element has a distinct Jones matrix.


When light crosses an optical element, the resulting polarization of the emerging light is found by taking the product of the Jones matrix from the optical element and the Jones vector from the incident light. 

The above picture can be mathematically represented as:

$$\begin{bmatrix}x' \\y' \end{bmatrix}= \begin{bmatrix}a & b \\c & d \end{bmatrix}\begin{bmatrix}x \\y \end{bmatrix}$$

**System Matrix**

If there is more than one optical component, we must multiply all the matrices to get the **system matrix**. It can be mathematically represented as: 

$$\begin{bmatrix}a & b \\c & d \end{bmatrix}=\begin{bmatrix}a_1 & b_1 \\c_1 & d_1 \end{bmatrix}\begin{bmatrix}a_2 & b_2 \\c_2 & d_2 \end{bmatrix}\begin{bmatrix}a_3 & b_3 \\c_3 & d_3 \end{bmatrix}...\begin{bmatrix}a_n & b_n \\c_n & d_n \end{bmatrix}$$

The system matrix is then multiplied with the input vector to get the output polarization vector.


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: Setting Up an Optical System

Preview