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

# Taylor series

SymPy expressions can be expanded as Taylor series using the `series()` function from the SymPy module. 

Taylor series about $x=a$ is given by:

$$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}a}{n!}(x-a)^n$$

where $f^{(n)}$ is the $n^{th}$ derivative of $f$.


For a generic expansion, we only need to specify the expression and the variable in the expansion for which the expression is to be expanded. 

```python 3
series(f(x), x)
```
or
``` python 3
f(x).series(x)
```
Let's see a basic implementation of the `series()` function below:

In this lesson, we will learn about Taylor series and formal power series.

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Series Expansion

Taylor series