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

Integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function $f$ of a real variable $x$ and an interval $[a, b]$ of the real line, the definite integral is denoted as:


$$\int_{a}^{b} f(x) \space dx$$

Integrals are calculated with the `integrate()` function. SymPy implements a combination of the Risch algorithm and an algorithm for computing integrals based on Meijer G-functions. These allow SymPy to compute a wide variety of indefinite and definite integrals. 

# Indefinite integrals

Integration uses syntax similar to differentiation. For the indefinite integral, we specify the function and the variable with respect to which the integration is performed.

```python 3
integrate(y, x)
```

> <img src="/api/collection/10370001/6066104977850368/page/4580102618742784/image/6441996354846720" width="35"> The `integrate()` function does not add the constant of integration in the indefinite integral. 

Let's see an example of integrating a polynomial below:

from sympy import *

def f(x):
    return (x**2 + x)

x = Symbol('x')

print(integrate(f(x), x))

SymPy allows for a range of integrals. Let's see them one by one

**Rational**

$$\int\frac{x^2}{x+1}dx$$

In this lesson, we will learn about definite and indefinite integrals of single and multiple integrations.  

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Integration

Indefinite integrals #