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

from sympy import *

def f(x):     # just a mathematical function
  return atan(x)

def g(x):       # just a mathematical function
  return exp(x)

x = Symbol('x')

def ts_integral(f, x, n=4, lim1=None, lim2=None):
  ts = f(x).series(x, 0, n).removeO()
  integral = integrate(ts, (x, lim1, lim2))
  return ts, integral.evalf(3) 

output_1 = ts_integral(f, x, 10, 0, pi/4)
output_2 = ts_integral(g, x)

print("Taylor Series of f(x):", output_1[0])
print("Integral of f(x):", output_1[1])
print("-----")
print("Taylor Series of g(x):", output_2[0])
print("Integral of g(x):", output_2[1])

## Explanation

* In the `ts_signal` function parameter, the default value of `n` is set to 4 and the default values of `lim1` and `lim2` are set to `None` . 

* In line 12, we compute the Taylor series up to the order `n` and remove the trailing term.

* In line 13, we compute the integral of the Taylor series `ts`. Integration limits of this integral are `lim1` and `lim2`. 

* In line 14, the `ts` is returned alongside the integral of `ts` with numerical values up to 3 significant figures. 

* If the user does not specify the parameters `lim1`, `lim2`, and/or `n` when calling the function, the default values of these parameters will be used. An example of this is shown in lines 16 - 17 where `ts_integral` is first called with 5 arguments and then it is called with 2 arguments.

This lesson provides a detailed solution review to integrating complex functions.

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Solution Review: Integrating Complex Functions

Solution