SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python. SymPy is used in many projects such as Cadabra, ChemPy, EinsteinPy, galgebra, Lcapy, SageMath, SfePy, Spyder, yt, etc. SimPy is free, lightweight and Python-based. We outline the contents of this lecture as follows:

00:00 What is SymPy ?

00:59 Installing SymPy using pip

01:53 Importing SymPy

02:16 Symbols

02:33 Defining a mathematical function

03:12 Operations

04:48 Functions & Plotting

11:43 Printing (and pretty printing)

14:12 Simplifying a mathematical expression

26:00 Differentiating

28:34 Integrating

30:59 Limits

33:02 Taylor Series Expansion

35:07 Solving f(x) = 0

26:00 Differentiating

37:39 Solving a system of linear equations

40:56 Solving a system of non-linear equations

41:54 Solving differential equations

43:36 Summary

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