Symbolic Computation in Mathematica

An introduction to Mathematica by Dr. Yi-Xin Liu at Fudan University (lyx@fudan.edu.cn).

This is a part of the course: Road to Scientific Research: Powerful Computer Applications (XDSY118019.01).

Lecture date: 2024.10.17

Symbolic Computation vs. Numerical Computation

Symbolic computation is a scientific area that refers to the study and development of algorithms and software for manipulating mathematical expressions and other mathematical objects.

• Symbolic computation is EXACT.
• Numerical computation approximates results with floating point numbers.

Example:

• reduce to in symbolic computation.
• is approximated by a floating point number such as in numerical computation.

What is Mathematica?

• Stephen Wolfram's Introduction to the Wolfram Language (12:55)

Introduction to Wolfram Notebooks

• Introduction to Wolfram Notebooks (7:49)

Get Started with Mathematica

• Hands-on Start to Mathematica (35:04)

Demo and Exercises

Go to Wolfram Cloud, and solve the following problems:

1. Given , find the coefficient of the term .
   1. Method 1: expand the expression and eyeball the coefficient.
   2. Method 2: google a clever way, use searching keywords such as mathematica find the coefficient of a term from expansion.
2. Solve .
3. for real and .
4. Integrate for .
5. Integrate .
6. Evaluate .