# Overview

*It was when I found out I could make mistakes that I knew I was on to something.*(Ornette Coleman)*Jazz is a mental attitude rather than a style. It uses a certain process of the mind expressed spontaneously through some musical instrument. I’m concerned with retaining that process.*(Bill Evans)- Jam Session} = An informal gathering of musicians to play improvised or unrehearsed music. (Online Jam Session)

The BodyandSoul Sessions help you to master basic tools of Calculus and Linear Algebra in interaction with a computer, including the following topics presented in \hyperref[partleibniz]{Leibniz World of Mathematics}:

- functions
- Lipschitz continuity
- derivatives
- Fundamental Theorems of Calculus and Linear Algebra,
- elementary functions
- geometry in $R^2$ and $R^3$
- fixed point iteration and Newton’s method
- time stepping and adaptive error control
- gradient, divergence and Laplacian
- piecewise linear interpolation
- finite element programming,

Each Session contains simple Python codes which you can use as templates to get a quick start.

A set of Sessions using Matlab is available as Sessions A-F}.

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A new set based on Python is coming up, including additional Sessions related to the material in

- \hyperref[partworldofde]{Part VII World of Differential Equations}.
- \hyperref[partfem]{Part VIII World of Finite Elements}.

The material covered by the Sessions is summarized in

- \hyperref[chapter1Dcalc]{1D Calculus}
- \hyperref[chaptermultiDcalc]{MultiD Calculus}
- \hyperref[chapterLA]{Geometry and Linear Algebra}.

# Python Code

The Sessions includes writing Python code for

- Functions.
- Computing derivatives, analytically and computationally.
- Time stepping of and . Quadrature in 1d.
- Computing elementary functions.
- Computing maximum of a Lipschitz continuous function.
- Fixed point iteration for .
- Newton’s method for .
- Transformation of matrix to row and column echelon form.
- Gaussian elimination.
- Jacobi iteration for linear system with diagonally dominant.
- Conjugate gradient method for linear system with positive definite.
- Least squares method for linear system .
- Geometry in and : scalar and vector product, projection, reflection, rotation,..
- Level curves of .
- Level surfaces of .
- Graphics: curves, surfaces and volumes.
- Quadrature in 2d and 3d.

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