Institut für Theoretische Physik

# Basic Physics Course withMATLAB's Symbolic Toolbox and Live Editor

### Introduction

This course is intended to help review and deepen the understanding of basics in physics.

We work out the essentials, we try to clarify why the laws of physics are as they are and how the details are connected. Since it is assumed that the reader possesses fundamental knowledge of physics and mathematics, a more modern view of physics, mathematics and computation can be taken.

In the center of our considerations is the action field. It is introduced as scalar field whose four-gradient determines the four-momentum. It is considered as fundamental invariant expression of physics.

We get to classical mechanics by action on point particles, and to quantum mechanics by action on detectors. The laws of interaction evolve from the continuity equation for the gradients of the momentum components, where the latter is the gradient of the action function.

For the derivation of physical laws, we sometimes use symbolic computer software. This helps avoid long calculations which distract from the actual physics. For exercises, we use symbolic and numeric computer software. This allows for more complicated problems, vivid graphics and a lot of animations. Students like it, it is play-like, and computers are their way to deal with all kind of affairs.

As computer language we apply MATLAB’s Symbolic Math Toolbox in the Live Editor. MATLAB itself offers powerful methods for diverse numerical problems and graphic representations. The Symbolic Math Toolbox is very modern, and having both the symbolic and the numerical methods in the same editor is fascinating. With a simple statement, one can convert symbolic expressions and continue with numerical methods.

Please note!

The file sube.m is required in MATLAB's work directory to run mlx-files in the Live Editor.

### Animation

Chapter 1 Theory: Vectors and Metric Chap01_1.pdf Chap01_1.mlx
Spherical coordinates Chap01_2.pdf Chap01_2.mlx
Metric of a Mexican hat Chap01_3.pdf Chap01_3.mlx
Chapter 2 Theory: Structure of Physical Spacetime Chap02_1.pdf Chap02_1.mlx
Lorentz transformation Chap02_2.pdf Chap02_2.mlx
Twin paradoxon ... Chap02_3.pdf Chap02_3.mlx
Chapter 3 Theory: Dynamics Chap03_1.pdf Chap03_1.mlx
Action field Chap03_2.pdf Chap03_2.mlx Kepler Action
Chapter 4 Theory: Classical mechanics Chap04_1.pdf Chap04_1.mlx
Keplerian orbits Chap04_2.pdf Chap04_2.mlx Keplerian orbits
Roll pendulum Chap04_3.pdf Chap04_3.mlx Roll pendulum
Roller coaster Chap04_4.pdf Chap04_4.mlx Roller coaster
Chapter 5 Theory: Quantum mechanics Chap05_1.pdf Chap05_1.mlx
Quantization and SG Chap05_2.pdf Chap05_2.mlx
Gauss wave packets Chap05_3.pdf Chap05_3.mlx Gauss interference
Bound states Chap05_4.pdf Chap05_4.mlx Bound states
Scattering states Chap05_5.pdf Chap05_5.mlx
Chapter 6 Theory: Interaction Chap06_1.pdf Chap06_1.mlx
Helmhotz coil Chap06_2.pdf Chap06_2.mlx
Charge over sphere Chap06_3.pdf Chap06_3.mlx
Hertzian dipole Chap06_4.pdf Chap06_4.mlx Herzian dipole
Schwarzschild metric Chap06_5.pdf Chap06_5.mlx
Chapter 7 Theory: Deterministic chaos Chap07_1.pdf Chap07_1.mlx
Fractals Chap07_2.pdf Chap07_2.mlx
Duffing oscillator Chap07_3.pdf Chap07_3.mlx
Billiard chaos Chap07_4.pdf Chap07_4.mlx Billard chaos