Table of Contents
TP1 Mechanics Sage Notebooks
This page provides the links to Sage Jupyter Notebooks that are provided on this Wiki, and to web pages where the interaction with Sage can be explored. Instructions on how to download the Notebooks, and start them on your computer are provided here.
The notebooks marked as intro are meant to help with first steps on a particular topic. To this end they contain more elaborate comments. Please notify me about places where you were struggling to understand a concept. I particularly appreciate feedback of notebooks where further comments and/or links to the sagemath help pages are added.
The links in the left column open a page displaying the output/features of the Sage Notebooks.
Plotting Functions
| aim | Sage features | download |
|---|---|---|
| Plot trigonometric functions | intro: plotting functions | Notebook (1.5kB) |
| Plot cycloids and curtate trochoids | intro: add lines and control layout | Notebook (2.3kB) |
| Explore trigonometric functions | exploring parameters by sliders | Notebook (1.8kB) |
| Animations for cycloids and curtate trochoids | intro: interactive plots and animations | Notebook (3.9kB) |
| Guess function parameters | provide parameters in text fields, checkboxes | Notebook (2.1kB) |
Derivatives and Taylor series
| aim | Sage features | download |
|---|---|---|
| Derivatives of functions | intro: determine the derivatives of a function, define your own functions | Notebook (1.6kB) |
| Determine derivatives and Taylor series | providing functions and parameters in text boxes, pretty-print expression to screen | Notebook (1.6kB) |
Analyzing EOM
| aim | Sage features | download |
|---|---|---|
| Exploring the solutions | numerical solution of ODEs, evolution in phase space, direction field | Notebook (1.8kB) |
| Mathematical Pendulum | mathematical pendulum: evolution in phase space, direction field | Notebook (2.3kB) |
==== Solutions for Exercises ==== After the submission deadline the links to worksheets with solutions of selected exercises will be published here. * 1.2 Challenges in drawing circles * 3.3 Retroreflector paths on bike wheels * 4.2 Contour lines and gradients * 4.3 Dynamics in phase space * 6.3 Bubbles rising in a fluid