# 3. Revision notes and plans#

## Recent changes#

**2024-09-13:**Revised the function`bisection1`

in module`numericalMethods`

.**2024-08-26/31:**Added further exercises**2024-06-18:**Renamed, dropping the “Introduction to” and correspondingly dropping “introduction-to-” from its URLs.

## To Do#

### Content improvements#

Add more exercises at the end of each section, gathering from assignments, the current separate sections on exercises, and other sources.

Add derivation of the formula for the matrix norm \(\| A \|_\infty\)

Add a derivation of the error bound \(\displaystyle Rel(x_a) := \frac{\|x - x_a\|}{\| x \|} \leq \|A\|\|A^{-1}\|\frac{\|r\|}{\|b\|} \)

Add notes on min-max (Chebychev) approximation of functions by polynomials.

Expand some sections that are only stubs or very brief; in particular those on

Minimization

Multi-step methods for ODEs and determining their stability.

Continue to port updates to and from the Julia version, mostly from Finding the Minimum of a Function of One Variable Without Using Derivatives — A Brief Introduction onwards.

About document “python-tutorial-introduction”: either omit it or add notes on speed/cost measurement, such as with module

`time`

.

### Formating, layout and style improvements#

**camelCase**everything (e.g. change from*numerical_methods*to*numericalMethods*), except where an underscore is used to indicate a subscript. (For one thing that harmonises with Julia style.)When using

`<br>`

, it should appear on its own line, not at end-of-line. (For PDF output; HTML output is more forgiving.) This is relevant to some pseudo-code appearence in the PDF; e.g in Basic Concepts and Euler’s Method:

### MyST markdown tips#

Move to MyST Markdown notation

`{doc}`

,`{ref}`

,`{eq}`

and so on as appropriate.However the enhanced mark-down style

`[text](label)`

is often preferable to uisng`{ref}`

becauseit renders better when viewing a section as a Jupyter notebook, and

it allows substituting an abbreviation or variant of the title as the link text.

To number equations for referencing, use MyST-Markdown-augmented

`$$...$$`

notation, as with`$$2+2=4$$ (eq-obvious)`

If the top-level section atop a file is labelled as with

(section-label)= then the usage`{ref}<section-label>`

can be used instead of`{doc}<file-base-name>`

This is useful for example if there are variant files distinguished by suffixes like “-python”/”-julia” but I want to use the same cross-reference text.