book:chap2:2.4_fields
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| book:chap2:2.4_fields [2021/10/31 17:17] – jv | book:chap2:2.4_fields [2024/11/09 10:12] (current) – jv | ||
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| + | [[forcestorques|2. Balancing Forces and Torques]] | ||
| + | * [[ 2.1 Motivation and Outline| 2.1 Motivation and outline: forces are vectors ]] | ||
| + | * [[ 2.2 Sets| 2.2 Sets ]] | ||
| + | * [[ 2.3 Groups| 2.3 Groups ]] | ||
| + | * ** 2.4 Fields ** | ||
| + | * [[ 2.5 Vector spaces| 2.5 Vector spaces ]] | ||
| + | * [[ 2.6 Physics application balancing forces| 2.6. Physics application: | ||
| + | * [[ 2.7 The inner product | 2.7 The inner product]] | ||
| + | * [[ 2.8 Cartesian coordinates | 2.8 Cartesian coordinates]] | ||
| + | * [[ 2.9 Cross products --- torques| 2.9 Cross products — torques ]] | ||
| + | * [[ 2.10 Worked example Calder' | ||
| + | * [[ 2.11 Problems| 2.11 Problems ]] | ||
| + | * [[ 2.12 Further reading| 2.12 Further reading ]] | ||
| + | |||
| + | ---- | ||
| + | |||
| ===== 2.4 Fields ===== | ===== 2.4 Fields ===== | ||
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| & = ( x_1 + \mathrm{i} y_1 ) \cdot ( x_2 + \mathrm{i} y_2 ) | & = ( x_1 + \mathrm{i} y_1 ) \cdot ( x_2 + \mathrm{i} y_2 ) | ||
| \\ | \\ | ||
| - | & = ( x_1 \, x_2 + \mathrm{i} | + | & = x_1 \, x_2 + x_1\, (\mathrm{i} |
| \\ | \\ | ||
| - | &= ( x_1\, x_2 - y_1\,y_2 ) + \mathrm{i} \, (y_1 \, x_2 + x_1 \, y_2) | + | &= ( x_1\, x_2 - y_1\,y_2 ) + \mathrm{i} \, (x_1 \, y_2 + y_1 \, x_2) |
| \end{align*} | \end{align*} | ||
| Checking the group axioms based on this representation of the complex numbers is tedious. | Checking the group axioms based on this representation of the complex numbers is tedious. | ||
book/chap2/2.4_fields.1635697050.txt.gz · Last modified: 2021/10/31 17:17 by jv