MST10030 notes wiki

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rupert (rupert@undisclosed.example.com) — 2019-11-25T17:56:22+00:00

lecture_19

rupert (rupert@undisclosed.example.com) — 2017-05-06T10:14:53+00:00

The orthogonal projection of one vector onto another Let $\def\ww{\vec{w}}\def\vv{\vec{v}}\def\uu{\vec{u}}\ww$ be a non-zero vector, and let $\vv$ be any vector. We call a vector $\def\pp{\vec p}\def\nn{\vec{n}}\pp$ the orthogonal projection of $\vv$ onto $\ww$, and write $\pp=\def\ppp{\text{proj}_{\ww}\vv}\ppp$, if * $\pp$ is in the same direction as $\ww$; and * the vector $\nn=\vv-\pp$ joining the end of $\pp$$\vv$$\ww$$\pp$$\pp$$\vv$$\ww$$\pp$$\ww$$\pp=c\ww$$c\in \mathbb{R}$$\nn=\vv-\p…

lecture_23

rupert (rupert@undisclosed.example.com) — 2017-05-06T09:59:41+00:00

The distance from a point to a line Cross product method Suppose $L$ is a line in $\def\rt{\mathbb{R}^3}\def\rn{\mathbb{R}^n}\rt$. Let $A$ be a point on $L$ and let $\def\vv{\vec v}\vv$ be a direction vector along $L$. Given a point $B$, how can we find $d=\text{dist}(B,L)$, the (shortest) distance from the point $B$ to the line $L$? Let $A$ be any point in $L$$\theta$$AB$$\vv$\[ d=\|\vec{AB}\|\,\sin \theta = \frac{\|\vec{AB}\|\,\|\vv\|\sin \theta}{\|\vv\|} = \frac{\|\vec{AB}\times \vv\|}{…

start - [Notes by lecture]

rupert (rupert@undisclosed.example.com) — 2017-04-25T09:19:54+00:00

Here you can find some lecture notes. The main course web page contains more general information about the course. MST10030 2016–2017 notes These will appear as the course progresses. Notes by lecture * Lecture 1 - Tuesday 24 January 2017 * linear equations in two variables$(i,j)$$AX=B$$A$$2\times 2$$(AB)^T=B^TA^T$$n\times n$$3\times 3$$n\times n$$n\times n$$\vec{AB}$$A$$B$$\|\vec v\|$$\vec v$$\vec v\cdot\vec w=\|\vec v\|\,\|\vec w\|\cos\theta$$\mathbb{R}^3$$\mathbb{R}^3$$\mathbb{R}^3…

lecture_23_slides - [Example using $\def\dist{\text{dist}}\dist(B,L)=\frac{\|\vec{AB}\times\vv\|}{\|\vv\|}$]

rupert (rupert@undisclosed.example.com) — 2017-04-24T11:30:29+00:00

* $\def\bR{\mathbb R}\def\nn{\vec n}\def\i{\vec \imath}\def\j{\vec \jmath}\def\k{\vec k}\def\cp#1#2#3#4#5#6{\left|\begin{smallmatrix}\i&\j&\k\\#1\\#4\end{smallmatrix}\right|}\def\cpc#1#2{\cp{#1_1}{#1_2}{#1_3}{#2_1}{#2_2}{#2_3}}\def\dist{\text{dist}}\dist(X,\Pi)=\frac{|\vec {XY}\cdot \vec n|}{\|\vec n\|}$ is the (shortest) distance from a point $X$ to a plane $\Pi$ * $Y$: any point in $\Pi$ * $\vec n$: a normal vector to $\Pi$ * parametric equation of a line in $\def\rt{\mat…

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rupert (rupert@undisclosed.example.com) — 2015-02-04T17:46:03+00:00

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rupert (rupert@undisclosed.example.com) — 2015-01-22T10:42:09+00:00

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rupert (rupert@undisclosed.example.com) — 2014-12-03T14:44:54+00:00

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rupert (rupert@undisclosed.example.com) — 2015-01-21T11:06:36+00:00

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rupert (rupert@undisclosed.example.com) — 2015-01-21T11:06:36+00:00

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rupert (rupert@undisclosed.example.com) — 2015-01-21T11:00:22+00:00

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rupert (rupert@undisclosed.example.com) — 2015-01-21T10:47:41+00:00