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| start [2017/02/28 12:23] – rupert | start [2017/04/25 09:19] (current) – [Notes by lecture] rupert | ||
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| Line 81: | Line 81: | ||
| * Lecture 12 - Thursday 2 March 2017 | * Lecture 12 - Thursday 2 March 2017 | ||
| * Midterm (no lecture) | * Midterm (no lecture) | ||
| - | /* * [[Lecture 13]] | + | |
| + | * [[Lecture 13]] - Tuesday 7 March 2017 | ||
| * the transpose of a matrix | * the transpose of a matrix | ||
| * $(AB)^T=B^TA^T$ | * $(AB)^T=B^TA^T$ | ||
| Line 88: | Line 89: | ||
| * cofactors | * cofactors | ||
| * the determinant of a $3\times 3$ matrix | * the determinant of a $3\times 3$ matrix | ||
| - | * [[Lecture 14]] | + | * [[Lecture 14]] - Thursday 9 March 2017 |
| * the determinant of an $n\times n$ matrix | * the determinant of an $n\times n$ matrix | ||
| * Laplace expansion along any row or column | * Laplace expansion along any row or column | ||
| * the determinant of an upper triangular matrix | * the determinant of an upper triangular matrix | ||
| * properties of the determinant | * properties of the determinant | ||
| - | | + | |
| + | | ||
| * the effect of EROs on the determinant | * the effect of EROs on the determinant | ||
| * finding determinants using EROs | * finding determinants using EROs | ||
| * the adjoint of a square matrix | * the adjoint of a square matrix | ||
| - | * [[Lecture 16]] | + | * [[Lecture 16]] - Thursday 30 March 2017 |
| * a formula for the inverse of an $n\times n$ square matrix | * a formula for the inverse of an $n\times n$ square matrix | ||
| * using EROs to find the inverse of a square matrix | * using EROs to find the inverse of a square matrix | ||
| * (column) vectors as instructions to move points | * (column) vectors as instructions to move points | ||
| - | | + | |
| + | | ||
| * the vector $\vec{AB}$ which moves point $A$ to point $B$ | * the vector $\vec{AB}$ which moves point $A$ to point $B$ | ||
| * the length $\|\vec v\|$ of a vector $\vec v$ | * the length $\|\vec v\|$ of a vector $\vec v$ | ||
| Line 107: | Line 110: | ||
| * Unit vectors | * Unit vectors | ||
| * Addition of vectors: the triangle and parallelogram rules | * Addition of vectors: the triangle and parallelogram rules | ||
| - | * [[Lecture 18]] | + | * [[Lecture 18]] - Thursday 6 April 2017 |
| - | * The dot product | + | * The dot product |
| + | * The geometric | ||
| * Calculating angles | * Calculating angles | ||
| + | |||
| + | * [[Lecture 19]] - Tuesday 11 April 2017 | ||
| * The orthogonal projection of one vector onto another | * The orthogonal projection of one vector onto another | ||
| - | * [[Lecture 19]] | ||
| * The cross product of vectors in $\mathbb{R}^3$: | * The cross product of vectors in $\mathbb{R}^3$: | ||
| * The area of a triangle using the cross product | * The area of a triangle using the cross product | ||
| - | * [[Lecture 20]] | + | * [[Lecture 20]] - Thursday 13 April 2017 |
| * Geometry of the cross product: areas and volumes | * Geometry of the cross product: areas and volumes | ||
| * Planes in $\mathbb{R}^3$ and their normal vectors | * Planes in $\mathbb{R}^3$ and their normal vectors | ||
| - | | + | |
| - | * Orthogonal | + | |
| + | * Parallel | ||
| * Examples: finding the equations of planes with various properties | * Examples: finding the equations of planes with various properties | ||
| + | * [[Lecture 22]] - Thursday 20 April 2017 | ||
| * The distance from a point to a plane | * The distance from a point to a plane | ||
| - | * [[Lecture 22]] | ||
| * The distance between planes | * The distance between planes | ||
| * The parametric equation of a line | * The parametric equation of a line | ||
| + | |||
| + | |||
| + | * [[Lecture 23]] - Tuesday 25 April 2017 | ||
| * The distance from a point to a line (using the cross product) | * The distance from a point to a line (using the cross product) | ||
| - | * [[Lecture 23]] | ||
| * The distance from a point to a line (using orthogonal projection) | * The distance from a point to a line (using orthogonal projection) | ||
| - | * The distance between | + | * The distance between lines in $\mathbb{R}^3$ |
| - | */ | ||
| Line 148: | Line 155: | ||
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| - | + | | |
| - | /* | + | |
| - | + | ||
| - | * [[https:// | + | |
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| Line 163: | Line 167: | ||
| * [[https:// | * [[https:// | ||
| * [[https:// | * [[https:// | ||
| - | | + | / |
| */ | */ | ||
start.1488284599.txt.gz · Last modified: by rupert