Here you can find some lecture notes. The [[http://mathsci.ucd.ie/courses/mst10030|main course web page]] contains more general information about the course. ====== MST10030 2016–2017 notes ====== These will appear as the course progresses. /* ===== Notes by chapter ===== These are the notes by lecture below, grouped together. * **Chapter 1: Systems of linear equations** (Lectures 1-6 and half of lecture 7) * [[chapter_1|on the web]] (might be slow to load) * {{:chapter_1.pdf|in pdf}} * **Chapter 2: The algebra of matrices** (half of lecture 7, lectures 8-16 and half of lecture 17) * [[chapter_2|on the web]] (might be slow to load) * {{:chapter_2.pdf|in pdf}} * **Chapter 3: Vectors and geometry** (the remaining lectures) * [[chapter_3|on the web]] (might be slow to load) * {{:chapter_3.pdf|in pdf}} */ ===== Notes by lecture ===== * [[Lecture 1]] - Tuesday 24 January 2017 * linear equations in two variables * [[Lecture 2]] - Thursday 26 January 2017 * linear equations in three or more variables * systems of linear equations (first example) * [[Lecture 3]] - Tuesday 31 January 2017 * the augmented matrix of a system of linear equations * the $(i,j)$ entry of a matrix * elementary operations on a system of linear equations * elementary row operations on a matrix * [[Lecture 4]] - Thursday 2 February 2017 * row echelon form * reduced row echelon form * [[Lecture 5]] - Tuesday 7 February 2017 * leading variables and free variables * solving a linear system in REF or RREF * Gaussian elimination * [[Lecture 6]] - Thursday 9 February 2017 * Examples * Inconsistent systems * Deciding whether or not a system has infinitely many solutions * Observations about Gaussian elimination and free variables * Matrices: definition of a matrix and matrix entries * [[Lecture 7]] - Tuesday 14 February 2017 * Equality of matrices * Addition and subtraction of matrices * The zero matrix * Scalar multiplication of matrices * Row-column matrix multiplication * An example of general matrix multiplication * [[Lecture 8]] - Thursday 16 February 2017 * Definition of matrix multiplication * Examples * Commuting and non-commuting pairs of matrices * The identity matrix * [[Lecture 9]] - Tuesday 21 February 2017 * Properties of the identity matrix: proof * The associative and distributive laws for matrix multiplication * [[Lecture 10]] - Thursday 23 February 2017 * Matrix equations * Invertibility of a square matrix * Uniqueness of inverses * [[Lecture 11]] - Tuesday 28 February 2017 * Solving $AX=B$ where $A$ is invertible * The determinant and invertibility of a $2\times 2$ matrix * Lecture 12 - Thursday 2 March 2017 * Midterm (no lecture) * [[Lecture 13]] - Tuesday 7 March 2017 * the transpose of a matrix * $(AB)^T=B^TA^T$ * determinants of $n\times n$ matrices: * minors * cofactors * the determinant of a $3\times 3$ matrix * [[Lecture 14]] - Thursday 9 March 2017 * the determinant of an $n\times n$ matrix * Laplace expansion along any row or column * the determinant of an upper triangular matrix * properties of the determinant * [[Lecture 15]] - Tuesday 28 March 2017 * the effect of EROs on the determinant * finding determinants using EROs * the adjoint of a square matrix * [[Lecture 16]] - Thursday 30 March 2017 * a formula for the inverse of an $n\times n$ square matrix * using EROs to find the inverse of a square matrix * (column) vectors as instructions to move points * [[Lecture 17]] - Tuesday 4 March 2017 * the vector $\vec{AB}$ which moves point $A$ to point $B$ * the length $\|\vec v\|$ of a vector $\vec v$ * Scalar multiplication and direction * Unit vectors * Addition of vectors: the triangle and parallelogram rules * [[Lecture 18]] - Thursday 6 April 2017 * The dot product * The geometric formula $\vec v\cdot\vec w=\|\vec v\|\,\|\vec w\|\cos\theta$ * Calculating angles * [[Lecture 19]] - Tuesday 11 April 2017 * The orthogonal projection of one vector onto another * The cross product of vectors in $\mathbb{R}^3$: definition and properties * The area of a triangle using the cross product * [[Lecture 20]] - Thursday 13 April 2017 * Geometry of the cross product: areas and volumes * Planes in $\mathbb{R}^3$ and their normal vectors * [[Lecture 21]] - Tuesday 18 April 2017 * Parallel and orthogonal planes * 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 between planes * 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 orthogonal projection) * The distance between lines in $\mathbb{R}^3$ ====== Lecture slides ====== Here are links to the slides I used in the lectures. They cover much the same material as the notes above, and are provided in response to a student request. * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_1_slides|Lecture 1 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_2_slides|Lecture 2 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_3_slides|Lecture 3 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_4_slides|Lecture 4 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_5_slides|Lecture 5 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_6_slides|Lecture 6 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_7_slides|Lecture 7 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_8_slides|Lecture 8 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_9_slides|Lecture 9 slides]] * [[https://maths.ucd.ie/~levene/w/mst100030/doku.php?do=export_revealjs&id=lecture_10_slides|Lecture 10 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_11_slides|Lecture 11 slides]] * Lecture 12 - no slides (midterm) * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_13_slides|Lecture 13 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_14_slides|Lecture 14 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_15_slides|Lecture 15 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_16_slides|Lecture 16 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_17_slides|Lecture 17 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_18_slides|Lecture 18 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_19_slides|Lecture 19 slides]] * [[https://maths.ucd.ie/~levene/w/mst100030/doku.php?do=export_revealjs&id=lecture_20_slides|Lecture 20 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_21_slides|Lecture 21 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_22_slides|Lecture 22 slides]] * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_23_slides|Lecture 23 slides]] /* * [[https://maths.ucd.ie/~levene/w/mst10030/doku.php?do=export_revealjs&id=lecture_24_slides|Lecture 24 slides]] */ ====== MST10030 2015–2016 notes ====== These have now been {{:mst10030_2015_2016_web_notes.pdf|archived as a PDF file}}. /* Notes will appear here once the course starts! */