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Each week's lectures will be available here as PDF files. To read PDF files
you will need the (free) Adobe Acrobat Reader. This is available from
within the University
(Macintosh,
Windows,
Unix)
or from Adobe's own site:
| Week 1 | Lecture 1 scalars, vectors, division of a line segment |
Lecture 2 Cartesian coordinates |
|---|---|---|
| Week 2 | Lecture 3 triangle inequality, vectors in 3-D, direction cosines |
Lecture 4 geometry problems, linear dependence, scalar product |
| Week 3 | Lecture 5 scalar product properties, projection |
Lecture 6 resolution into components, vector product |
| Week 4 | Lecture 7 area of triangle, scalar triple product, volume of parallelepiped, shortest distance calculations |
Lecture 8 various forms of the equation of a line |
| Week 5 | Lecture 9 various forms of the equation of a plane |
Lecture 10 simultaneous linear equations, Gaussian elimination, row operations |
| Week 6 | Lecture 11 row echelon form, back substitution, reduced row echelon form, consistency of equations |
Lecture 12 row and column vectors, matrix notation |
| Week 7 | Lecture 13 matrix algebra: associative law, distributive law. matrix multiplication and substitution of variables |
Lecture 14 the identity matrix, Kronecker delta notation, inverses |
| Easter | No lecture | No lecture |
| Week 8 | Lecture 15 calculating the inverse, elementary matrices |
Lecture 16 proofs of properties of elementary matrices and inverses |
| Week 9 | Lecture 17 rank of a matrix, uniqueness of the reduced row echelon form. Introduction to permutations |
Lecture 18 properties of permutations |
| Week 10 | Lecture 19 determinants, minors, cofactors, the transpose, adjoints |
Lecture 20 fundamental properties of determinants: the effect of row operations |
| Week 11 | Lecture 21 determinants and permutations: the standard definition; transpositions and row swaps |
Lecture 22
determinant of a product; introduction to eigenvalues |
| Week 12 | Lecture 23 eigenvalues, eigenvectors and the characteristic equation |
Lecture 24 linear combinations, linear independence, diagonalization of matrices |
| Week 13 | Lecture 25 applications of eigenvalues and eigenvectors: powers of matrices, recurrence relations, population models; transformations of the plane |
Lecture 26 rotations and reflections |
From time to time there are reports that not all characters in the PDF documents are displayed and that there are problems when printing. Unfortunately this seems to depend on the individual system being used and it is therefore hard to debug.
However, for printing, there is the following advice in the Acrobat 4.0 Reader help file: "If Acrobat Reader fails to print a file correctly, try selecting the Print as Image option in Acrobat Reader's Print dialogue."
| Quiz 1 | Quiz 2 |
| Quiz 3 | Quiz 4 |
| Quiz 5 | Quiz 6 |
Last major change: 29 May 2001
Don Taylor