Note 1: Table of Laplace transforms. pdf or ps. This is the table of Laplace transforms which will be given to you in the exam.
Note 2: Laplace transform of cosh(at)cosh(bt). pdf or ps. This is an example of using the first shift theorem.
Note 3: A long example of solving a second
order problem using Laplace transforms. pdf, short pdf, ps or short ps
Note 4: Examples with complex roots, pdf, short pdf, ps or short ps
Note 5: Simple example with Heaviside function. pdf
or ps
Note 6: The convolution cost*cost. pdf
or ps.
Note 7: Another convolution example. pdf or ps.
Note 8: The Laplace transform of a periodic function. pdf
or ps.
Note 9: The Laplace transform of a rectified wave. pdf, ps, short pdf or short ps.
Note 10: The Heaviside function and discontinous functions, some examples: to appear.
Note 11: Table of Z-transforms. pdf or ps. This is the table of Z-transforms which will be given to you in the exam. This table is different from last years, it is shorter, this reflects the fact that the Z-transform part of the course is shorter than it was last year.
Note 12: Notes on Z-transforms, part 1. pdf, ps, short pdf or short ps.
Note 13: Notes on Z-transforms, part 2. pdf, ps, short pdf or short ps.
Note 14: Notes on Z-transforms, part 3. pdf, ps, short pdf or short ps.
Note 15: Notes on Z-transforms, part 4. pdf, ps, short pdf or short ps.
Note 16: Christmas Quiz 2001. pdf
or ps, with answers pdf
or ps or short pdf
or short ps. The problem sheet references are to the problem sheets given in that year.
Note 17: Christmas Quiz 2002. to appear.
Note 18: A rough note on eigenvectors and
eigenvalues: ps or pdf or short ps or short pdf. See also K 370-375.
Note 19: Examples of inward improper nodes: ps or pdf or short ps or short pdf.
Note 20: A list of the different types of critical points for a pair of linear homogeneous equation with two distinct eigenvectors:
ps or pdf or short ps or short pdf.
Note 21: Solving an ordinary inhomogeneous equation:
ps or pdf or short ps or short pdf.
Note 21: An example of solving an inhomogeneous linear
system:
ps or pdf or short ps or short pdf.
Note 22: Example of solving a linear second order differential equation:
ps or pdf.
Note 23: An example of a phase diagram for a nonlinear differential equation:
ps or pdf or short ps or short pdf.
Note 24: Another example of a phase diagram for a nonlinear differential equation:
ps or pdf or short ps or short pdf.
Note 25: The phase portraits were plotted in xmaple. As an example of
this, the maple programme used to do the second phase portrait in
Note 24 is available as a xmaple work sheet or as an ascii file.
Note 26: Method of Frobenius. Example and problem Postscript or pdf, solution Postscript or pdf .
Note 27: An alternative version of the heat equation problem sheet which the other boundary conditions. Postscript or pdf, short postscript or short pdf