Z Transform Engineering Mathematics 3 Pdf

2E2 2005-06

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02/03 Q and A

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Notes.

As of this year, I am not changing the note numbers but I will reorder the notes so that their order will correspond to what we do in class while the order of hteir numbers might not.

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: Simple example with Heaviside function. pdf or ps
Note 5: The Dirac delta function. pdf or ps or short pdf
Note 6: Another Heaviside function example and a Dirac delta function example, pdf or ps or short pdf or short ps.

Note 9: Examples with complex roots, pdf, short pdf, ps or short ps

Note 7: The convolution cost*cost. pdf or ps.
Note 8: Another convolution example. pdf or ps.

Note 10: The Laplace transform of a periodic function. pdf or ps.
Note 11: The Laplace transform of a saw tooth function. pdf, ps, short pdf or short ps.

Note 12: Table of Z-transforms. pdf or ps. This is the table of Z-transforms which will be given to you in the exam.

Note 13: Notes on Z-transforms, part 1. pdf, ps, short pdf or short ps.
Note 14: Notes on Z-transforms, part 2. pdf, ps, short pdf or short ps.
Note 15: Notes on Z-transforms, part 3. pdf, ps, short pdf or short ps.
Note 16: Notes on Z-transforms, part 4. pdf, ps, short pdf or short ps.

Note 17: An old Z-transform problem sheet, gives some examples, might be useful for revision. pdf or ps. Solutions pdf, small pdf, ps or small ps.

Note 18: 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 19: Christmas Quiz 2002. pdf or ps, with answers pdf or ps or short pdf or short ps.
Note 20: Christmas Quiz 2003. to appear.
Note 21: Christmas Quiz 2004. to appear.

Note 22: A rough note on eigenvectors and eigenvalues: ps or pdf or short ps or short pdf. See also K 370-375.

Note 23: Examples of inward improper nodes: ps or pdf or short ps or short pdf.
Note 24: 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 34: A spiral example: ps or pdf or short ps or short pdf.

Note 25: Solving an ordinary inhomogeneous equation: ps or pdf or short ps or short pdf.
Note 26: An example of solving an inhomogeneous linear system: ps or pdf or short ps or short pdf.

Note 27: Example of solving a linear second order differential equation: ps or pdf.
Note 28: An example of a phase diagram for a nonlinear differential equation: ps or pdf or short ps or short pdf.
Note 29: Another example of a phase diagram for a nonlinear differential equation: ps or pdf or short ps or short pdf.
Note 30: The phase portraits were plotted in xmaple. As an example of this, the maple programme used to do the second phase portrait in Note 29 is available as a xmaple work sheet or as an ascii file.

Note 31: A series solution example. Postscript or pdf and short Postscript or pdf .
Note 32: Method of Frobenius. Example and problem Postscript, pdf, short postscript or short pdf, solution Postscript or pdf .
Note 33: Bessel equation Postscript or pdf, solution short ps or short pdf .