Please do not divulge the URL
for this page to the undergraduates.
Currently being edited....
The webpage for the undergraduates is here and it contains further information and links.
The typeset course notes are here
What I do and when may be found
here.
Both of the weekly lectures take place before the Thursday tutorial, which is from 11.15 to 12.05 in 4E 3.40/44.
Problem sheets and solutions
Week 1.
ODEs 1,2:
Sheet 1
on the classification of ODEs, the method of separation of variables and the solution of first order linear equations.
Solutions
Week 2.
ODEs 3,4:
Sheet 2
on the solution of linear constant-coefficient equations. Homogeneous ODEs. Start of Inhomogeneous ODEs.
Solutions
Week 3.
ODEs 5: Final section on the solution of Inhomogeneous ODEs.
Sheet 2 (supplementary)
on the solution of more advanced equations. These are optional with more difficult questions than will
be tested by the exams.
Solutions
Matrices:
Sheet 1
on terminology, notation, classification, multiplication and compatibility.
Solutions
Week 4.
Matrices:
Sheet 2
on determinants, Cramer's rule, their geometric interpretation and Gaussian Elimination.
Solutions
Week 5.
Matrices:
Sheet 3
on eigenvalues and the solution of linear ODE systems.
Solutions
Laplace Transforms
Sheet 0. This will be given out before next week's first lecture on LTs!
Solutions covered in that lecture.
Week 6.
Laplace Transforms:
Sheet 1
Definitions. Examples, unit impulse, derivatives, solution of some ODEs.
Solutions
Week 7.
Laplace Transforms:
Sheet 2
Shift theorems, the unit step function, convolution.
Solutions
Week 8.
Numerical Mathematics:
Sheet
on root-finding using ad hoc and Newton-Raphson iteration. Includes convergence analyses.
Solutions
Week 9.
Fourier Series:
Sheet
Solutions
Easter break for two weeks.
Week 10.
Least Squares:
Sheet
Solutions (text)
Solutions (figures)
Ounces/grams data for Q2
Week 11.
No lectures.