ENGINEERING TRIPOS PART IB - 2012/2013
PAPER 7 - MATHEMATICAL METHODS (2)
Leader: Dr J. P. Jarrett
Timing: Weeks 4 & 8 Lent Term 1 lecture/week; weeks 5-7 Lent Term 2 lectures/week
Structure: 8 lectures
Linear Algebra provides
important mathematical tools which are not only essential to solve many
technical and computational problems, but also help in obtaining a deeper
understanding of many areas of engineering.
The aims of this course are to:
- Introduce the ideas and techniques of Linear
Algebra, and illustrate some of their applications in engineering.
For all objectives, the
student should be able to complete calculations by hand for small problems, or
by using Matlab for larger problems (the IB Computing Course deals with this in
detail). By the end of the course students should:
- Be able to solve a set of linear equations
using Gaussian elimination, and complete the LU factorisation of
- Understand, and be able to calculate bases for the
four fundamental subspaces of a matrix;
- Be able to calculate the least squares
solution of a set of linear equations;
- Be able to orthogonalize a set of vectors,
complete the QR factorisation of a matrix, and be able to use
this to find the least squares solution of a set of linear equations;
- Be able to find the eigenvalues and
eigenvectors of a matrix, and complete the A = SL S-1
or A = QL QT factorisations as appropriate;
- Be able to find the SVD of a matrix,
and to understand how this can be used to calculate the rank of the
matrix, and to provide a basis for the each of its fundamental subspaces
- Solution of the matrix equation Ax = b: Gaussian elimination, LU
factorization, the four fundamental subspaces of a matrix.
- Least squares solution of Ax = b
for an m x n matrix with n independent columns: Gram-Schmidt orthogonalization, QR decomposition.
- Solution of Ax = l x,
eigenvectors and eigenvalues.
- Singular Value Decomposition (if time)
Please see the Booklist for Part IB Courses for references for this module.
Last updated: September 2012