Download AM20RA Real Analysis

AM20LM LINEAR MATHS
Level: 5
Credits: 10
Teaching Period: 1
Module Tutor: Dr J Neirotti
Aims:
Students should understand:
The use vector spaces to illustrate the basic concept of an axiomatic system.
The fundamental ideas of Linear Algebra.
The study of the solutions of sets of linear equations.
Content:
Vectors Spaces and their Properties.
Definition (axioms) of a vector space. Examples of vector spaces. Proofs of
Simple rules of manipulation deduced from the axioms.
Subspaces and a test for subspaces. Linear dependence. Basis and
dimensions. Eigenvalues and eigenvectors.
Linear Equations
Reduction of a set of linear equations to row echelon form. Rank of a matrix. The
solution space of homogeneous equations as a subspace and its dimension. Condition
for a set of inhomogeneous equations to have solution(s).
Linear Transformation
Definition and properties. Image and kernel and the dimensionality theorem. Application
to linear equations.
Teaching:
Lectures 22 hours
Tutorials 11 hours
Self study and examination 67 hours
Assessment: Coursework 10% (please hand in to Coursework Office MB133)
Examination (1.5 hours) 90% (January Examination)
Feedback on the module will be given via the coursework assessment.
All provisional marks will be available within 4 weeks.
Feedback from both the coursework assessment and the Examination will take the form
of a mark.
In the case of the coursework worked solutions will be provided.
Module outcomes
What the student should gain from successful completion of the
module
Teaching/Learning
Methods
Assessment
Methods
Knowledge and Understanding
Lectures
1.Understand the underlying principles of linear algebra
2.Understand the concepts of linear dependence and how these
concepts can be used in solving sets of linear equations.
Coursework
and
Examination
Intellectual Skill
1.Apply techniques from linear algebra and multivariate calculus.
2.Apply axioms of a vector space to solving sets of equations
Lectures
Coursework and
Examination
Lectures
Coursework and
Examination
Professional/Subject-Specific Skills
1.Use vector spaces to illustrate the basic concept of an
axiomatic system.
Transferable Skills
Reading Lists: Lipschutz, S. Linear Algebra (Schaum’s Outlines).
Whitelaw, T. A. An Introduction to Linear Algebra.
SEAS, Aston University – AM Module Specification 2011/12
Last update 09/09/11
Krause. E.F. Introduction to Linear Algebra.
Prerequisites: Calculus and Ordinary Differential Equations (AM10CO)
Vector Algebra and Geometry (AM10VA)
SEAS, Aston University – AM Module Specification 2011/12
Last update 09/09/11