About this course
MATH4402 - Ordinary Differential Equations
COURSE CONTENT:
This course covers topics in Ordinary Differential Equations.
WHERE IS IT USED:
The study of differential equations is a field of pure and applied mathematics studied by researchers in nonlinear analysis. Bifurcation theory is an important tool used by engineers and applied mathematicians in fields as diverse as combustion theory, dynamical systems and chaos.
Researchers are currently working on bifurcation theories for noncompact operators. Research into fixed point theory is a popular topic, especially with multivalued maps.
The material in this course is complemented by the topics in MATH4404 (Functional Analysis) which continues covers other important topics in analysis.
WHO IS INTERESTED:
Students with interests in the application of pure mathematics and the theory behind topics in applied mathematics will be interested. A research career in analysis requires good understanding of the topics in this courses such as operator equations, the topological degree, the Ascoli-Arzela theorem, the contraction mapping principle, and the Schauder fixed point theorem. The topics in bifurcation will be useful for applied mathematicians who intend pursuing theory behind physical phenomena such as combustion, phase transitions or stability analysis. The subject is suitable for both third and fourth year students.
WHAT DO I NEED:
This course is based on some founding analysis. Students should know about metric spaces, multivariate calculus and the inverse function theorem. Some knowledge about Hilbert spaces preferred and the Riesz representation theorem will be used extensively. In particular, Advanced Analysis assumes that the student knows the material in MATH2400.
WHEN IS IT AVAILABLE:
Semester 1 even numbered years.
