Courses Detail Information
MATH2860J – Honors Mathematics IV
Instructors:
Credits: 4 (No credits after Vv216 or Vv256.)
Pre-requisites: MATH2850J Obtained Credit
Description:
Topics include ordinary differential equations (ODEs) of first order; systems of first-order equations; the existence and uniqueness theorem of Picard-Lindeloef; eigenvalue problems, diagonalization and the spectral theorem; Jordan normal form; application to linear systems of first-order equations; linear second-order equations; elements of complex analysis and residue theory; the Laplace transform and its inverse with applications to ODEs; power series solutions of ODEs by the Frobenius method; Bessel’s and Legendre’s differential equations; generalized Fourier series; introduction to the classical partial differential equations of physics and some basic solutions by separation of variables.
Course Topics:
- Single first-order ODEs (8 hrs at 45 min each)
- Eigenvalue problems, systems of ODEs and vibrations (12 hrs)
- Introduction to complex analysis and residue theory (8 hrs)
- The Laplace and Fourier transforms (8 hrs)
- Power series solutions and Bessel functions (8 hrs)
- Orthonormal functions and Fourier series (4 hrs)
- Introduction to PDEs and BVPs (6 hrs)
- Three exams (6 hrs)