Courses Detail Information

VV286 – Honors Mathematics IV

Instructor: Horst Harold Hohberger

Instructors (Faculty):

Credits: 4 (No credits after Vv216 or Vv256.)

Pre-requisites: Vv285


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:

  1. Single first-order ODEs (8 hrs at 45 min each)
  2. Eigenvalue problems, systems of ODEs and vibrations (12 hrs)
  3. Introduction to complex analysis and residue theory (8 hrs)
  4. The Laplace and Fourier transforms (8 hrs)
  5. Power series solutions and Bessel functions (8 hrs)
  6. Orthonormal functions and Fourier series (4 hrs)
  7. Introduction to PDEs and BVPs (6 hrs)
  8. Three exams (6 hrs)

Sample Syllabus