Courses Detail Information
MATH2860J – Honors Mathematics IV
Instructors:
Credits:
4 (No credits after Vv216 or Vv256.)
Pre-requisites:
MATH2850J
Description:
The Honors Mathematics sequence is an introduction to calculus at the honors level. New concepts are often introduced in an abstract context, so that they can be applied in more general settings later. Most theorems are proven and new ideas are shown to evolve from previously established theory. Initially, there are fewer applications, as the emphasis is on first establishing a solid mathematical background before proceeding to the analysis of complex models.
The present course focuses on the analytic theory of differential equations and introduces a selection of tools from linear algebra and complex analysis for their solution.
Course Topics:
1. Inverse and implicit function theorems
2. Eigenvalue problems, matrix diagonaliuzation, spectral theorem, Jordan normal form
3. Single first-order ODEs
4. Systems of first-order ODEs and vibrations
5. Introduction to complex analysis and residue theory
6. The Laplace and Fourier transforms
7. Power series solutions and Bessel functions
8. Orthonormal functions and Fourier series
9. Introduction to PDEs and BVPs