Courses Detail Information
MATH2850J – Honors Mathematics III
Instructors:
Credits:
4 (No credits after Vv215 or Vv255.)
Pre-requisites:
MATH1860J
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 gives an introduction to linear algebra of finite-dimensional spaces and applies these results to the theory of functions of several variables. A strong emphasis is based on concepts that play an important role in physics and engineering applications, such as line and surface integrals and vector fields.
Course Topics:
1. Systems of linear equations, finite-dimensional vector spaces, inner product spaces
2. Linear maps, matrices and determinants
3. Convergence, continuity, and differentiation in vector spaces
4. Vector-valued functions and geometry of curves
5. Integration of scalar-valued, multi-variable functions
6. Parametrized surfaces and surface integrals
7. Potential functions, vector fields and line integrals
8. Flux and circulation
9. Theorems of Green, Gauß and Stokes
10. The second derivative and its applications