Courses Detail Information

MATH2850J – Honors Mathematics III

Instructors:

Horst Harold Hohberger

Credits: 4 (No credits after Vv215 or Vv255.)

Pre-requisites: MATH1860J Obtained Credit

Description:

Topics include systems of linear equations, finite-dimensional vector spaces, inner product spaces, linear maps, matrices, theory of systems of linear equations, determinants, sets and equivalence of norms, convergence and continuity, the first derivative, the regulated integral for vector-valued functions, curves, orientation, and tangent vectors, curve length, normal vectors, and curvature, the Riemann integral for scalar-valued functions, integration in practice, parametrized surfaces and tangent spaces, surface integrals in Rⁿ, potential functions, vector fields and line integrals, flux and circulation, theorems of Green, Gauß and Stokes, the second derivative, free and constrained extrema.

Course Topics:

1. Systems of linear equations, finite-dimensional vector spaces, inner product spaces (8 hrs at 45 min each)
2. Linear maps, matrices and determinants (10 hrs)
3. Convergence, continuity, and differentiation in vector spaces (6 hrs)
4. Vector-valued functions and geometry of curves (6 hrs)
5. Integration of scalar-valued, multi-variable functions (4 hrs)
6. Parametrized surfaces and surface integrals (3 hrs)
7. Potential functions, vector fields and line integrals (4 hrs)
8. Flux and circulation (2 hrs)
9. Theorems of Green, Gauß and Stokes (3 hrs)
10. The second derivative and its applications (8 hrs)
11. Three exams (6 hrs)