Courses Detail Information

MATH2550J – Honors Calculus III

Instructors:

OLGA DANILKINA;Jing Liu;Runze Cai

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

Pre-requisites: MATH1560J Obtained Credit||MATH1160J Obtained Credit||MATH1860J Obtained Credit

Description:

Topics include Euclidean linear spaces; vectors, matrix algebra, inverse and determinant; dot and cross products in 2D and 3D; lines, planes, and vector-valued functions (derivatives and integrals, arc length and curvature); functions of several variables (continuity, partial derivatives, differentiability, the chain rule, directional derivatives and the gradient, extreme values, Lagrange multipliers); multivariable integrals; vector fields, line integrals, Green’s theorem, curl and divergence; surface integrals, Stokes’s theorem, divergence theorem

Course Topics:

1. Euclidean linear spaces. Vectors, matrix algebra, inverse and determinant. Dot product and cross product in 2D and 3D. Lines, planes, and vector-valued functions (derivatives and integrals, arc length and curvature) (10 hrs at 45 min each)
2. Functions of several variables (continuity, partial derivatives, differentiability, the chain rule, directional derivatives and the gradient, extreme values, Lagrange multipliers)  (14 hours)
3. Multivariable integrals (the Darboux and Riemann definitions): double and triple integrals and their applications. (10 hours)
4. Vector fields, line integrals, Green’s theorem, curl and divergence (10 hours)
5. Surface integrals, Stokes’s theorem, divergence theorem (10 hours), Three exams (6 hrs)