Courses Detail Information
VV255 – Applied Calculus III
Instructor: Olga Danilkina
Instructors (Faculty):
Credits: 4 (No credits after Vv215 or Vv255.)
Pre-requisites: Vv156 or Vv186.
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:
- 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)
- Functions of several variables (continuity, partial derivatives, differentiability, the chain rule, directional derivatives and the gradient, extreme values, Lagrange multipliers) (14 hours)
- Multivariable integrals (the Darboux and Riemann definitions): double and triple integrals and their applications. (10 hours)
- Vector fields, line integrals, Green’s theorem, curl and divergence (10 hours)
- Surface integrals, Stokes’s theorem, divergence theorem (10 hours), Three exams (6 hrs)