Friday, 19 04 2019

Multivariable Functions and Vector Analysis


Multivariable Functions and Vector Analysis
Lesson Code:  22Υ201
Level:  Undergraduate
Semester:  2ο



Functions of two variables. Continuity at a point and in a region. Partial Derivative. Functions of three (or more) variables. Higher order derivatives. Implicit functions and functional determinants. Mean value theorem. Taylor expansion. Extremum points and conditional extremum points. Lagrange multipliers. Multiple integrals. Change of variables. Vectors. Dot, cross and mixed product. Curves in space. Frenet formulas. Surfaces. Directional derivative. Vector operators. Curvilinear coordinates. Rotation of a coordinate system. Curve and surface integrals. Surface area and volume of a three dimensional region. Green?s, Gauss? and Stokes? Theorems.



Kalantonis Vasileios
Perdios Efstathios