Course: MAT 221 2.0 Functions of Several Variables (Compulsory)
Course content:
Point Sets in Higher Dimensions: The Euclidean Space , Open ball in and Open sets in , Closed set, Adherent Point, Accumulation point of set and Closure of a set, Bounded sets, Bolzano-Weierstrass Theorem; Functions in Higher Dimensional Space: Linear Functions in Rational Functions in Algebraic Functions in ; Limit of Functions: Neighbourhoods of a point, Limit point of a set, Algebra of limits, Non-existence of limit; Continuity of a function: Continuity, Function Continuous on compact sets, Intermediate value theorem; Partial Derivatives: Partial derivatives, Directional derivatives, Mean Value Theorem; Differentiability: Total differential, Sufficient condition for differentiability of a function; Composite Functions: Chain Rules, Homogeneous functions and Euler’s Theorem, Partial derivatives of higher order, Change of Variables, Jacobins and their important properties; Implicit Functions: Existence Theorem, Functional Equations
Recommended Readings: