Elementary row and column operations in the Matrices. Row-Echelon form and reduced row-echelon form. Rank of a matrix. Inverses of matrices and some applications about this.
Directional Derivatives and Gradient Vector: Definition and Calculation of Directional Derivative in the Plane, Gradient Vector, Tangents to Level Curves and Gradients, Directional Derivative in Space.
Some Special Matrices and matrix applications.(Symmetric Matrix,Anti symmetric matrix, periodic matrix, idempotent matrix, Nilpotent matrix, orthogonal matrix, A conjugate of a matrix and its properties, hermitian matrix,Anti hermitian matrix, regular matrix, singuler matrix, and their applications.
Functions of More Than Two Variables. Partial Derivatives: Partial Derivatives of Functions of Two and Three Variables, Partial Derivatives and Continuity, Equality of Second Order Partial Derivatives and Mixed Derivatives, Higher Order Partial Derivatives, with "Chain Rule for Functions of Two and Three Variables [For Functions with One and Two Independent Variables], Implicit Derivative"
Definition of matrix, types of matrix, Equality of Matrices, Addition and subtraction of matrices, matrix multiplication by a scalar, Some properties about them. Multiplying matrices and Some properties about it. Transposes of matrices and properties of the transpose.
Functions of Several Variables: Functions of Two and Three Variables: Domain and Range, Graphs, Level Curves and Level Surfaces, Limits and Continuity in Functions of Two Variables (Two-Way Test for the Absence of Limit, Continuity of Composite Functions),