Linear Algebra, Calculus of vector and functions in several variables

Part 1 : Linear Algebra
System of linear equations- Methods for solving systemof linar equations- Gauss elimination method-Gauss Jordan method- Row echelon form- Reduced row echlon form-Homogeneous system- Matrix and algebra of matrices- Scalar multiplication-Matrix multiplication-Inverse of matrix-Power of matrix - elementary matrix - Methods of finding inverse of matrix-Solving linear system by inverse matrix-Determinant- -properties of determinantial function -Crammer's rule.
Part 2: Vectors and the geometry of space 
Vetors in the plane and in the space, Dot product, the cross product, Lines and planes in space, Surfaces in space, Vector valued functions, Limits ,Derivatives, Velocity, Acceleration, Curvature, Unit tangent vector, Principal normal vector, Tangential and normal components of acceleration.
Part 3 : Functions of several variables and differentiation
-Functions of several variables
Limits and continuity- Partial derivatives- Tangents planes and linear approximations, Increments and differentials- The chain rule - The gradient and directional derivatives- Extrema of functions of several variables - Constrained optimization and Lagrange Multipliers