107 ريض - المتجهات والمصفوفات

Linear Algebra
WEEK 1
Chapter 1:   System of Linear Equations
1.0           Basic Definitions of Matrices
 

1. System of linear equation
2. Methods for  solving system of linear equations
3. Gauss Elimination Method

WEEK   2
 

1. Gauss Jordon Method
2. Row Echlon form
3. Reduced Row Echlon form
4. Homogeneous system

WEEK   3
Chapter 2:   Matrices
2.1           Properties of Matrices and Algebra of matrices
2.2           Scalar Multiplication
2.3           Matrix Multiplication
2.4           Inverse of 2x2 matrix
2.5           Power of Matrix
2.6           Elementary Matrix
2.7           Methods of finding inverse of matrix
2.8           Solving Linear system by Inverse Matrix
WEEK   4
Chapter 3:  Determinant
3.1           Determinant
3.2           By Direct Multiplication
3.3           By cofactor
3.4           By row operation
WEEK   5
3.5           Properties of Determinantial function
3.6           Minor and cofactors, Inverse by cofactors
3.7           Crammer’ Rule
Calculus
WEEK   6
Chapter 10: Vectors and the Geometry of Space
10.1 Vectors in the Plane
10.2 Vectors in Space
10.3 The Dot Product
WEEK   7,8
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Surfaces in Space
WEEK   9
Chapter 11: Vector-Valued Functions
11.1 Vector-Valued Functions
11.2 Limits, Derivatives
11.3Velocity, Acceleration.
WEEK   10
11.4 Curvature , Unit Tangent Vector, Principal Normal Vector
11.5 Tangential and Normal Components of Acceleration
WEEK   11
Chapter 12: Functions of Several Variables and Differentiation
12.1 Functions of Several Variables
12.2 Limits and Continuity
WEEK   12
12.3 Partial Derivatives
WEEK   13
12.4 Tangent Planes and Linear Approximations, Increments and Differentials
12.5 The Chain Rule
12.6 The Gradient and Directional Derivatives
WEEK   14
12.7 Extrema of Functions of Several Variables
12.8 Constrained Optimization and Lagrange Multipliers