M-107   Vectors and Matrices (3+0) credit-hours.

First  Semester I 1429 – 1430 H

Prerequisite: M - 150           Language of instruction: English

Course Details

Linear Algebra

Systems of linear equations, matrices, determinants, inverse of a matrix, Cramer's rule.

Vector and several variables calculus

Vectors in two and three dimensions, scalar and vector products, equations of lines and planes in space, surfaces, cylindrical and spherical coordinates.

Vector valued functions their limits, continuity, derivatives and integrals. Motion of a particle in space, tangential and normal components of acceleration.

Functions in two or three variables, their limits, continuity, partial derivatives, differentials, chain rule, directional derivatives, tangent planes and normal line to surfaces. Extrema of functions of several variables, Lagrange multipliers.

Weekly Course Details

Linear Algebra

WEEK 1

Chapter 1:   System of Linear Equations

1.1                 System of linear equation

1.2                 Methods for  solving system of linear equations

1.3                 Gauss Elimination Method

WEEK   2

1.4                 Gauss Jordon Method

1.5                 Row Echlon form

1.6                 Reduced Row Echlon form

1.7                 Homogeneous system

WEEK   3

Chapter 2:   Matrices

2.1           Matrix 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 The Calculus of Vector-Valued Functions

WEEK   10

11.3 Motion in Space
11.4 Curvature
11.5 Tangent and Normal Vectors,Tangential and Normal Components of Acceleration

WEEK   11
11.6 Parametric Surfaces

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

WEEK   15

Revision     WEEK

1. Lecture Notes on Linear Algebra by Khawaja Zafar Elahi

2. Calculus by Smith and Milton 3th Ed    (Early Transcendental Editions ).

Lecture Notes on Vector and Several Variables Calculus  by Khawaja Zafar Elahi

Midterm Examination I:       Material covered in first 6 week

Midterm Examination II:     Material covered in 7th  week to 13th week

Group Number : 23347

Final Exam : Mon.14/2/1430H (1-4 PM)  B.6(ج3 )