INTRODUCTION

INTRODUCTION Some Preliminaries Concepts

Some preliminaries concept • Linear Equation • Quadratic Equation • Exponent • Logarithms • Determinants

Solution of two simultaneous first degree equations in two unknowns • The general form : • The solutions are x and y that satisfy both equations • Ex: solve this equation!

Solution of three simultaneous first degree equations • The general form: • Example: find the value of x, y and z from these simultaneous equation :

Trigonometry • The trigonometric functions • The trigonometric functions for special angles • Important identities • Relations for triangles • Inequality and absolute value

The Point and Plane Vectors FaridaNurhasanah

2-2. The Rectangular Coordinate System • A Point is an undefined object which we shall represent pictorially by a dot • Coordinates of point are two real number that represent the distance of the point from axis of abscissa and ordinate. It is represent by (x,y) • (See demonstration using GSP)

2-3. Symetry • A Point can be symmetric to a point and to a line

2-4. Projection • The projection of a point on a given line is the foot of the perpendicular dropped from the point to the line

2-5. Scalar Components of a segment • Let and Then the scalar component of AB can be write as [∆X, ∆Y] in which: • Example : back to previous GSP

2-6. Distance between Two Points • Try to find the distance between point A and B from the previous example!

2-7. Direction Cosines of a Segment • Let and any two distinct points in the plane • The direction cosine of AB are defined to be the cosine of the angles between AB and the rays, or half-lines, through A parallel to the positive x-axis and positive y-axis, respectively

Ilustration

INTRODUCTION

INTRODUCTION

Presentation Transcript

Introduction to introduction to introduction to … Optimization

INTRODUCTION/ INTRODUCTION

Introduction

INTRODUCTION

Introduction

Introduction