Analytic Geometry 2015
-
Upload
ahmed-yousry -
Category
Documents
-
view
19 -
download
0
description
Transcript of Analytic Geometry 2015
-
Math 2 : 0 Analytic Geometry
1
BS002: Mathematics 2 Analytic Geometry
1
Plane Geometry
Space Geometry
Algebra Series
Complex Numbers
Linear Algebra
Assessment
Participation . 10%
Quizzes .... 20%
Midterm .. 20%
Final Exam .. 50%
2
-
Math 2 : 0 Analytic Geometry
2
Textbooks
Smith and Minton
Calculus
4th ed., McGraw Hill 2012
Duffy
Advanced Engineering Mathematics,
CRC Press 1998
3
Learning Material https://sites.google.com/site/sahaggag
4
Syllabus Slides Problem sheets Bonus Questions Announcements Grades
-
Math 2 : 0 Analytic Geometry
3
Plane Geometry
0 Review of Analytic Geometry
1 Conic Sections
2 Parametric Equations
3 Polar Coordinates
5
0 Review of Analytic Geometry
6
Reading Stewart
Review of Analytic Geometry
Problems Sheet 0
-
Math 2 : 0 Analytic Geometry
4
Analytic Geometry
7
Point ?
origin
x-coordinate
Rectangular (Cartesian) Coordinates
x-axis y-axis
y-coordinate
in the plane
The Cartesian Plane
8
4 quadrants
-
Math 2 : 0 Analytic Geometry
5
Example 1
9
x = 4 ?
y = 2 ?
equation? line
Example 2
10
x 0 ? |y| < 1 ?
1 < y < 1
inequality region
-
Math 2 : 0 Analytic Geometry
6
Distance Between 2 Points
11
1 2P P 2 2
2 1 2 1x x y y
Lines
12
m y
x
2 1
2 1
y y
x x
slope ?
Parallel Lines ?
-
Math 2 : 0 Analytic Geometry
7
Example 3
13
Perpendicular Lines ?
Equations of a Line
14
( , ),1 1P x y m
1
1
y ym
x x
Point-Slope
( , ), ( , )1 1 1 2 2 2P x y P x y
1 2 1
1 2 1
y y y y
x x x x
Two Points
,m by m x b
Slope-Intercept
-
Math 2 : 0 Analytic Geometry
8
Equation of a Curve
15
is an equation satisfied by x and y of the points on the curve
The circle is the set of all points that are at a fixed distance (called the radius) from a fixed point (called the center).
The Circle ?
The Line ? 0a x by c
Definition Equation ?
Simple Equation of a Circle
16
Center Radius
at origin r
equation ?
2 2 2x y r
?
?
22 2
2
rx y
r
inside
outside
r = 1 unit circle
-
Math 2 : 0 Analytic Geometry
9
General Circles
17
general ?
Center Radius
(h , k) r
equation ?
2 2 2x h y k r
?
?
22 2
2
rx h y k
r
inside
outside
More Examples
18
See Stewarts Review of Analytic Geometry Examples 1 6
Problems Sheet 0 Problems from Stewarts Exercises