MATH 251 – LECTURE 1
JENS FORSGÅRD
http://www.math.tamu.edu/~jensf/
This week: 11.1–3
webAssign: 11.1–2, due 1/25 11:55 p.m.
Next week: 11.4–7
webAssign: 11.3–6, opens 1/25 12 a.m.
Help Sessions:
yet to be posted
Office Hours:
BLOC 641C
M 12:30–2:30 p.m.
W 2–3 p.m.
or by appointment.
Rectangular coordinates
Choose a point O to be the origin, and introduce the three coordinate axes.
Rectangular coordinates
Definition 1. The coordinate system is positively oriented if it fulfills the right hand rule.
Points in 3-dimensional space
We represent a point P ∈ R3 by its coordinates P = P (a, b, c).
Points in 3-dimensional space
Exercise 2. What surface in R3 is represented by the equation y = 2?
Points in 3-dimensional space
Exercise 3. What surface in R3 is represented by the equation x2 + y 2 = 1?
Points in 3-dimensional space
Exercise 4. What surface in R3 is represented by the equation y + 2x = 2?
Distance in R3
Let P1(x1, y1, z1) and P2(x2, y2, z2) be two points in R3. The distance |P1P2| is given by the formula
p
|P1P2| = (x2 − x1)2 + (y2 − y1)2 + (z2 − z1)2.
Distance in R3
The sphere with radius R and center C(a, b, c) consists of all points with distance R from C(a, b, c).
Local maximum and minimum
Exercise 5. Find the equation of a sphere that has center C(0, 1, 2) and contains the origin.