Lecture 1, Monday, 8/25/08:
Sections 10.1/10.2: Vectors in the plane and in space
Topics
- Vectors. Algebraic representation (via
components) and geometric representation (via direction and length).
Notations (angle brackets, and boldface/arrow). Vectors versus scalars.
- Position vectors
- Magnitude (length) of a vector
- Arithmetic with vectors:
Addition, subtraction, and scalar multiplication.
Algebraic definitions, and geometric interpretations.
- Parallel vectors
- Unit vectors. Normalizing a given vector (i.e., finding a unit vector
in the same direction as the given vector).
- The 3-dimensional coordinate system, coordinate axes, coordinate
planes, octants. Right-hand rule (screwdriver rule)
- Standard basis vectors i, j, k.
Representation of a vector as linear combination of basis vectors.
- Distance formula
- Equation of a sphere
Read
Section 10.1/10.2. Optional: Examples 1.5, 1.6 in 10.1.
(Material marked "optional" will not be tested on quizzes and exams.)
Homework
Section 10.1: Problems 3, 9, 11, 15, 19, 25.
Solutions.
Section 10.2: Problems 5, 17, 21, 23, 27, 29, 43, 45.
Solutions.
(The exercises at the end of each section in Smith/Minton are
split into three separately numbered parts: Exercises labeled "Writing
Exercises", ordinary exercises (the main part),
and exercises labeled "Exploratory Exercises".
The above problem numbers all refer to the middle part,
the main exercise section.)
Notes
-
Homework.
Homework will not be collected, but the material covered by these
problems will be tested in quizzes and exams.
See the Course Information Sheet for
complete grading policies.
-
Arrow notation for vectors.
It is important to distinguish vectors from scalars.
Make sure you use the arrow notation
for vectors; the arrow notation serves
as a substitute for boldface when writing by hand or on the blackboard.
Back to the Course Homepage
Last modified Sun 31 Aug 2008 05:37:48 PM CDT