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MATH 310: CALCULUS III

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Title: MATH 310: CALCULUS III


1
MATH 310 CALCULUS III
  • Prerequisite MATH 202 Calculus
    II
  • Textbook Calculus (Early
    Transcendentals)
  • 5th
    edition by James Stewart
  • Solutions by Dan Clegg
    Barbara Frank
  • order on the SU Bookstore website

2
FIND ME ON THE WEB
  • NETWARE APPLICATION LAUNCHER
  • NETSCAPE
  • http//faculty.salisbury.edu/peluft/310/
  • http//faculty.salisbury.edu/peluft/310/
  • PRINT THE GRADING RULES
  • PRINT THE POLICIES
  • READ THE POLICIES

3
(No Transcript)
4
Lesson 1b
5
12.2 Introduction to VECTORS
  • vector a quantity having magnitude and
    direction
  • bound vector arrow from one point to another
  • free vector a class of all bound vectors with
    a given length and direction

A bound vector in 3 dimensions is described by
two triples (a1, a2, a3) and (b1, b2, b3). A free
vector is described by one triple ? c1, c2, c3 ?
A bound vector is fixed, but a free vector is
movable.
6
EQUIVALENT BOUND VECTORS
HAVE THE SAME LENGTH AND DIRECTION
7
EQUIVALENT BOUND VECTORS
GENERATE A PARALLOGRAM
8
ADDING TWO FREE VECTORS
NOTICE THE COMMUTATIVITY OF VECTOR ADDITION
9
SUBTRACTING TWO FREE VECTORS
10
MULTIPLY VECTOR BY A POSITIVE REAL NUMBER (SCALAR)
If cgt0, then ca has the same direction as a,
but the length (magnitude) of ca is c times
the length of a.
11
MULTIPLY VECTOR BY A NEGATIVE REAL NUMBER (SCALAR)
If clt0, then ca has a direction opposite to
a, but the length (magnitude) of ca is c
times the length of a.
12
12.2 0 The bound vector for 2 points
The bound vector from A(2, -3, 4) to B(-2, 1,
1) is the directed line segment AB. A

B
13
12.2 1 The free vector for 2 points
The bound vector from A(2, -3, 4) to B(-2, 1,
1) is the directed line segment AB. A The
corresponding free vector is B
? (-2)-(2), (1)-(-3), (1)-(4) ? ? -4, 4, -3 ?
14
12.2 Magnitude or Length of a Vector
15
12.2 Multiplying a Vector by a Scalar
Vectors which are parallel or antiparallel
differ only by a scalar multiplier.
16
EXAMPLE OF PARALLISM
17
12.2 Adding Vectors
18
12.2 4 Adding Vectors
19
12.2 Standard Basis Vectors
The standard basis vectors Can be used to express
any vector. Heres how
20
12.2 6 Find the Unit Vector Parallel
EXAMPLE
21
12.2 5 Find Tensions in Both Wires
22
Fundamental Theorems of Calculus III
  • Single Variable
  • Line Integrals
  • Green's Theorem
  • Stokes' Theorem
  • Gauss' Theorem
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