MATH 310: CALCULUS III

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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

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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

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(No Transcript)
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Lesson 1b
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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.
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EQUIVALENT BOUND VECTORS
HAVE THE SAME LENGTH AND DIRECTION
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EQUIVALENT BOUND VECTORS
GENERATE A PARALLOGRAM
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ADDING TWO FREE VECTORS
NOTICE THE COMMUTATIVITY OF VECTOR ADDITION
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SUBTRACTING TWO FREE VECTORS
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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.
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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.
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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
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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 ?
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12.2 Magnitude or Length of a Vector
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12.2 Multiplying a Vector by a Scalar
Vectors which are parallel or antiparallel
differ only by a scalar multiplier.
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EXAMPLE OF PARALLISM
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12.2 Adding Vectors
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12.2 4 Adding Vectors
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12.2 Standard Basis Vectors
The standard basis vectors Can be used to express
any vector. Heres how
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12.2 6 Find the Unit Vector Parallel
EXAMPLE
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12.2 5 Find Tensions in Both Wires
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Fundamental Theorems of Calculus III

• Single Variable
• Line Integrals
• Green's Theorem
• Stokes' Theorem
• Gauss' Theorem