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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)
  • 4th
    edition by James Stewart
  • Solutions by Dan Clegg
    Barbara Frank
  • order on the SU Bookstore website

2
D r. P h i l i p E. L u f t
  • On-campus email Philip
    Luft
  • Off-campus email peluft_at_salisbury.edu
  • Office Telephone 410-54
    3-6467
  • Office Hours in HS 126
  • See my Schedule on the web.
  • http//faculty.salisbury.edu/peluft/310/

3
SU COMPUTER SYSTEM
  • REGISTRAR GAVE/MAILED YOU PASSWORDS
  • CHANGE YOUR GROUPWISE PASSWORD
  • Tools gt Settings gt Options gt Security
  • TAKE SPECIAL PROBLEMS TO FH 149

4
FIND ME ON THE WEB
  • NETWARE APPLICATION LAUNCHER
  • NETSCAPE
  • http//faculty.salisbury.edu/peluft/310/
  • PRINT THE GRADING RULES
  • PRINT THE POLICIES
  • READ THE POLICIES

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MATH 310 CALCULUS IIIPREREQUISITE MATERIAL
INCLUDES
  • COMPLETING THE SQUARE
  • TRIGONOMETRIC IDENTITIES
  • POLAR COORDINATES

CONSIDER TAKING ENGR 101 (ART 130?)
11
QUIZZES
  • EVERY DAY except when a test is returned
  • ONE OR MORE HOMEWORK PROBLEMS
  • AFTER the REQUIRED number of QUIZZES,
  • THE REST ARE MAKEUPS.
  • NO MAKEUP QUIZZES OUTSIDE CLASS

12
EXTRA CREDIT
  • CHOOSE A TOPIC FROM THE LIST
  • AGREE WITH ME ON A PROBLEM
  • PREPARE A SOLUTION SHEET WITH A
  • COPY FOR EVERY CLASS MEMBER
  • PRESENT THE SOLUTION AT THE REVIEW

13
I WILL CALL ON EVERYONEYOU MAY
  • ANSWER
  • SAY I DONT KNOW
  • SAY I PASS

I hope you will learn from the experience, but I
will not grade you.
14
CALCULUS IIIMATHEMATICS 310
  • LESSON 1
  • 3-D COORDINATES
  • INTRODUCTION TO VECTORS

15
12.1 3-D COORDINATES
  • Coordinate Axes
  • Right-hand rule
  • Coordinate planes
  • Octants
  • Plotting a point
  • Projecting points in different octants.
  • Cartesian product ????? ?3

16
12.1 1-2 page 784Linear Equations Missing
Variables
  • 0 Sketch z 0 the xy plane
  • 1a Sketch z 3 plane parallel to xy plane
  • 1b Sketch y 5 plane parallel to xz plane
  • 2 Sketch y x plane parallel to z axis

17
12.1 3 Distance Between Two Points
18
12.1 Distance Between Two Pointsin the zz1
plane
19
12.1 3 Distance Between Two Points
20
12.1 4 Equation of a Sphere Centered at (h,
k, l)
21
12.1 5 Show that a Given Equation Describes
a Sphere
Center at (-2, 3, -1) Radius 2?2
22
Lesson 1b
23
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 2 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.
24
EQUIVALENT BOUND VECTORS
HAVE THE SAME LENGTH AND DIRECTION
25
EQUIVALENT BOUND VECTORS
GENERATE A PARALLOGRAM
26
ADDING TWO FREE VECTORS
NOTICE THE COMMUTATIVITY OF VECTOR ADDITION
27
SUBTRACTING TWO FREE VECTORS
28
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.
29
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.
30
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
31
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 ?
32
12.2 Magnitude or Length of a Vector
33
12.2 Multiplying a Vector by a Scalar
Vectors which are parallel or antiparallel
differ only by a scalar multiplier.
34
12.2 Adding Vectors
35
12.2 2 Adding Vectors
36
12.2 3 Standard Basis Vectors
The standard basis vectors Can be used to express
any vector. Heres how
37
12.2 4 Find the Unit Vector Parallel
EXAMPLE
38
12.2 5 Find Tensions in Both Wires
39
Fundamental Theorems of Calculus III
  • Single Variable
  • Line Integrals
  • Green's Theorem
  • Stokes' Theorem
  • Gauss' Theorem

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