Title: MATH 310: CALCULUS III
1MATH 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
2D 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/
3SU COMPUTER SYSTEM
- REGISTRAR GAVE/MAILED YOU PASSWORDS
- CHANGE YOUR GROUPWISE PASSWORD
- Tools gt Settings gt Options gt Security
- TAKE SPECIAL PROBLEMS TO FH 149
4FIND 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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10MATH 310 CALCULUS IIIPREREQUISITE MATERIAL
INCLUDES
- COMPLETING THE SQUARE
- TRIGONOMETRIC IDENTITIES
- POLAR COORDINATES
CONSIDER TAKING ENGR 101 (ART 130?)
11QUIZZES
- 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
12EXTRA 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
13I 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.
14CALCULUS IIIMATHEMATICS 310
- LESSON 1
- 3-D COORDINATES
- INTRODUCTION TO VECTORS
1512.1 3-D COORDINATES
- Coordinate Axes
- Right-hand rule
- Coordinate planes
- Octants
- Plotting a point
- Projecting points in different octants.
- Cartesian product ????? ?3
1612.1 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
1712.1 3 Distance Between Two Points
1812.1 Distance Between Two Pointsin the zz1
plane
1912.1 3 Distance Between Two Points
2012.1 4 Equation of a Sphere Centered at (h,
k, l)
2112.1 5 Show that a Given Equation Describes
a Sphere
Center at (-2, 3, -1) Radius 2?2
22Lesson 1b
2312.2 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.
24EQUIVALENT BOUND VECTORS
HAVE THE SAME LENGTH AND DIRECTION
25EQUIVALENT BOUND VECTORS
GENERATE A PARALLOGRAM
26ADDING TWO FREE VECTORS
NOTICE THE COMMUTATIVITY OF VECTOR ADDITION
27SUBTRACTING TWO FREE VECTORS
28MULTIPLY 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.
29MULTIPLY 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.
3012.2 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
3112.2 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 ?
3212.2 Magnitude or Length of a Vector
3312.2 Multiplying a Vector by a Scalar
Vectors which are parallel or antiparallel
differ only by a scalar multiplier.
3412.2 Adding Vectors
3512.2 2 Adding Vectors
3612.2 3 Standard Basis Vectors
The standard basis vectors Can be used to express
any vector. Heres how
3712.2 4 Find the Unit Vector Parallel
EXAMPLE
3812.2 5 Find Tensions in Both Wires
39Fundamental Theorems of Calculus III
- Single Variable
- Line Integrals
- Green's Theorem
- Stokes' Theorem
- Gauss' Theorem
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