MATH 121

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Summer 2013:�
� USPP MATH 121:�
� Calculus III
June 3, 2013 � July 31, 2013
MATH 121 covers vectors; vector-valued functions; calculus of functions of several variables:�
� partial
derivatives, gradient, divergence, curl, multiple integrals, line integrals, Stokes�
�s and Green�
�s
theorems.
�
Instructress: Joan Rosebush, (Rosi)
Office: Votey Hall 103
Telephone: (802) 656-8858
Fax: (802) 419-3847
E-mail: [email protected]
Web-Site Address:�
� www.cems.uvm.edu/~jrosebus
Office Hours
Tuesday 10:30 AM � 12:00 PM
Thursday 12:00 PM � 1:30 PM
If you need help, please ask!�
� If you wish to meet with me other than during my office
hours, please e-mail me days and times that are convenient for you to meet.�
� I would be
happy to make an appointment with you!
REQUIRED COURSE MATERIALS
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Text and Online Homework Access Card
You will need the paperback or eBook version of the required text, and an access card for Enhanced
WebAssign online homework. If you took Math 21 and/or Math 22 at UVM any time between Fall 2011
and Summer 2012, this is the same text that you used, and your WebAssign access code should still be
active. If you do not already have the text and WebAssign access, choose one of the following options.
Option 1
Enhanced WebAssign with eBook Access Card for Multi Term Math and Science. ISBN 0-538-73807-3
This includes a homework access card and online access to the eBook.
Option 2
Calculus: Early Transcendentals, Hybrid Edition (with Enhanced WebAssign with eBook Access Card for
Multi Term Math and Science), 7th Edition, Stewart. ISBN 1-111-42668-6
This includes a homework access card and online access to the eBook, plus a paperback textbook.
Note About Used Books
If you purchase a used copy of the paperback textbook, you will need to separately purchase an access
code for Enhanced WebAssign with eBook (ISBN 0-538-73807-3) or Enhanced WebAssign without eBook
(ISBN 0-538-73811-1). This can be easily purchased online from within WebAssign after class begins.
Software
The Mathematica software used in the course is provided by UVM; you do not need to purchase it. You
may install Mathematica on your own computer free of charge under UVM�s site license. Mathematica
is also available for use in various computer labs and classrooms on campus.
Final grade for the class is based upon:
Quiz Average: 50%,
Mid-Term Grade:�
� 30%, and
Final Examination: 20%.
FINAL EXAMINATION:�
� Wednesday, July 31st:�
� 1:30 PM � 4:30 PM
Make-up quizzes are not given.�
� It is in your best interest to take every quiz, the mid-term,
and the final examination. If you miss any of these, you earn a 0% for it.
No make-up evaluations are given.�
�
Homework!
You are expected to actively participate in this course.�
� Perfect attendance may help your final average
in the class. Less than perfect attendance will not help your final grade. Comprenez-vous?
Do you require special accommodations? Please let me know by noon on Friday, June 7, 2013.�
� I would
be happy to accommodate you!��
��
�
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SUMMER 2013 USPP MATH 121 TOPICS
Learning Objectives
�Three-Dimensional Coordinate Systems�
�
�Vectors�
�
�The Dot Product�
�
�The Cross Product�
�
�Equations of Lines and Planes�
�
Lines
�Equations of Lines and Planes�
�
Planes
�Vector Functions and Space Curves�
�
�Derivatives and Integrals of Vector Functions�
�
�Arc Length and Curvature�
�
Arc Length
�Arc Length and Curvature�
�
Curvature
�Arc Length and Curvature�
�
Unit Tangent, Unit Normal, & Binormal
�Motion in Space:�
� Velocity and Acceleration�
�
�Functions of Several Variables�
�
�Vector Functions and Space Curves�
�
�Derivatives and Integrals of Vector Functions�
�
�Arc Length and Curvature�
�
Arc Length
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�Arc Length and Curvature�
�
Curvature
�Arc Length and Curvature�
�
Unit Tangent, Unit Normal, & Binormal
�Motion in Space:�
� Velocity and Acceleration�
�
�Functions of Several Variables�
�
�Limits and Continuity�
�
�Partial Derivatives�
�
First Partial Derivatives
�Partial Derivatives�
�
Implicit Differentiation
�Partial Derivatives�
�
Higher-Order Partial Derivatives
�Tangent Planes and Linear Approximations�
�
�Tangent Planes and Linear Approximations�
�
Differentials
�The Chain Rule�
�
�Directional Derivatives and the Gradient Vector�
�
�Directional Derivatives and the Gradient Vector�
�
Tangent Planes & Normal Lines
�Maximum and Minimum Values�
�
Local
�Maximum and Minimum Values�
�
Absolute
�Lagrange Multipliers�
�
Single Constraint
�Lagrange Multipliers�
�
Multiple Constraints
�Double Integrals Over Rectangles�
�
�Iterated Integrals�
�
�Iterated Integrals�
�
Volumes
�Iterated Integrals�
�
Average Value
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�Double Integrals Over General Regions�
�
�Double Integrals Over General Regions�
�
Volumes
�Double Integrals Over General Regions�
�
Reverse Order
�Double Integrals in Polar Coordinates�
�
�Double Integrals in Polar Coordinates�
�
Volumes
�Double Integrals in Polar Coordinates�
�
Convert to Polar
�Applications of Double Integrals�
�
�Surface Area�
�
�Triple Integrals�
�
�Triple Integrals�
�
Volumes
�Triple Integrals in Cylindrical Coordinates�
�
�Triple Integrals in Spherical Coordinates�
�
�Change of Variables in Multiple Integrals�
�
Jacobians
�Change of Variables in Multiple Integrals�
�
�Vector Fields�
�
�Line Integrals�
�
�The Fundamental Theorem for Line Integrals�
�
�Green�
�s Theorem�
�
�Curl and Divergence�
�
�Parametric Surfaces and Their Areas�
�
�Surface Integrals�
�
�Stokes�
� Theorem�
�
�The Divergence Theorem�
�
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