WELCOME TO MATH 126 – CALCULUS & ANALYTIC GEOMETRY III
Single-variable calculus – which you have studied over the past two quarters – deals,
surprisingly perhaps, with the simplest possible case of a function: the input is a single number.
This quarter, we will extend the scope of the kinds of functions that we will consider, to include
functions in which the input is an ordered list of numbers, for example considering the functions
z = f(x, y) = x + y or w = g(x, y, z ) = xyz.
This will mean in part learning to draw and interpret graphs like these:
The real world is filled with situations like these. For example, think of all of the factors that
have an impact on the first blooms of spring: the amount of sunlight, the amount of rain, the
average temperature as well as the high and low temperatures… the list could go on.
Another example might be the process of predicting the size of the returning salmon run – a
very important and very complicated question.
NOTE: This class will focus on the concepts, and de-emphasize formal symbolic manipulation
(solving equations, simplifying expressions, etc.) so if your career goals include more
mathematics (e.g. math, engineering, physics, or chemistry) you may consider also taking a
class that emphasizes those skills.
Get ready to expand your mind!
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MATH 126 – CALCULUS & ANALYTIC GEOMETRY III (5 CR): Fall 2015
Class Time and Location: TBD.
Instructor Information:
Matteo Tamburini
Office: FAC (two-story building) 205
Office Hours:
TBD
Phone: (360) 392 4348 Math and writing Center: (360) 392 4235
Fax: (360) 647 7084
Email: [email protected]
Course Description: Covers multiple-dimensional coordinate systems, vector geometry in three dimensions,
functions of multiple variables and their multiple representations, partial derivatives, and their applications
including optimization and motion. Includes an introduction to multivariable integral calculus. Prerequisite: C
or better in MATH 125.
Textbook: Hughes-Hallett, Gleason, McCallum et al, Calculus: Multivariable (6th Ed, 2012)
Course Policies:
 I strongly recommend that you purchase a three-ring binder, and use graph paper to take notes.
 As a courtesy to your fellow students and the instructor, refrain from using headphones and cell phones
(including text messaging) in class. Make sure your cell phone is silenced before coming to class. You
may not use your cell-phone as a calculator during quizzes or exams.
 It is required that have either a TI-83 or a TI-89 (preferred) graphing calculator for this class.
 Late homework assignments or exams will not be accepted under any circumstance.
Course Requirements, Assignment and Assessments:
 Homework will be collected at the beginning of each class session. You will be graded for both the
completeness of the assignment and the accuracy of your solution of certain problems.
o From one class session to the next, there will be an extensive list of assignments. You will be
expected to turn in five exercises and five problems of your choosing from that list. You must
select at least one problem from each section. I will select a subset of the ten and provide you
with feedback.
o One-word or one-number answers do not demonstrate your understanding of any concept or
process: you should show clear work accompanied by clear and precise descriptions of your
reasoning that would be understood by another student.
o It is an expectation that you look over all of the problems that were assigned; you should discuss
the content of the assignments with your classmates or with me.
o It is an expectation of this class that you ask me questions about at least one problem in the list
of assignments the day before the assignment is due. During the weekend, this means that you
will send me an email.
 There will be three (or four) exams and comprehensive final exam
o The exams will be closed book/closed notes.
 As a part of your regular study routine, you should be compiling a “review sheet” of important concepts.
You will be expected to complete one and turn it in to me before each exam.
Attendance: Your presence in this class will be crucial to your success. You will be expected to be in class
every day. I understand that life may bring unexpected complications, but understanding math involves
participation and time, both in and out of class. If you must miss class for any reason (personal, health-related,
or cultural) you will be expected to contact me ahead of time and stay current on class assignments.
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Course Outcomes
As a part of the expectations for this class, by the end of the quarter students will be able to:
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Evaluate functions of two or more variables described by a table, equation, or graph.
Use various coordinate systems (e.g. rectangular, polar, cylindrical) and convert among them.
Create and interpret pictorial representations of functions of two variables, such as graphs, contour diagrams
and cross-sections by hand and using a graphing utility.
Find formulas for linear functions with given properties, create and interpret their graphical representations,
and use linear approximation.
Apply and interpret the operations of vector algebra, including addition, scalar multiplication, dot and cross
product.
Use and interpret the geometric definitions of partial and directional derivatives, the gradient, tangent planes
(and their equations) as they relate to graphs and surfaces; explain the connection between these derivatives
and the graph, contour diagram and cross-sections of a function.
Interpret the various derivatives of multivariable functions as rates of change.
Use and interpret the geometric definition of the integral as a limit of Riemann sums.
Apply the geometric understanding of multiple integrals to practical situations, such as computing average
values, areas, volumes and total amount from a density.
Grading:
In order to pass this class, you must demonstrate that you understand the material covered in the class: this
means that you should be able to do the things listed above.
You will have multiple opportunities to demonstrate your understanding: through exams, homework, in-class
activities, and by completing optional assignments.
For each of the outcomes in the list above, I will measure your understanding using the words below:
Fluent
Proficient
You demonstrate a
thorough understanding
of the concept in a variety
of contexts.
You consistently
demonstrate an
understanding of the
fundamental aspects of
the concept.
Emerging
On at least one occasion
you demonstrate that you
understand some of the
important features of the
concept
Incomplete
There is insufficient
evidence to assess your
understanding of the
course outcome.
A “C” grade in this class means
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at least a Proficient understanding of each of the course outcomes;
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you attend class at least 70% of the time
16 homework assignments and 16 ‘points’.
A “B” grade in this class means that you have fulfilled the requirements for a “C” grade and:
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A Fluent understanding of three or more course outcomes
18 homework assignments and 25 ‘points’.
An “A” grade in this class means that you have fulfilled the requirements for a “C” grade and:
 Demonstrate a Fluent understanding of more than half of the course outcomes
 20 homework assignments and 40 ‘points’.
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