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\newcommand{\coursenumber}{251}
\newcommand{\coursename}{Calculus I}
\newcommand{\classroom}{CLASSROOM}
\newcommand{\classtime}{TIME}
\newcommand{\crn}{CRN}
\newcommand{\quarter}{Fall 2012}
\newcommand{\officehours}{OFFICE HOURS}
\newcommand{\textbook}{{\textbf{\textsl{Single Variable Calculus:
Concepts and Contexts}}, 4th edition. By James Stewart, Brooks/Cole}}
\newcommand{\prereqs}{MATH 112 or satisfactory placement test score}
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\markright{\sc MATH \coursenumber --- \quarter --- C. Sinclair}
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\centerline{
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\vspace{6pt}
\begin{centering}
\Large \bf \coursename \\
\normalsize \bf MATH \coursenumber---CRN \crn \\[1pt]
\normalsize \bf \quarter \\[1pt]
\end{centering}
\vspace{6pt}
}}
}
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\normalsize
\begin{tabular}{lp{5.2in}}
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\textbf{Instructor:}
& {\bf name:} Christopher Sinclair \\
& {\bf office hours:} \officehours\\
& \textbf{office:} Deady 215M \\
& {\bf email:} csinclai@uoregon.edu \\
\textbf{Course webpage:}
&\url{http://uoregon.edu/~csinclai/}
\\[6pt]
%
\textbf{Class Meetings:}
&{\bf room:} \classroom \\[-1pt]
&{\bf lecture:} \classtime \\[-1pt]
\\
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\textbf{Text:}
& \textbook
\\[6pt]
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\textbf{Calculators:}
& Calculators can be helpful for homework and actually may be
needed for some of the problems, however, to even the
field for everybody, \textsl{they are not allowed during exams.}
\\[6pt]
%
\textbf{Prerequisite:}
& \prereqs
\\[6pt]
%
\textbf{Work Load:}
& This course will require \textsl{between eight and twelve
hours of work per week} outside class and recitation
attendance, depending on your preparation.
\\[6pt]
%
\textbf{Homework:}
& Homework is assigned weekly ...
\\[8pt]
%
\textbf{Tests:}
& $\triangleright$~Midterm dates will be announced at least a
week before.
\\
& $\triangleright$~The final exam will be given on the date and
time assigned by the registrar
(http://registrar.uoregon.edu/calendars/final\_exam). Final exam
week is part of the regular quarter, and you are expected to be
present. If you cannot attend the final exam due to a
conflicting obligation, do not take the course.
\\
& $\triangleright$~The final exam will be held jointly and
concurrently with all other sections of Math 251. (Instructors:
questions regarding this policy should be directed to the faculty
coordinator for Math 251).
\\
& $\triangleright$~Bring your UO student-ID to all your exams.
\\
& $\triangleright$~The use of cellular phones, or any type of headset
during tests is strictly forbidden.
\\[8pt]
%
\end{tabular}
\vspace{.25cm}
\textbf{Documented Disabilities:} Students who have a documented
disability and anticipate needing accommodations in this course should
make arrangements to see the instructor as soon as possible. They
should also bring a letter to the instructor from the Counselor for
Students with Disabilities verifying the
disability. \\
\textbf{Academic Misconduct:}
You are expected at all times to do your own work. Copying content
from other students and submitting it as your own work is grounds for
failing the class. The University Student Conduct Code (available at
http://conduct.uoregon.edu) defines academic misconduct. Students are
prohibited from committing or attempting to commit any act that
constitutes academic misconduct. By way of example, students should
not give or receive (or attempt to give or receive) unauthorized help
on assignments or examinations without prior permission from the
instructor. \\[8pt]
\textbf{Learning Objectives:} The successful student will be able to
apply the basic precepts of differentiation and derivatives in order
to investigate the quantitative and qualitative behavior of
mathematical functions. This will include finding local and global
extrema, sketching graphs (interpreting derivatives as rates of change
and calculating limits to resolve questions about behavior at infinity
and points of discontinuity).
A significant proportion of the graded effort for the course will
encompass the ability to use mathematical methods, in particular
differentiation, to model phenomena that arise in the natural and
social sciences (this means lots of word problems). This includes
optimization, related rates of change, linear approximation and
applications of exponential growth and decay.
\vspace{.25cm}
More specifically, by the end of the quarter the successful student
will be able to differentiate combinations of common mathematical
functions, produce linear approximation for these functions, and apply
these mathematical tools to solve problems of the type which may arise
in real world situations. \\[8pt]
\textbf{Community Standards:}
The University of Oregon community is dedicated to the advancement of
knowledge and the development of integrity. In order to thrive and
excel, this community must preserve the freedom of thought and
expression of all its members. The University of Oregon has a long and
illustrious history in the area of academic freedom and freedom of
speech. A culture of respect that honors the rights, safety, dignity
and worth of every individual is essential to preserve such
freedom. We affirm our respect for the rights and well-being of all
members.
\newpage
\textbf{Syllabus:}
Included are typical problems that I would expect the students to be
able to do. This list is not meant to be exhaustive! This is not
meant to necessarily be used as a list of problems to be assigned for
homework, especially since many instructors will use webwork homework
assignments. Nor is it necessarily meant to be a list of
problems to be done in class. Merely the problems should (perhaps) be
used to guide what topics you emphasize during lecture.
The schedule below is for one midterm in week 6. More typical is two midterms in weeks 4 or 8. This gives students earlier feedback if they are doing poorly in the course, but it also means two midterms for them to take and two midterms for you to grade. Either scenario is reasonable.
\vspace{.25cm}
\textbf{Week 1:}
Chapter 1 should be read by the students, and it would not be a bad
idea to assign homework on the first day covering basic mathematical
concepts, even though (most) of Chapter 1 will not be covered in
class. On the first day I would cover some portion of $\S$1.2
Mathematical Models: A Catalog of Essential Functions. In particular,
I would emphasize the material outlined by Figure 1. You might also
cover Example 3, and some subset of Problems 1, 8, 13 and relevant
background material. $\S$2.1 The Tangent and Velocity Problems.
$\S$2.2 The Limit of a Function. \\
{\bf Problems:} 1.1: 1, 14, 41, 59. 1.2: 12, 13, 19,
20. 1.3: 26, 29, 33, 51, 54. 1.5: 1, 2, 19, 23, 24, 29. 1.6: 9,
14, 18, 23, 35, 38, 49, 60. 2.1: 5, 9. 2.2: 3, 8, 12, 30.
\\
\textbf{Week 2:}
$\S$2.3 Calculating Limits Using the Limit Laws. $\S$2.4
Continuity. $\S$2.5 Limits Involving Infinity. \\
{\bf Problems:} 2.3: 6, 8, 17, 18, 28, 37, 42. 2.4: 10, 11, 34, 35,
37, 55. 2.5: 9, 11, 17, 23, 28, 51, 55, 56.
\\
\textbf{Week 3:}
$\S$2.6 Derivatives and Rates of Change. $\S$2.7 The Derivative as
a Function. $\S$2.8 What does $f'$ say about $f$? \\
{\bf Problems:} 2.6: 3, 8, 11, 12, 16, 21, 35, 37, 41, 45, 47, 50.
2.7: 3, 12, 13, 20, 25, 41, 53. 2.8: 4, 9, 12, 14, 22, 28, 31.
\\
\textbf{Week 4:}
$\S$3.1 Derivatives of Polynomials and Exponential Functions. $\S$3.2
The Product and Quotient Rules. $\S$3.3 Derivatives of Trigonometric
Functions. \\
{\bf Problems:} 3.1: 2, 15, 20, 22, 28, 29, 42, 45, 60,
65. 3.2: 1, 2, 9, 15, 22, 25, 40, 41, 42, 49, 50, 60. 3.3: 1, 2, 13,
29, 35, 37.
\\
\textbf{Week 5:}
$\S$3.4 The Chain Rule. $\S$3.5 Implicit Differentiation. $\S$3.7
Derivatives of Logarithmic Functions. (Here I would actually teach
differentiation of inverse functions using the chain rule. More
specifically, since
\[
f( f^{-1}(x) ) = x, \qquad f'(f^{-1}(x)) \cdot \frac{d}{dx} f^{-1}(x) = 1
\]
means we can solve for $\frac{d}{dx} f^{-1}(x)$). Several
applications of this can be given including derivatives of logs and
inverse trignometric functions ($\S$3.6). \\
{\bf Problems:} 3.4: 1, 2,
4, 7, 34, 37, 52, 70, 71, 74, 94. 3.5: 15, 16, 47. 3.6: 10, 11, 23,
28. 3.7: 2, 10, 14, 29, 39, 40.
\\
\textbf{Week 6:}
Midterm. $\S$3.8 Rates of Change in the Natural and Social
Sciences. $\S$3.9 Linear Approximation and Differentials. (I would
deemphasize differentials and concentrate on linear approximations). \\
{\bf Problems:} 3.8: 9, 11, 13, 15, 18, 20, 21, 24, 27, 29, 33. 3.9:
2, 15, 18, 22, 33, 34, 36.
\\
\textbf{Week 7:}
$\S$4.1 Related Rates. (Spend two days, do lots of examples).
$\S$4.2 Maximum and Minimum Values. \\
{\bf Problems:} 4.1: 2, 5, 6, 10,
11, 12, 13, 14, 18, 21, 23, 24, 25, 28, 29, 33, 34, 35, 40, 44. 4.2:
5, 8, 11, 23, 29, 28, 36, 41,43, 47, 51.
\\
\textbf{Week 8:}
$\S$4.2 Maximum and Minimum Values (cont). $\S$4.3 Derivatives and
the Shapes of Curves. (Again, lots of examples). \\
{\bf Problems:} 4.2: 61, 62, 63, 65. 4.3: 1, 7, 8, 13, 17, 20, 41,
49, 53, 54, 55, 56, 58, 63.
\\
\textbf{Week 9:}
$\S$4.5 Indeterminate Forms and l'Hospitals's Rule. $\S$4.6
Optimization Problems. (Lots of examples). \\
{\bf Problems:} 4.5: 1, 2, 4, 6, 12, 16, 61, 64, 65, 66, 67, 75. 4.6:
2, 5, 8, 9, 10, 15, 19, 25, 27, 32, 33, 35, 43, 50, 51, 54, 56, 60.
\\
\textbf{Week 10:}
$\S$4.7 Newton's Method. $\S$4.8 Antiderivatives. Review of the
quarter. \\
{\bf Problems:} 4.7: 1, 4, 8, 23, 25, 33, 34. 4.8: 3, 9,
12, 25, 35, 41, 43, 56, 58.
\vspace{.5cm}
Notice that the suggested syllabus covers fewer sections per week
after the midterm. This is to allow for significant emphasis on
mathematical modeling and applications of concepts of differentation
to problems arising in various domains, and using this information to
determine various features of mathematical functions.
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