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\textbf{\Large SINGLE VARIABLE CALCULUS I}\\
The University of Toledo\\ Mathematics \& Statistics Department, College of Natural Sciences and Mathematics\\ MATH1850-0XX, CRN XXXXX
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\textbf{Instructor:} & \footnotesize{(Insert Name)} & \textbf{Class Location:} & \footnotesize{(Insert Building/Room)}\\
\textbf{Email:} & \footnotesize{(Insert Email Address)} & \textbf{Class Day/Time:} & \footnotesize{(Insert Days/Time)}\\
\textbf{Office Hours:} & \footnotesize{(Insert Days/Time)} & \textbf{Lab Location:} & \footnotesize{(Insert Bldg/Office \#, if applicable)} \\
\textbf{Office Location:} & \footnotesize{(Insert Building/Office \#)} & \textbf{Lab Day/Time:} & \footnotesize{(Insert Days/Time, if applicable)}\\
\textbf{Office Phone:} & \footnotesize{(Insert Phone Number)} & \textbf{Credit Hours:} & 4\\
\textbf{Term:} & \footnotesize{(Insert Semester/Year)} & &\\
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\medskip\noindent {\bf COURSE DESCRIPTION}\\
Limits, differentiation, Fundamental Theorem of Calculus, Mean Value Theorem, curve sketching, maxima/minima, definite and indefinite integrals, applications.\\
\noindent{\bf STUDENT LEARNING OUTCOMES}\\
The successful Calculus I student should be able to apply the following competencies to a
wide range of functions, including piecewise, polynomial, rational, algebraic,
trigonometric, inverse trigonometric, exponential and logarithmic:
\begin{itemize}
\item {\bf\emph{Limits}}: Determine the existence of, estimate numerically and graphically and find
algebraically the limits of functions. Recognize and determine infinite limits and limits
at infinity and interpret them with respect to asymptotic behavior.\vspace{-.1in}
\item {\bf\emph{Continuity}}: Determine the continuity of functions at a point or on
intervals and to distinguish between the types of discontinuities at a point.\vspace{-.1in}
\item {\bf\emph{Derivatives}}: Determine the derivative of a function using the
limit definition and derivative theorems. Interpret the derivative as the slope of a tangent line to a graph, the slope of a graph at a point, and the rate of change of a dependent variable with respect to an
independent variable.\vspace{-.1in}
\item {\bf\emph{Indeterminate Forms}}: Evaluate limits that result in indeterminate
forms, including the application of L'Hopital's Rule.\vspace{-.1in}
\item {\bf\emph{Higher Order Derivatives}}: Determine the derivative and higher order
derivatives of a function explicitly and
implicitly and solve related rates problems.\vspace{-.1in}
\item {\bf\emph{Graph Sketching}}: Determine absolute extrema on a closed interval
for continuous functions and use the first and second derivatives to analyze and
sketch the graph of a function, including determining intervals on which the
graph is increasing, decreasing, constant, concave up or concave down and
finding any relative extrema or inflection points. Appropriately use these
techniques to solve optimization problems.\vspace{-.1in}
\item {\bf\emph{Antiderivatives}}: Determine antiderivatives, indefinite and definite
integrals, use definite integrals to find areas of planar regions, use the
Fundamental Theorems of Calculus, and integrate by substitution.
\end{itemize}
\noindent {\bf PREREQUISITES}\\
Before enrolling in MATH 1850, students must
attain sufficient ACT MATH, College Algebra and Trigonometry placement test results or
minimum grade of C- in MATH 1320 and MATH 1330 or MATH 1340. Students with marginal trig
placement test scores take MATH 1980 concurrently. For details on the scores on the ACT
MATH, College Algebra and Trigonometry placement tests required for MATH 1850, see the
Department's placement table.\\
\noindent{\bf TEXTBOOK:} {\it Calculus -- Volume I}, OpenStax (ISBN: 9781938168024), Contributing Authors: Edwin Jed Herman and Gilbert Strang. The book is available for free at \url{https://openstax.org/details/books/calculus-volume-1}. \\
\newpage
\medskip\noindent{\bf UNIVERSITY POLICIES:}\\
\noindent{\bf POLICY STATEMENT ON NON-DISCRIMINATION ON THE BASIS OF DISABILITY (ADA)}\\
The University is an equal opportunity educational institution. Please read The University's Policy Statement on Nondiscrimination on the Basis of Disability Americans with Disability Act Compliance.\\
\noindent{\bf ACADEMIC ACCOMMODATIONS}\\
The University of Toledo is committed to providing equal access to education for all students. If you have a documented disability or you believe you have a disability and would like information regarding academic accommodations/adjustments in this course please contact the Student Disability Services Office (Rocket Hall 1820; 419.530.4981; studentdisabilitysvs@utoledo.edu) as soon as possible for more information and/or to initiate the process for accessing academic accommodations. For the full policy see: \url{http://www.utoledo.edu/offices/student-disability-services/sam/index.html}\\
\medskip\noindent{\bf ACADEMIC POLICIES:}\\
\noindent{\bf STUDENT PRIVACY}\\
Federal law and university policy prohibits instructors from discussing a student's grades or class performance with anyone outside of university faculty/staff without the student's written and signed consent. This includes parents and spouses. For details, see the Confidentiality of Student Records (FERPA) section of the University Policy Page at \url{http://www.utoledo.edu/policies/academic/undergraduate/index.html}\\
\noindent{\bf MISSED CLASS POLICY}\\
If circumstances occur in accordance with The University of Toledo Missed Class Policy (found at \url{http://www.utoledo.edu/policies/academic/undergraduate/index.html}) result in a student missing a quiz, test, exam or other graded item, the student must contact the instructor in advance by phone, e-mail or in person, provide official documentation to back up his or her absence, and arrange to make up the missed item as soon as possible.\\
\noindent{\bf ACADEMIC DISHONESTY}\\
Any act of academic dishonesty as defined by the University of Toledo policy on academic dishonesty (found at http://www.utoledo.edu/dl/students/dishonesty.html) will result in an F in the course or an F on the item in question, subject to the determination of the instructor. Please note that any use of, or visibility of, a cell phone or smart watch (or any other device capable of connecting to the internet or storing information, or anything not approved by the instructor) during a test, quiz or exam will be considered academic dishonesty.\\
\medskip\noindent{\bf GRADING AND EVALUATION}\\
Your syllabus should describe the methods
of evaluation, whether by quizzes, exams or graded assignments. (There should be at least
two one-hour in-class exams. If quiz scores are not included in the final grade
computation, there should be three one-hour exams.) If a grading scale is used, it should
be clearly stated. A statement of the proportion that each evaluation component
contributes toward the final grade should also be included. A sample reasonable
distribution for this class would be:
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Homework and/or Quizzes & 30\% \\
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Midterm Exams & 40\% \\
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Final Exam & 30\% \\
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In scheduling quizzes and exams, it should be kept in mind that the last day to add/drop
the class is the end of the second week of classes and the last day to withdraw is the end of the tenth week. By these dates, students should have sufficient data
to realistically gauge their progress in the class.
For program assessment purposes, each semester a committee of all Calculus I instructors
will prepare a set of six common exam questions to appear on the final exams of all
sections of the course.
Information about the algebra and trigonometry placement (including practice tests) may be
found on the Math Department website at
\url{http://www.math.utoledo.edu/placement_index.html}
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\medskip\noindent{\bf IMPORTANT DATES}\\
*The instructor reserves the right to change the content of the course material if he perceives a need due to postponement of class caused by inclement weather, instructor illness, etc., or due to the pace of the course.\\
\noindent{\bf MIDTERM EXAM:}\\
{\bf FINAL EXAM:}\\
\noindent{\bf OTHER DATES}\\
The last day to drop this course is:\\
The last day to withdraw with a grade of ``W'' from this course is:\\
\medskip\noindent{\bf STUDENT SUPPORT SERVICES}\\
Students should be made aware of the tutoring help
available during each week of the semester in the Mathematics Learning and Resource
Center, located in Rm B0200 in the lower level of Carlson Library (phone ext 2176). The
center operates on a walk-in basis. MLRC hours can be found on their web page at
\url{http://math.utoledo.edu/mlrc/MLRC.pdf.}\\
\medskip\noindent{\bf CLASS SCHEDULE}\\
The syllabus should provide a list of sections to
be covered and ideally, should indicate the material that might be covered on each
in-class examination. Please include in your syllabus a list of important dates, including
mid-term exam dates, the drop and withdrawal dates, and the time and place of the final
exam.
A recommended schedule of the class time to be devoted to each section is listed below.
While individual experiences may vary somewhat, the schedule is a template for completing
all of the topics in the course and it should be consulted periodically to ensure that you
are on track to complete the syllabus with an appropriate amount of time devoted to each
section. Most students passing this course will proceed to MATH 1860. (If you are not
familiar with our calculus sequence, please consult the course coordinator.) \textbf{It
is critically important that you do not shortchange them or hamper MATH 1860 instructors
by skipping important sections or by rushing through the introduction to integration
because of poor planning.}
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\noindent {\bf SUGGESTED SCHEDULE}\hfill
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& & & \\
Chapter & 1 & \textbf{Functions} & (total 4 hr) \\
&1.1 &\textbf{(Op.)}Review of Functions & \\
&1.2 &\textbf{(Op.)} Basic Classes of Functions & \\
&1.3 & Trigonometric Functions & 1 \\
&1.4 & Inverse Functions & 1 \\
&1.5 & Exponential and Logarithmic Functions & 2 \\
& & & \\
Chapter & 2 & \textbf{Limits and Continuity} & (total 5 hr) \\
&2.1 &\textbf{(Op.)} A Preview of Calculus & \\
&2.2 &The Limit of a Function; {\it Limits} & 1.5 \\
&2.3 &The Limit Laws; {\it Limits} & 2 \\
&2.4 &Continuity; {\it Continuity} & 1.5 \\
& & & \\
Chapter & 3 & \textbf{Differentiation} & (total 11 hr) \\
&3.1 &Defining the Derivative; {\it Derivatives} & 1 \\
&3.2 &The Derivative as a Function; {\it Derivatives} & 1 \\
& 3.3 &Differentiation Rules; {\it Derivatives} & 1.5\\
&3.4 & Derivatives as Rates of Change; {\it Derivatives} & 1 \\
&3.5 &Derivatives of Trigonometric Functions; {\it Derivatives} &1 \\
&3.6 &The Chain Rule; {\it Derivatives} &1.5 \\
&3.7 & Derivatives of Inverse Functions; {\it Derivatives} & 1.5 \\
&3.8 &Implicit Differentiation; {\it Derivatives} & 1 \\
& 3.9 & Derivatives of Exponential and Logarithmic Functions; {\it Derivatives} & 1.5 \\
& & & \\
Chapter & 4 & \textbf{Applications of Derivatives} & (total 9 hr)\\
&4.1 & Related Rates; {\it Higher Order Derivatives} & 1 \\
&4.2 & Linear Approximations and Differentials; {\it Derivatives} &1 \\
&4.3 & Maxima and Minima; {\it Graph Sketching} & 1.5 \\
&4.4 & \textbf{(Op.)} The Mean Value Theorem & \\
&4.5 & Derivatives and the Shape of a Graph; {\it Graph Sketching} & 1.5 \\
&4.6 & Limits at Infinity and Asymptotes; {\it Graph Sketching} &1 \\
&4.7 &Applied Optimization; {\it Graph Sketching} &2 \\
&4.8 & L'H\^{o}pital's Rule; {\it Indeterminate Forms} &1 \\
&4.9 & \textbf{(Op.)} Newton's Method & \\
&4.10 & \textbf{(Op.)} Antiderivatives & \\
& & & \\
Chapter & 5 & \textbf{Integration} & (total 7 hr) \\
&5.1 & Approximating Areas; {\it Antiderivatives} & 1 \\
&5.2 & The Definite Integral; {\it Antiderivatives} & 1.5 \\
&5.3 & The Fundamental Theorem of Calculus; {\it Antiderivatives} &1.5 \\
&5.5 &Substitution; {\it Antiderivatives} &1 \\
&5.6 & Integrals Involving Exponential and Logarithmic Functions; {\it Antiderivatives}&1\\
&5.7 & Integrals Resulting in Inverse Trigonometric Functions; {\it Antiderivatives}&1\\
& & & \\
Chapter & 6 & \textbf{Applications of Integration} & (total 1 hr) \\
&6.1 & Areas between Curves; {\it Antiderivatives} & 1 \\
& & & \\
& & Total Hours & 37
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