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\textbf{\Large CALCULUS II FOR MATHEMATICIANS, SCIENTISTS AND EDUCATORS}\\
The University of Toledo\\ Mathematics \& Statistics Department, College of Natural Sciences and Mathematics\\ MATH1840-0XX, CRN XXXXX
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\textbf{Office Phone:} & \footnotesize{(Insert Phone Number)} & \textbf{Credit Hours:} & 4\\
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\noindent {\bf COURSE DESCRIPTION}\\
Techniques of integration, polar coordinates and calculus or plane curves, infinite series and Taylor series. Of interest to students requiring a conceptual understanding of calculus.
\medskip\noindent{\bf STUDENT LEARNING OUTCOMES}\\
A more detailed list of learning objectives is given below. At least 70\% of the course time will be devoted to these essential outcomes. These objectives are listed again in the chronological list of topics at the end of this syllabus. The successful Calculus II student should be able to:
\begin{itemize}
\item {\bf\emph{Definite Integrals}}: Use antiderivatives to evaluate
definite integrals and apply definite integrals in a variety of applications to
model physical, biological or economic situations. Whatever applications (e.g.
determining area, volume of solids of revolution, arc-length, area of surfaces
of revolution, centroids, work, and fluid forces) are chosen, the emphasis
should be on setting up an approximating Riemann sum and representing its limit
as a definite integral.\vspace{-.1in}
\item {\bf\emph{Techniques of Integration}}: Employ a variety of integration
techniques to evaluate special types of integrals, including substitution,
integration by parts, trigonometric substitution, and partial fraction
decomposition.\vspace{-.1in}
\item {\bf\emph{Improper Integrals}}: Evaluate improper integrals, including integrals
over infinite intervals, as well as integrals in which
the integrand becomes infinite on the interval of integration.\vspace{-.1in}
\item {\bf\emph{Sequences and Series}}: Determine the existence of and find
algebraically the limits of sequences. Determine whether a
series converges by using appropriate tests, including the comparison, ratio,
root, and integral.\vspace{-.1in}
\item {\bf\emph{Power Series}}: Find the nth Taylor polynomial at a specified
center for a function and estimate the error term. Use appropriate techniques to
differentiate, integrate and find the radius of convergence for the power
series of various functions.\vspace{-.1in}
\item {\bf\emph{Parametric Curves}}: Analyze curves given parametrically and in polar
form and find the areas of regions defined by such curves.\vspace{-.1in}
\item {\bf\emph{Lines and Planes}}: Perform and apply vector operations, including the
dot and cross product of vectors, in the plane and space.
\end{itemize}
\medskip\noindent {\bf PREREQUISITES}\\
Minimum grade of C- in MATH 1830 or Math 1850 or Math 1920 (Calculus I)\\
\noindent{\bf TEXTBOOK:} {\it Thomas' Calculus, A Custom Edition for the University of Toledo}, 1st Edition, by George B. Thomas, Maurice D. Weir packaged with MyLabsPlus (ISBN: 9781269644334), Pearson.
%The text is available online at a 30\% discount in
%electronic form from \url{www.coursesmart.com.} Students should be aware that in
%purchasing an electronic copy they will be responsible for printing it or accessing it
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\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 \url{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.\\
\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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Component & points\\
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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 from the
class is the end of the tenth week. By these dates, students should have sufficient data
to realistically gauge their progress in the class. \\
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\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://www.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 2850. (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 2850
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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\noindent
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& & & \\
Chapter & 6 & \textbf{Applications of Definite Integrals} & (total 4.5 hr)
\\
&6.1 & Volumes using Cross Sections; {\bfseries\slshape Definite Integration} & 2 \\
&6.2 & Volumes using Cylindrical Shells; {\bfseries\slshape Definite Integration} & 1.5 \\
&6.3 & Arc Length; {\bfseries\slshape Definite Integration} & 1 \\
&6.4 & \textbf{(Op.)} Graphing with Calculators and Computers & \\
& & & \\
Chapter & 8 & \textbf{Techniques of Integration} & (total 8 hr) \\
&8.1 & Integration by Parts; {\bfseries\slshape Techniques of Integration} & 1.5 \\
&8.2 & Trigonometric Integrals; {\bfseries\slshape Techniques of Integration} & 1 \\
&8.3 &Trigonometric Substitution; {\bfseries\slshape Techniques of Integration} & 1.5\\
&8.4 &Integration of Rational Functions by Partial Fractions; {\bfseries\slshape
Techniques of Integration} & 2 \\
&8.5 & \textbf{(Op.)} Integral Tables & \\
&8.6 &\textbf{(Op.)} Numerical Integration & \\
&8.6 & Improper Integrals; {\bfseries\slshape Improper Integrals} & 2 \\
& & & \\
Chapter & 10 & \textbf{Infinite Sequences and Series} & (total 12.5 hr) \\
&10.1 & Sequences; {\bfseries\slshape Sequences and Series}& 2 \\
&10.2 & Infinite Series; {\bfseries\slshape Sequences and Series} & 1 \\
& 10.3 & The Integral Test; {\bfseries\slshape Sequences and Series} & 1\\
&10.4 & Comparison Tests; {\bfseries\slshape Sequences and Series} & 1 \\
&10.5 & Ratio and Root Tests; {\bfseries\slshape Sequences and Series} &1 \\
&10.6 & Alternating Series, Absolute and Conditional Convergence*; {\bfseries\slshape
Sequences and Series} & 1.5 \\
&10.7 & Power Series; {\bfseries\slshape Power Series} & 2 \\
&10.8 & Taylor and Maclaurin Series; {\bfseries\slshape Power Series} & 1.5 \\
& 10.9 & Convergence of Taylor Series; {\bfseries\slshape Power Series} & 1 \\
&10.10 & Applications of Taylor Series; {\bfseries\slshape Power Series} & 0.5 \\
& & & \\
Chapter & 4 & \textbf{Parametric Equations and Polar Coordinates}
& (total 6.5 hr) \\
&11.1 & Parameterizations of Plane Curves; {\bfseries\slshape Parametric Curves} & 1 \\
&11.2 & Calculus of Parametric Curves; {\bfseries\slshape Parametric Curves} & 2\\
&11.3 & Polar Coordinates; {\bfseries\slshape Parametric Curves} & 1 \\
&11.4 & Graphing in Polar Coordinates; {\bfseries\slshape Parametric Curves} &1 \\
&11.5 & Areas and Lengths in Polar Coordinates; {\bfseries\slshape Parametric Curves}
&1.5 \\
&11.6 &\textbf{(Op.)} Conic Sections & \\
&11.7 & \textbf{(Op.)} Conic Sections in Polar Coordinates & \\
& & & \\
Chapter & 12 & \textbf{Vectors and Geometry of Space} & (total 6.5 hr)\\
&12.1 & Three Dimensional coordinate system; {\bfseries\slshape Lines and Planes} & 0.5
\\
&12.2 & Vectors; {\bfseries\slshape Lines and Planes} & 1 \\
&12.3 & The Dot Product; {\bfseries\slshape Lines and Planes} & 1.5 \\
&12.4 & The Cross Product; {\bfseries\slshape Lines and Planes} &1.5
\\
&12.5 & Lines and Planes in Space; {\bfseries\slshape Lines and Planes} & 2 \\
&12.6 & \textbf{(Op.)} Cylinders and Quadric Surfaces & \\
& & & \\
& & Total Hours & 38
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* Absolutely convergent series should be covered in an earlier section such as
10.4.
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