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{\bf Syllabus
Math 119: Calculus A
Fall, 1996}
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Text: \=Elements of Mod\= er n Algebra, by Gilbert and Gilbert\kill
{\bf Instructors:} \>\> Mario Borelli \\
\>\> Juan Migliore (course chair)\\
\>\> Chris Peterson\\ \\
{\bf Text:} \>\> Single Variable Calculus (third edition), by James Stewart
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\noindent {\bf Comments on Text:} (from Migliore)
I didn't have any real problem with the text, and I would be willing to use it
again next year if I were to teach the course. A consideration for me is the
fact that there are potentially hundreds of students that would be interested
in selling the book, so it should have the inside track. (Note: Math 120 uses
the same book, of course.)
\medskip
\noindent The course covered, essentially, the following. A photocopy of the
table of contents is attached.
\begin{tabbing}
Text:\= xxxxxx \=Elements ofxxxxxxxxxx Mod\= er n Algebra, by Gilbert and
Gilbert\kill
{\bf Chapter 0} \>\> Functions \> \\
\> (Graphs and a preview of calculus) \\
{\bf Chapter 1} \>\> Limits and Rates of Change\\
\> (Getting them used to limits, and talking about the notion of tangent line
vs.\\
\> secant line, instantaneous velocity vs.\ average velocity, etc.) \\
{\bf Chapter 2} \>\> Derivatives \\
\> (The usual material, including related rates and implicit differentiation.
We\\ \> omitted differentials and Newton's method.)\\
{\bf Chapter 3} \>\> The Mean Value Theorem and Curve Sketching \\
\> (The usual discussion of the first and second derivative tests, and curve \\
\> sketching. Also applied max/min problems.)\\
{\bf Chapter 4} \>\> Integrals\\
\> (We may not finish the chapter. Just sigma notation, discussion of
area,\\ \> Fundamental Theorem of Calculus. But substitution may have to wait
until \\ \> next semester.)\\
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\medskip
On the following pages you will find the handout that was given to the
students. After that will be a photocopy of the table of contents.
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{\bf Mathematics 119, Fall Semester 1996-97}
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\bf Are you in the right course?
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Math 119-120 is intended for students planning to enter pre-professional or
biology programs. {\bf It is not intended for students who intend to major in
engineering, physics, mathematics, or most of the chemistry programs. Those
majors require Math 125-126.}
\smallskip
\begin{tabbing}
Text: \=Elements of Mod\= er n Algebra, by Gilbert and Gilbert\kill
{\bf Instructor:} \>\> Professor Juan Migliore\\
\>\> 364 CCMB (On Juniper, just south of the library)\\
\>\> Phone: 631-7345 \\ \\
{\bf Office Hours:} \>\> Monday 1:15--2:15 \\
\>\> Tuesday 10:00--11:00 \\
\>\> Wednesday 1:15-2:15 \\
\>\> Or by appointment. \\ \\
{\bf Tutorial Instructor:} \>\> Paul Weiner \\ \\
(The Tutorial instructor will also have office hours;
these will be announced soon.)\\ \\
{\bf Text:} \>\> Single Variable Calculus (third edition), by James Stewart
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\bf Classes, Tutorials and Help Sessions
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Class meets at 10:40 AM MWF in DeBartolo 141. Students are required to attend
these classes.
\smallskip
Each student is also assigned to
a Thursday tutorial section. {\it It is your responsibility to know the
time, place
and section number of your tutorial section. You are not allowed to change
tutorials.}
At the tutorial, the previous week's
homework will be returned. Students will then be encouraged to ask questions
about that homework or about the current homework. The purpose of the
tutorial is
to help students master the material currently being covered.
\smallskip
In addition to the tutorials, the professor and the TAs will have office hours
each week at which you can get assistance in understanding the course work and
doing the homework problems. Times and rooms for the TAs' office hours will be
announced soon.
In previous years, prepared overhead transparencies were used for this
course. Copies
of these, just as they appeared on the screen during the lectures, will
be available
in the reserve room of the Hesburgh library and in the Freshman Learning
Resource
Center. This course will roughly follow these notes, so they are a useful study
guide.
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\bf Examinations, homework and grades
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\smallskip
There will be three one-hour examinations and one final
examination (whose dates, times and locations are listed below). Each one-hour
exam will be worth 100 points. The final exam is a two-hour exam and will be
worth 150 points. The final exam will cover all the material of the course.
Homework grades will be scaled at the end of the semester so that there will be
a total of 50 possible points for homework. So the total number of possible
points for the semester is 500. Exams will be returned at the following
tutorial session.
Homework will be due at the Thursday tutorial and returned the following
week. Two or three assignments will be due each Thursday; specific assignments
due each week will be announced in that week's lectures.
The main purpose of collecting and returning homework is to let you know if you
are doing the problems correctly. The homework grade (50
points out of a total of 500) is designed to reward effort. Each problem is
graded either 0 (if missing or complete nonsense) or 1 (for any honest
attempt). So the total number of points on any assignment is simply the number
of problems honestly attempted.
Both examinations and homework are conducted under the honor code.
While cooperation in doing homework is permitted (and encouraged),
copying is not. Exams are closed book and are to be done completely by
yourself with no help from others. {\em Calculators are not allowed on the
exams.}
A student who misses an examination will receive zero points for
that exam unless he or she has written permission from the Dean of the
First Year of
Studies. (An excuse is almost certainly not going to be accepted if it is
presented
after the exam takes place.) Please be aware that travel plans are not
considered to
be a valid excuse by the Dean of the First year of Studies.
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\bf Exams
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Exam 1:\ \ \ \= Thursday, September 29, 1994\ \ \ \= 8:00 AM\ \ \ \= DBRT 101
(Last name A-K)\kill
\> Date \> Time \> Place \\
Exam 1 \> Tuesday, September 24, 1996 \> 8:00 AM \>STEP 100 \\
Exam 2 \> Tuesday, October 29, 1996 \> 8:00 AM \>STEP 100 \\
Exam 3 \> Tuesday, November 26, 1996 \> 8:00 AM \>STEP 100 \\
Final \> Monday, December 16, 1996 \> 1:45 PM \\
\> (Location of final exam will be announced later.)
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\begin{tabular}{|c|cp{4in}|}
\hline
\multicolumn{3}{|c|}{\bf Mathematics 119, Fall Semester 1996-97} \\
\multicolumn{3}{|c|}{HOMEWORK ASSIGNMENTS} \\ \hline
{\bf Number} & \multicolumn{2}{l|}{\bf Assignment} \\
\hline \hline
1 & p.\ A15 & \# 7--10, 21--23, 25--28, 31--33, 37--40 \\ \hline
2 & p.\ 14 & \# 2--4, 11--14, 20--22, 27, 31, 32, 41, 43, 44, 51--53 \\ \hline
3 & p.\ A22 & \# 1--8 \\
& p.\ A15 & \# 1--4 \\ \hline
4 & p.\ 50 & \# 2--6 \\
& p.\ 59 & \# 3--5, 7--10 \\ \hline
5 & p.\ 68 & \# 1, 15--20, 23, 24, 26 \\ \hline
6 & p.\ 68 & \# 27, 29, 31--33 \\
& p.\ 96 & \# 1, 4, 5, 6, 11, 12 \\ \hline
7 & p.\ 109 & \# 1, 3--5, 8, 11, 13--15, 23--26 \\ \hline
8 & p.\ 120 & \# 1, 2, 4, 10--13, 23, 24, 34, 36--39, 59, 60 \\ \hline
9 & p.\ 87 & \# 1, 2, 32--34, 37--39 \\ \hline
10 & p.\ A30 & \# 1--3, 7, 9, 10, 13--15, 23--30, 32 \\ \hline
11 & p.\ A30 & \# 42--46, 53, 54 (use only the identities on pages
A27--A28) \\
& p.\ A30 & \# 65--67, 69--71 \\ \hline
12 & p.\ 137 & \# 1--8, 10--14, 16 \\ \hline
13 & p.\ 137 & \# 20--22, 24, 25, 27, 30, 32--34, 37 \\ \hline
14 & p.\ 144 & \# 9--11, 13, 17, 21--26, 35--38 \\ \hline
15 & p.\ 144 & \# 49--52, 57, 59, 60 \\
& p.\ 150 & \# 5, 8, 9, 13, 14, 16, 25 \\ \hline
16 & p.\ 155 & \# 3--6, 13, 14, 17--20, 27, 43, 44 \\ \hline
17 & p.\ 130 & \# 7, 8, 11, 12, 13, 16, 23, 24 \\
& p.\ 155 & \# 35--37, 40--42 \\ \hline
18A & p.\ 160 & \# 1, 3, 7--12 \\ \hline
18B & p.\ 160 & \# 16--18, 25, 26, 29, 30 \\ \hline
19 & p.\ 188 & \# 21--24, 31--33, 37, 38, 41--43, 47--50, 51 \\ \hline
20 & p.\ 199 & \# 3, 4, 12, 15, 16, 18, 20, 22, 23, 25, 26 \\ \hline
21 & p.\ 205 & \# 1, 4, 7, 8, 13, 14, 15, 17, 21-- 24 \\ \hline
22 & p.\ 216 & \# 9--14, 24, 36, 37, 39, 42 \\ \hline
23 & p.\ 224 & \# 4, 5, 15, 16, 28 \\ \hline
24 & p.\ 236 & \# 1, 3, 6--14 \\ \hline
25 & p.\ 236 & \# 22, 26--30, 32, 46 \\ \hline
26 & p.\ 249 & \# 2, 5, 8--10, 13, 15, 16, 27, 28 , 35, 43,44, 47, 48, 50,
53, 55
\\
\hline 27 & p.\ 262 & \# 2, 12, 13, 19, 21, 26, 29, 30 \\
& \multicolumn{2}{l|}{Additional (area) problems will be assigned} \\ \hline
28 & p.\ 271 & \# 1, 2, 3, 23, 24 \\ \hline
29 & p.\ 280 & \# 7, 9, 15, 16, 23, 24, 26, 34, 35 \\ \hline
30 & p.\ 291 & \# 5, 6, 9, 10--13, 17, 18, 23, 32, 46, 51, 52 \\ \hline
31 & p.\ 291 & \# 63--66, 69--72, 74, 79 \\ \hline
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\obeylines
SYLLABUS
REVIEW AND PREVIEW 2
1 Functions and Their Graphs 2
2 Types of Functions; Shifting and Scaling 17
5 A Preview of Calculus 39
1. LIMITS AND RATES OF CHANGE 46
1.1 The Tangent and Velocity Problems 46
1.2 The Limit of a Function 50
1.3 Calculating Limits using the Limit Laws 61
1.5 Continuity 80
1.6 Tangents, Velocities, and Other Rates of Change 90
2. DERIVATIVES 100
2.1 Derivatives 100
2.2 Differentiation Formulas 112
2.3 Rates of Change in the Natural and Social Sciences 122
2.4 Derivatives of Trigonometric Functions 131
2.5 The Chain Rule 138
2.6 Implicit Differentiation 146
2.7 Higher Derivatives 152
2.8 Related Rates 156
3. THE MEAN VALUE THEOREM AND CURVE SKETCHING 182
3.1 Maximum and Minimum Values 182
3.2 The Mean Value Theorem 190
3.3 Monotonic Functions and the First Derivative Test 195
3.4 Concavity and Points of Inflection 201
3.5 Limits at Infinity; Horizontal Asymptotes 206
3.6 Curve Sketching 218
3.8 Applied Maximum and Minimum Problems 231
3.10 Antiderivatives 244
4. INTEGRALS 258
4.1 Sigma Notation 258
4.2 Area 264
4.3 The Definite Integral 272
4.4 The Fundamental Theorem of Calculus 283
5. APPLICATIONS OF INTEGRATION 308
5.1 Areas between Curves 308
5.2 Volume 315
5.3 Volumes by Cylindrical Shells 326
5.4 Work 331
5.5 Average Value of a Function 335
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