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{\bf University of Notre Dame}


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{\bf  Math. 165, Fall of 1996}
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 {\bf Instructor}:

 Dr. Hong-Ming Yin.
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 {\bf Text Book}:

 Calculus, vol. 1 (second edition) by Tomm. Apostol.

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{\bf Final Grade}

Final Grade will be based on the following percentage:

Homework: $15\% $. There will be about 10 homework assignments.

Test 1: $15\% $, on Sept.26 from 11:00-12:00 a.m., at DBRT 318

Test 2: $15\% $, on Oct. 17 from 11:00-12:00 a.m., at DBRT 318

Test 3: $15\% $, on Nov. 21 from 11:00-12:00 a.m., at DBRT 318

Final Exam.: $40\% $, Time and place will be announced later.

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{\bf Sections Covered}: See Attached material A.

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{\bf Daily Progress}: See Attached Lecture numbers and titles.

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{\bf Comments on the text book}:

(1) In general,  the textbook is very good and could be used in future.

(2)  The definition of integral is good, but students have hard time to
understand
how to use step functions to approximate a rather simple function such as
$y=x^{n}$.
It needs one full lecture to derive the formula
\[ \int_{a}^{b} x^ndx=\frac{ b^{n+1}-a^{n+1} }{n+1}, n \neq -1.\]
The same problem occurs for $sine$ and $cosine$ functions.

(What I did is to assume the formulas, then use fundamental theorems to
derive these formulas, since
it is much easy to derive the derivative formula for $x^n$).

(3) I suggest that in Chapter 5, one may give an alternative definition for
integrals (i.e.
partition, summation and taking limits). My experience
indicated that with two definitions the students have better understanding
of definite integrals.

(4) The students in this class generally have no trouble to find basic
limits, derivatives,
integrals etc. Most students can do very complicated calculations. The
$\varepsilon-\Delta$ definition is
still a very difficult topic to students. But after one semester, most
students understand the proofs.
>From the test and homework, I found that most students were able to carry
out proofs.

(5) As I taught Math.365-Math 366 before,  I feel that some of good
students in my class felt
that the math365-math366 have similar contents to Math165-Math166.
 It would be a good idea to choose
a textbook for Math365-366  with less repeated contents to the first year
calculus.



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