Last update: 12/3/2003

# MATH 116 -- INTERMEDIATE CALCULUS III

**Important announcements are to be placed here.
Check often!**

**Midterm I results are to be announced soon.**
You can see your papers/bring your objections on Monday, June 25, at 16:30--18:00,
**at SAZ01**. **Make sure to read the
****solutions
first!**

Exam dates:
First Midterm Exam: June 17, 2007 @16.00-18.00 **Solutions [NEW]**
Second Midterm Exam: June 30, 2007 @10.00-12.00 [**Sample**]
Final Exam: July 18, 2007 (Wednesday) @18.00-20.00
[**Sample 1**]
[**Sample 2**]
Make-up Exam: July 23, 2007 (Monday) @18.00-20.00 at SA 141 (Matematics Seminar Room)

Exam places
Using a wrong room may result in a penalty!!!

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**Instructor:** Alex Degtyarev
**Office:** SA 130
**Phone:** x2135
**Mail:** degt-nospam-fen.bilkent.edu.tr ^{no spam}

Course syllabus
Natalia Zheltukhina's Calculus 116 page (including sample exams, quizzes, etc.)
Mefharet Kocatepe's Calculus 116 page (including sample exams, quizzes, etc.)
Metin Gürses' Calculus 116 page (including sample exams)
Suggested Exercises **[Highly recommended!!!]** (Natalia Zheltukhina)
Suggested Exercises **[Highly recommended!!!]** (Mefharet Kocatepe)
**This page is under construction**

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**Midterm I**
(25%)
**June 17, 2007, Sunday, 16:00--18:00**
See **important remarks** and
**room assignment**

**Topics covered** (tentative):
Functions of several variables; domain and range (simple cases) (**14.1**)
Limits: simple cancellation tricks, simple estimates + sandwich theorem,
two path test for non-existence (**14.2**)
Continuity: definition and properties; continuity of elementary functions;
using the definition in simple special cases (**14.2**)
Partial derivatives: differentiation using the usual rules; finding
partial derivatives using the definition in simple special cases (**14.3**)
The multi-variable chain rule and applications (**14.4**)
Gradient and directional derivatives: definitions, relations, simple properties
(direction of fastest increase, direction(s) of zero increase, etc.) (**14.5**)
Tangent and normal lines/planes (all flavors: graphs, level curves/surfaces,
intersections, etc.) (**14.6**)
Linear approximation and its error estimate (just learn the formulas) (**14.6**)
Local extrema and critical points; the second derivative test (**14.7**)
The method of Lagrange multipliers for constrained extrema/critical points (**14.8**)
Maximal and minimal values of functions ^{*} (**14.7, 8**)

^{*}
In the case of a closed bounded region the solution is known to exist; so, we
find the critical points of the function and its restriction to the faces, edges,
and vertices and pick the smallest/largest value. If the region is unbounded or
not closed, we do the same **hoping** that the solution exists; in this case
it would be nice (unless the point is found via Lagrange multipliers)
to identify the types of the critical points found
(maxima/minima/saddle)

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**Midterm II**
(25%)
June 30, 2007, Saturday, 10:00--12:00
See **samples**,
**important remarks**, and
**room assignment**

**Topics covered** (tentative):
Double integrals: definition, calculation (Fubini's theorem),
and applications (area
and volume only) (**15.1, 2**)
Double integrals in polar coordinates (**10.5, 6; 15.3**)
Triple integrals: definition, calculation (Fubini's theorem), and
applications (volume only) (**15.4**)
Triple integrals in cylindrical and spherical coordinates (**15.6**)
Substitution in double and triple integrals (**15.7**)

**Important skills to be developed:** Visualizing the region of integration;
choosing a convenient order of integration and setting correct limits in
the iterated integral; detecting a convenient change of variables that would
simplify the calculation (e.g., a number of 'round' shapes like circles,
spheres, or cylinders, calls for polar/cylindrical/spherical coordinates)

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**Final**
(40%) TBA
See
**important remarks** and **room assignment**

**Topics covered*** (tentative):
(Under construction)

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**Remarks**

** Most exam problems will be taken from the textbook
or its ****web page. Solve them
in advance, and you will do well!**

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**Quizzes and Homeworks**
(10%) Quizzes are to be held weekly in class (10-15 mins at the end)
except midterm weeks. Hopefully, 12 quizzes will be
given, with the two worst disregarded.
**All questions ** regarding the quizzes are to be directed to the
assistant. The assistant is instructed to **give no credit**
to identical papers. The same applies to the exams.

**During the exams please keep in mind the following:**
Calculators are **not** allowed
Identical solutions (especially identically wrong ones) will
**not** get credit. I reserve the right to decide what
"identical" means. You still have the right to complain
Do not argue about the distribution of the credits among different
parts of a problem. I only accept complaints concerning my
misunderstanding/misreadung your solution
Show all your work. Correct answers without sufficient explanation
might **not** get full credit
Indicate clearly and unambiguously your final result. In
proofs, state explicitly each claim
Do not misread the questions or skip parts thereof. If you did,
do not complain
If you believe that a problem is misstated, do not try to
solve it; explain your point of view instead. However, do not take advantage
of this option: usually problems are stated correctly!
Each problem has a reasonably short solution. If your calculation
gets completely out of hand, something must be wrong
(e.g., you might have chosen a wrong coordinate system/substitution/approach etc.)

**Grading policy *******

I will take off a few (2-3) points for arithmetical mistakes. However,
**a lot** of points will be taken off for `obvious'
mistakes, i.e., either those that you can easily avoid or those
showing a deep misunderstanding of the subject. This includes, but
is not limited to, the following:
Wrong dimension in a physical problem
Things that don't make sense
Mismatch of the data obtained in a graph (say, the only minimum of a
continuous function lies above the only maximum, or function is concave
up at a point of maximum, etc.)
Negative values for integrals of positive functions or for things
like area, volume, mass, etc.

Furthermore, solving a different problem (other than stated), even if perfect,
will give you **no credit**

* Of course, this only applies to problems that I am grading personally

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