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!!!
[Top]     [Home]             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)

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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.)