Honors
Calculus II
Instructor
Franz Pedit, LGRT 1542 & 1535
pedit@math.umass.edu
Office hours: Wed 2:00-3:30 and by appointment
TA
Tetsuya
Nakamura, LGRT 1423C
nakamura@math.umass.edu
Discussion meeting: Fr 9:05-9:55
Office hours: Tu 9:00-10:00, Fr 10:00-12:00, Tu 10:00-11:00 in
CTC
Group project meetings: TBA
Grader
Manan Patel
mjpatel@umass.edu
This
4-credit course, which is part of a TEFD project and thus run somewhat
differently from the other sections, will cover integration, infinite
series, and applications to differential equations, geometry, and physics.
Historical perspectives, wider contexts, and emphasis of the underlying
theory will be central to the development of the material. Prospective
students must have a very thorough understanding and very good working
knowledge of Calculus I. If Calculus I were etudes, this course will be
your first (easy) Beethoven sonata. Intellectual curiosity, the ability to
deviate from a formulaic/recipe oriented thought process, and active
participation during class and home work projects are crucial to be
successful in this course. Peer collaboration, weekly meetings with the
TA, and seminar style interactions are strongly encouraged. Recommended,
but not obligatory, texts include
Calculus (any edition) by Michael Spivak.
Analysis by its
History, Ernst Hairer & Gerhard Wanner.
Calculus:
Early Transcendentals (any edition) by James Stewart.
Grading
Home work problems will be
assigned on a regular basis and graded. There will be a midterm exam and a
final exam.
The total grade will be the equally weighted average of those three
grades. D is in the range of 50-61, C 62-74, B 75-87, and A 88-100.
Midterm Exam: Tuesday,
October 22, in class (please arrive on time or a bit earlier)
Final Exam: scheduled
Home
Work
class
notes • hw
1 •
hw
2 • hw
3 • hw
4 • hw
5•
hw
6 • midterm
solutions •
hw
7 • hw
8 • hw
9 • hw
10 • final
projects •
Last year's home work problems
hw
1 •
hw
2 • hw
3 • hw
4
• hw
5
•
hw
6
• midterm
•
hw
7 •
hw
8
•
hw
9
•
hw
10
•
hw
11
•
final
Course contents
Week 1: Concepts of length and area;
definition of the Riemann integral.
Week 2: Fundamental Theorem of Calculus. Antiderivatives. Area.
Week 3: Techniques of integration and examples.
Week 4: Special substitutions.
Week 5: Improper integrals and curve length.
Week 6: Volume of solids. Area of rotational surfaces.
Week 7: y'=y and infinite series.
Week 8: Applications of Taylor series.
Week 9: Complex numbers and Taylor series 1.
Week10: Complex numbers and Taylor series 2.
Week11: Euler's formula.
Week 12: Applications to geometry and physics.
Week13: What comes next? An outlook.