Honors Calculus II
Franz Pedit, LGRT 1542 & 1535
Office hours: Wed 2:00-3:30 and by appointment
Tetsuya Nakamura, LGRT 1423C
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
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
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.
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 60-70, C 70-80, B 80-90, and A 90-100.
Midterm Exam: TBA
Final Exam: scheduled
classnotes • hw 1 • hw 2 • hw 3 •
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
Week 1: Concepts of lenght and area; definition of the Riemann integral.
Week 2: Fundamental Theorem of Calculus. Antiderivatives. Area.
Week 3: Techniques of integration and examples.
Week 4: Length of curves and volumes of solids.
Week 5: Improper integrals. y'=y, the exponential function revisited.
Week 6: Power series. Convergency.
Week 7: Taylor series of a function.
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.