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 60-70, C 70-80, B 80-90, and A 90-100.

Midterm Exam:  TBA
Final Exam:  scheduled


Home Work

classnoteshw 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


Course contents

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.