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

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

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.