Calculus II - MATHV1102 - Fall 2011

Section 8  TUESDAY, THURSDAY   4:10PM - 5:25PM
MATHEMATICS  203

Instructor: Fabio Louallen-Nironi


Email: nironi@math.columbia.edu
Office: Mathematics 415
Tel:  (212) 854 4354

Office hours:

  Monday and Wednesday from 11:00am to 12:00pm and by appointment

TA:

  Pakorn Srimongkol
  Elizabeth Brigham  eab2164@columbia.edu

Textbook:

J.Stewart - Calculus, Early Transcendentals (Seventh edition), available in the university bookstore.

Overview of the course and Suggested Reading:

This is a second course in calculus and as  matter of fact this (as well as Calc4) is the hardest course in the Calc series. The two main topics are: techniques to solve Riemann integrals and series/sequences. We will also spend some time studying complementary topics like: parametric equations and some calculations of lengths and volumes.
I would like to spend a considerable part of the course studying Taylor series and its numerous applications, in particular applications to the calculation of limits and improper integrals. The textbook doesn't cover this material in a completely adequate way, so I will provide additional notes and exercises.
I will try to provide adequate and exhaustive material for the class, but I strongly recommend that you take notes in class and  I would also like to encourage independent research and reading. I will follow the textbook but not faithfully; you will be held responsible for everything I teach in class and you can safely ignore all the material in the book that I ignore.

Recitations:

  In my opinion, the lack of recitations in the calculus series is the main reason why students struggle so much. The course is structured in a way that there is not enough time for practicing in class. For this reason I have decided to offer an unofficial recitation hour every week. This additional hour will be entirely used for practicing.  Recitation hours are not mandatory and do not substitute office hours, the purpose of the two things is different.

Recitation is  scheduled on Friday from 4pm to 5pm someplace

Prerequisites:

  Calculus I.

Grading:

Homework 20%; Best  Midterm  25%; the Midterm Not Necessarily as Good as the Best  15%; Final 40% 
Depending on the circumstances I might decide to evaluate extracredit assignments.
I pride myself of assigning many A+'s each semester (students must have at least an A+ on a midterm or the  final). The A+ grade is at my personal discretion and I assign it to people who have an impressive average (compared to the curve of the class) or who have shown outstanding improvements through the course.

Midterms:

There will be two midterm exams during class. Make-up exams will not be given unless a written excuse for missing the exam is provided from either a doctor in the case of illness or from a dean in other exceptional circumstances.

Midterm 1 :   October 6 (in class)
Midterm 2 : November 22 (in class)

Final:

The final exam projected date is December 20-th from 4:10pm to 7:00pm. All students must take the final at the time scheduled by the university.

Homework:

There will be weekly written assignments which can be found on courseworks and below along with the due date. Problem sets are due on Friday by 5.00pm and can be dropped in my drop-box. The solutions will be posted on Courseworks. I have decided not to make use of Webassign.

 

Help room:

Mathematics 406. There is more information here.

Calculators:

Calculators are not needed for this course, and they will not be allowed in the exams.

Honesty:

Copying your written work from somebody else or from any other source is considered cheating and will be dealt with severely. Any cheating during midterms or finals will result in you failing the course and the matter being reported to your dean.



Class files (these files are part of the syllabus, they integrate the textbook and you are held responsible for them!):

Trigonometry (cheatsheet)
Hyperbolic functions (cheatsheet)
Integration of rational functions
Limit comparison
Sequences (cheatsheet)
Stolz-Cesaro
Series (cheatsheet)
A criterion of Cauchy (from baby Rudin)
Summation by parts (from baby Rudin)
Taylor polynomials and series

Old exams:

1st midterm (spring 2011)
2nd midterm (spring 2011)
Final (spring 2011)

Syllabus (might be subject to changes)


Date Reading Homework
Sep 6, 8
 7.1: Review of Riemann integrals. Integration by parts.
 Uploaded on courseworks every week. Due by Friday.
Sep 13, 15
 7.2, 7.3: Trigonometric integrals. Trigonometric and hyperbolic substitutions

Sep 20, 22
 7.4, 7.5: Integration of rational functions, integration of rational trig. functions. Integration strategies
Sep 27, 29
 7.8: Improper integrals, limit comparison
Oct 4
 Review
Oct 6
 Midterm 1
Oct 11, 13
 8.1, 8.2: Arc length, area of surfaces of revolution
Oct 18, 20
 10.1, 10.2, 10.3: Parametric and polar curves
Oct 25, 27
 11.1, 11.2, 11.3, 11.4: Sequemces, Series, Integral test, comparison tests, Cauchy criterion, Stolz-Cesaro
Nov 1, 3, 10
 11.5, 11.6: Alternating series and summation by parts, Absolute convergence
Nov 15, 17
 11.6, 11.8: Root and Ratio tests, Power series
Nov 22
 Midterm 2


Nov 29, Dec 1
 11.9, 11.10: Representing functions as power series, Taylor series
Dec 6, 8
 Taylor polynomials, Landau symbols and applications to the calculation of limits, Integrals and series
Dec 20
 Projected Final exam