Calculus II (Fall 2014)

Instructor
Daniel Gulotta
Email
dgulotta .at. math.columbia.edu
Location and time
Monday, Wednesday 6:10-7:25pm in Math 407
Textbook
Calculus: Early Transcendentals, 7th edition by James Stewart. Please make sure that you have the correct edition as the numbering of problems varies between editions. This class will not require WebAssign. I have been told that it is cheaper to buy the textbook directly from the publisher than from the Columbia bookstore.
Office Hours
Monday, Wednesday 5-6pm in Math 408 or by appointment. You can also get help in the Math Help Room in 333 Milbank ( Schedule | Map ). Some other tutoring options are listed here.
Homework
Homework assigments are due on Wednesdays by 7:30pm. They should be placed in the homework box on the fourth floor. Late homework will not be accepted. However, your lowest homework score will be dropped. Homework solutions and grades will be posted on CourseWorks.
Exams
There will be two midterm exams and a final exam. The midterms will be on October 1 and November 5 in class. The final exam is scheduled for December 15 from 7:10-10:00pm.
Grading
Homework20%
Midterm I20%
Midterm II20%
Final40%
Disability Services
In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online at www.health.columbia.edu/ods. Registered students must present an accommodation letter to the professor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.

Tentative Schedule

DateTopicsHomework Due
Wednesday, Sep 3Introduction, Review of Integrals, Fundamental Theorem (5.1-5.4)
Monday, Sep 8Substitution (5.5), Integration by parts (7.1)
Wednesday, Sep 10Trig integrals (7.2)
  • 5.2: 37
  • 5.3: 18,26,40,52
  • 5.4: 11,30
Monday, Sep 15Trig integrals (7.2), Trig/hyperbolic substitution (7.3)
Wednesday, Sep 17Hyperbolic substitution (7.3), Partial fractions (7.4)
  • 5.5: 24,32,62
  • 7.1: 2,14,18,22,36,41
Monday, Sep 22Partial fractions (7.4), Improper integrals (7.8)
Wednesday, Sep 24Improper integrals (7.8), Volumes (6.2-6.3)
  • 7.2: 2,10,18,38
  • 7.3: 2,6,8,14,18,32
  • 7.4: 4,8,10,20
Monday, Sep 29Review
Wednesday, Oct 1Midterm
  • Suggested practice problems (not to be turned in)
  • 5.1: 24
  • 5.2: 45
  • 5.3: 13,15
  • 7.5: 5,11,13,21,33,35,45,51,57,59,69,71,75,79
  • 7.8: 15,39
  • 6.2: 27,49,61
  • 6.3: 17
Monday, Oct 6Arc length (8.1), Surfaces of revolution (8.2), Probability (8.5)
Wednesday, Oct 8Probability (8.5), Intro to differential equations (9.1-9.5)
  • 7.4: 28,36,44
  • 7.5: 28,44
  • 7.8: 16,20,34,40,54
  • 6.2: 28,30,50,54
  • 6.3: 12,48
Monday, Oct 13Methods for solving differential equations (9.3-9.5)
Wednesday, Oct 15Differential equations (9.3-9.5), Parametric equations (10.1-10.2)
  • 8.1: 12,14,18
  • 8.2: 6,30,34
  • 8.5: 4,6,10
  • 9.1: 2,10,12
  • 9.2: 3,4,5,6,10,22
Monday, Oct 20Parametric equations (10.1-10.2), Polar coordinates (10.3)
Wednesday, Oct 22Polar coordinates (10.3-10.4), Conic sections (10.5-10.6)
  • 9.3: 2,10,12,16,22,42
  • 9.4: 4,16,20
  • 9.5: 8,14,18,20,24,26
  • 10.1: 8
  • 10.2: 4,12
Monday, Oct 27Conic sections (10.5-10.6), Sequences (11.1)
Wednesday, Oct 29Review
  • 10.1: 4,6,20,26
  • 10.2: 20,34,54,74
  • 10.3: 12,24,32,38,52
  • 10.4: 2,16,24,36,46
  • 10.5: 2,12
  • For problem 10.5.12, also find the directrices.
Monday, Nov 3No class
Wednesday, Nov 5Midterm
  • Suggested practice problems (not to be turned in)
  • 8 Review Exercises: 1,3,7
  • 8 Problems Plus: 6,11
  • 9 Review Exercises: 7,11,13,19,21,25
  • 9 Problems Plus: 9,15
  • 10 Review Exercises: 1,9,13,17,31,33,39,47,49,51,53,57
  • 10 Problems Plus: 5
Monday, Nov 10Sequences (11.1), Series (11.2)
Wednesday, Nov 12Series (11.2), Integral tests (11.3), Comparison test (11.4)
  • 10.4: 56
  • 10.5: 18,28,48,57
  • 10.6: 2,10,12
  • 11.1: 32,36,38,46,50
Monday, Nov 17Comparison test (11.4), Alternating series (11.5), Absolute convergence (11.6)
Wednesday, Nov 19Ratio and root tests (11.6), Power series (11.8-11.9)
  • 11.1: 54,78,92
  • 11.2: 32,34,36,44,50,54,78
  • 11.3: 4,18,24,44
  • 11.4: 6,20,28,44
  • 11.5: 14
Monday, Nov 24Power series (11.8-11.9)
Wednesday, Nov 26No class
Monday, Dec 1Functions as series (11.9)
Wednesday, Dec 3Taylor series (11.10)
  • Due Friday 12/5
  • 11.5: 16,24
  • 11.6: 12,14,20,34,36
  • 11.7: 6,26,32,36
  • 11.8: 6,8,14,24,40
  • 11.9: 8,12,16,18,28
  • 11 Problems Plus: 24
Monday, Dec 8Review
Monday, Dec 15Final Exam (7:10-10:00)
  • Suggested practice problems (not to be turned in)
  • 5 Problems Plus: 10,17
  • 6 Problems Plus: 10
  • 7 Review Exercises: 11,13,21,37,43,49
  • 8 Review Exercises: 15,21
  • 9 Review Exercises: 5,15,17
  • 10 Review Exercises: 3,21,25,35
  • 11.10: 27,37,49,74
  • 11 Review Exercises: all odd problems
  • 11 Problems Plus: 5,14