Calculus II (Spring 2015)

Instructor
Daniel Gulotta
Email
dgulotta .at. math.columbia.edu
Location and time
Monday, Wednesday 6:10-7:25pm in Hamilton 516
Textbook
Calculus: Early Transcendentals, 7th edition by James Stewart. More information is available here. Please make sure that you have the correct edition as the problems vary between editions. This class will not require WebAssign, but if you want to use it for practice, you can use the code listed here.
Office Hours
Monday 2:30-3:30pm, Wednesday 5-6pm in Math 408 or by appointment.
Getting Help
In addition to office hours, 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 Mondays by 7:40pm. You can either give them to me in class or place them in the homework box on the fourth floor of the Mathematics building. Late homework will not be accepted. However, your lowest two homework scores 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 February 18 and April 1 in class. The final exam is is scheduled May 11 from 7:10-10:00pm in the usual room.
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, Jan 21Introduction, Review of Integrals, Fundamental Theorem, Substitution (5.1-5.5)
Monday, Jan 26No class
Wednesday, Jan 28Substitution (5.5), Integration by parts (7.1)
Monday, Feb 2Trig integrals (7.2)
  • 5.2: 37
  • 5.3: 18,26,40,52
  • 5.4: 11,30
  • 5.5: 24,32,62
  • 5 Problems Plus: 10
  • 7.1: 2,14,18,22,36,41
Wednesday, Feb 4Trig integrals (7.2), Trig/hyperbolic substitution (7.3)
Monday, Feb 9Trig/hyperbolic substitution (7.3), Partial fractions (7.4)
  • 7.1: 50
  • 7.2: 2,10,18,22,38,40,44,48
  • 7.3: 2,6
  • 7 Problems Plus: 2
Wednesday, Feb 11Partial fractions (7.4), Improper integrals (7.8)
Monday, Feb 16Review
  • 7.3: 8,14,18,32
  • 7.4: 4,8,10,20,28,36,44
  • 7.5: 28,40,44
  • 7.8: 16,20
  • 7 Problems Plus: 8
Wednesday, Feb 18Midterm
  • Suggested practice problems:
  • Old Midterm 1 (on CourseWorks): 1,3-7
  • 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
Monday, Feb 23Improper integrals (7.8), Volumes (6.2)
Wednesday, Feb 25Volumes (6.3), Arc length (8.1), Surfaces of revolution (8.2), Probability (8.5)
Monday, Mar 2Probability (8.5), Sequences (11.1)
  • 7.8: 34,40,54
  • 6.2: 6,28,30,50,54
  • 6.3: 10,12,48
  • 6 Problems Plus: 8
  • 8.1: 12,14,18
  • 8.2: 6
Wednesday, Mar 4Sequences (11.1), Series (11.2), Comparison tests (11.4)
Monday, Mar 9Integral test (11.3)
  • 8.2: 30,34
  • 8.5: 4,6,10
  • 8 Problems Plus: 12
  • 11.1: 26,32,36,38,40,44,46,50,54,78,92
  • 11.2: 32,34,36
Wednesday, Mar 11Comparison tests (11.4), Alternating series (11.5), Absolute convergence (11.6)
Monday, Mar 23Absolute convergence, Ratio test (11.6)
  • 11.2: 44,50,54,72ab,78,84
  • 11.3: 4,18,24,44
  • 11.4: 6,20,28,44
  • 11.5: 14,16,24
Wednesday, Mar 25Ratio and root tests (11.6), Power series (11.8)
Monday, Mar 30Review
  • 11.6: 12,14,20,24,34,36
  • 11.7: 4,6,8,20,26,28,32,36
  • 11.8: 6,8,14,24
Wednesday, Apr 1Midterm
  • Suggsted practice problems:
  • Old Midterm 1: 2,8
  • Old Midterm 2: 4,6
  • Old Final: 2,5a,6,10,11
  • 7.8: 15,39
  • 6.2: 27,49,61
  • 6.3: 17
  • 8 Review Exercises: 1,3,7
  • 11.7: all odd problems
  • 11 Review Exercises: 1,3,5,7,9,35,37
  • (power series will not be on the exam)
Monday, Apr 6Power series (11.8-11.9)
Wednesday, Apr 8Power series (11.8-11.9)
Monday, Apr 13Functions as series (11.9), Taylor series (11.10)
  • 11.8: 10,18,26,30,32,38,40
  • 11.9: 4,6,8,10,12,16,18,26,28,40,42
  • 11 Problems Plus: 24
Wednesday, Apr 15Taylor series (11.10)
Monday, Apr 20Taylor series (11.10), Intro to differential equations (9.1-9.2)
  • 11.10: 2,4,6,10,12,16,20,28,30,32,36,38,44,46,50,56,64,66,72
  • 11.11: 36
Wednesday, Apr 22Intro to differential equations (9.1-9.2), Separable differential equations (9.3-9.4)
Monday, Apr 27Linear differential equations (9.5)
  • 11.10: 74a
  • 9.1: 2,10,12
  • 9.2: 3,4,5,6,10,22
  • 9.3: 2,10,12,16,22,42
  • 9.4: 4,16,20
Wednesday, Apr 29Parametric Equations (10.1-10.2)
Monday, May 4Review
  • 9.5: 8,14,18,20,24,26
  • 11.9: 34
  • 10.1: 4,6,8,20,26
  • 10.2: 4,12,20,34,54,74
Monday, May 11Final Exam (7:10-10:00)
  • Suggested practice problems:
  • Old Midterm 2: 1,2,5
  • Old Final: 1,3,4,5b,7,8,9
  • 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: 5,7,11,13,15,17,19,21,25
  • 10 Review Exercises: 3,21,25
  • 11 Review Exercises: all odd problems