Math S1102.D Section 001, Calculus II
Summer 2011
Instructor: Kristen Hendricks
E-mail: hendricks@math.columbia.edu
Office: 408 Mathematics
Office hours: Thursday 11-12 in Math 622
TA: Tim Heath
E-mail: timheath@math.columbia.edu
Help room hours: TBA
Course webpage: http://www.math.columbia.edu/~hendricks/CalculusIISummer2011
Location and Time: Monday-Thursday 1:00-2:35, Mathematics 417
Note that we will not meet Monday May 30 (Memorial Day). There will be a make-up class Friday June 3.
Textbook: Calculus, Early Transcendentals (7th Ed.), James Stewart, Thomson Brooks/Cole
This textbook is available at the Columbia bookstore (114th between Broadway and Amsterdam) and also on amazon.com and used textbook websites such as redline.com for lower prices. It is also on reserve in the Mathematics library (Mathematics 303). Please make sure that you use the correct edition. The exercises are quite different from edition to edition; I will try to supply you with the 6th edition numbers as well if possible but the same exercise won't always exist in both texts. There are also copies of the new edition in the Math Help Room and on reserve in the Mathematics Library.
Course Description: This is a standard Calculus II course. Our main topics will be integration and infinite series. The material corresponds to most of Chapters 6, 7, 8, 10, and 11 of the textbook. The first two days of class will be a lightning review of Chapter 5.
Homework: Homework is a critical portion of the course – you can’t learn calculus without doing a lot of problems. You should expect to spend two to three hours doing exercises or studying for every hour of class. There will be five weekly assignments due on Mondays at 1 p.m. sharp. Some portion of each assignment will be graded by Tim and returned later in the week. There will also be a single question due in class every day, graded by me and returned the next day, to ensure that you are keeping up. If you’re not going to be in class on a particular day, you can leave your homework in the class box on the fourth floor outside 406 Mathematics by 12 p.m. sharp.
Collaboration on homework is highly encouraged; toward that end, a google group will be created for the course at the end of the first week. You must, however, write up all solutions yourself.
Because of the fast-paced nature of the course, no late homework will be accepted under any circumstances not involving a dean’s or doctor’s note. This includes having forgotten to bring your homework to class, having neglected to hand in the homework while in class, having done the wrong problems, having been unforeseeably delayed by a flock of ostriches, and so on. However, your lowest weekly homework and lowest three daily homeworks will be dropped, so don’t panic if any of these things happen.
Getting Help: The Math Help Room (406 Mathematics) is open every weekday; you can find their schedule here.This is an excellent place to sit and work on your homework, asking questions when you get stuck. They are first come first serve, so you should come well in advance and bring work to do while waiting for a TA to be available.
I also have office hours, which I am only too delighted to have you attend. Bring questions!
Exams: There will be a midterm on Thursday, June 9 and a final on Thursday, June 30, both in class. Make-up midterms will only be offered with a note from your doctor or dean; make-up finals can only be arranged through your dean’s office, and you should contact them immediately if you become ill or encounter a serious family crisis on that date.
Grading: Grades will be calculated approximately as follows:
15% daily homework
25% weekly homework
25% midterm
35% final
A reasonable curve will be applied to the final scores.
Tentative Schedule:
Week 1: Introduction and Review, Integration by parts (7.1), Trigonometric Integrals (7.2, 7.3)
Lecture 1 (Sections 5.1-5.3, Review of the Definite Integral)
Lecture 2 (Sections 5.4-5.5, Interpretation of the Definite Integral and Substitution)
Lecture 3 (Section 7.1, Integration by Parts; Section 7.2, Trigonometric Integrals)
Lecture 4 (Section 7.3, Trigonometric Substitution)
Week One Homework Solutions – Daily
Week One Homework Solutions - Weekly
Week 2: Integration of Rational Functions (7.4), Strategies of Integration(7.5), Applications of Integration (6.1-6.5)
Lecture 5 (Section 7.4, Integration by Partial Fractions; Section 7.5, Strategies of Integration)
Lecture 6 (Section 6.5, Average Value of a Function; Section 6.1, Areas Between Curves; Section 6.2, Intro to Volume)
Lecture 7(Section 6.2, Volumes by Cross-Sectional Area Ctd; Section 6.3, Volumes by Cylindrical Shells)
Lecture 8 (Section 6.4, Work)
Week Two Homework Solutions – Daily
Week Two Homework Solutions - Weekly
Week 3: Arc Length (8.1), Area of a Surface of Revolution (8.2), Improper Integrals (7.8), Midterm
Lecture 9 (Section 8.1, Arc Length; Section 8.2, Surface Area)
Lecture 10 (Section 7.8, Improper Integrals)
Week Three Homework Solutions - Daily
Week Three Homework Solutions - Weekly
Week 4: Parametric Equations and Polar Coordinates (10.1 – 10.4), Sequences (11.1)
Lecture 11 (Section 10.1, Parametric Curves; Section 10.2, Calculus with Parametric Curves)
Lecture 12 (Section 10.2, Calculus with Parametric Curves Contd.; Section 10.3, Polar Coordinates)
Lecture 13 (Section 10.4, Calculus with Polar Coordinates)
Lecture 14 (Section 11.1, Intro to Sequences)
Week Four Homework Solutions – Daily
Week Four Homework Solutions - Weekly
Week 5: Infinite sequences and series (11.2 – 11.8)
Lecture 15 (Section 11.2, Intro to Series)
Lecture 16 (Section 11.3, The Integral Test; Section 11.4, The Comparison Test)
Lecture 17 (Section 11.5, Alternating Series; Section 11.6, Absolute Convergence and the Ratio and Root Tests)
Lecture 18 (Section 11.7, Strategies for Series; Section 11.8, Intro to Power Series)
Week 5 Homework Solutions – Daily
Week 5 Homework Solutions - Weekly
Week 6: Infinite sequences and series (11.9 – 11.11), Review, Final
Lecture 19 (Section 11.9 contd, Representations of Functions as Power Series; Section 11.10, Taylor and Maclaurin Series)
Lecture 20 (Section 11.10, Taylor and Maclaurin Series; Section 11.11, Applications of Taylor Series) Note: Less organized than other lectures.
Practice Final (Given last year by Min Lee. We may focus less on power series.)