Math 114, Calculus II, Section 004
Instructor: Martha Yip
Email: myip [at] math.upenn.edu
Office: DRL 3N4C
Office Hours: Mondays 2:00pm -- 3:00pm and Wednesdays 1:00pm -- 2:00pm, or by appointment

Lecture: MWF 12:00pm -- 12:50pm, DRL A1

TA: Xiaofei Jin (231-234) jinx [at] math.upenn.edu
      Office Hours: Tuesdays 1:00pm -- 3:00pm or by appointment, in DRL 3C15
TA: Sea Moon Cho (235-238) seamcho [at] math.upenn.edu
      Office Hours: Fridays 1:00pm -- 3:00pm or by appointment, in DRL 4E14
 		hypar
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Announcements: The Final Examination is on Monday May 5, 12pm - 2pm, held in JMHH G06.

The exam covers all material from the sections 12.1-12.6, 13.1-13.6, 14.1-14.8, 15.1-15.8, 16.1-16.8.
It will consist of fifteen multiple choice questions and open answer questions.
You may bring one sheet of notes on 8.5"x11" paper, handwritten, two-sided. No other aids are allowed.
Remember to bring your Penn ID. We will definitely be checking them.

To prepare for the final examination, I recommend that you do a few Old Exams.
In particular, at minimum, you should complete the three most recent finals.
During lecture on Wednesday April 30, I will focus on answering problems from Spring 2012.
Two additional review sessions have been scheduled:
Thursday May 1 4-6pm in DRL A6: focus on Fall 2012,
Friday May 2 4-6pm in DRL A6: focus on Spring 2013,
And of course I'll answer any other questions you may have on the course material. For the above two review sessions, the first hour will be devoted to going through solutions to the finals. What we do in the second hour is entirely the audience's choice.

I still have my regular office hours this Wednesday 1-2pm. That's a good opportunity for you to get personal questions answered.

New: here's the exam from last semester: Fall 2013

[29-Apr-2014]

Midterm 3 solutions.

I've added many comments regarding common mistakes made.

[25-Apr-2014]

Lecture 33 notes (15.6, Center of Mass + Review)

[21-Apr-2014]

Announcements: Your third in-class midterm is on Monday April 28.

The midterm covers all material from the sections 15.8, 16.1-16.8.
It will consist of multiple choice questions.
You may bring one sheet of notes on 8.5"x11" paper, handwritten, two-sided. No other aids are allowed.
Remember to bring your Penn ID.

Here are many Practice Problems to help you study for the midterm. These questions are taken from old exams, and are a good indication of the level of difficulty of the problems you can expect to see on your test.

I will run a Review Session on Sunday April 27 from 1--3pm in DRL A6. I will go over some of the questions on the Practice Problems sheet.

Some extra tips for Midterm 3:
In this part of the course, we covered a lot of major theorems, such as the Fundamental Theorem of Line integrals, Green's Theorem, Stokes' Theorem, and Gauss' Theorem. You may find it easier to organize your thoughts if you write down the name of the theorem you are using to solve your problems. Moreover, this will usually help the grader identify where partial marks can be allotted.

[21-Apr-2014]

Lecture 32 notes (16.8, Divergence Theorem) (updated 23-Apr)

[17-Apr-2014]

Lecture 31 notes (16.7, Stokes' Theorem) (fully updated 21-Apr)

We will continue with Stokes' Theorem on Monday.

[14-Apr-2014]

Lecture 30 notes (16.6, Surface Integrals) (updated 18-Apr)

An application of the non-orientability of Mobius strips in real life.

[12-Apr-2014]

Lecture 29 notes (16.5, Surface Area) (updated 17-Apr)

[09-Apr-2014]

Lecture 28 notes (16.4, Circulation and Flux) (updated 12-Apr)

[08-Apr-2014]

Announcements: Curve parametrization bootcamp will be held Wednesday April 9, 6-7pm, in DRL 4C8.

Here's the worksheet that we will be looking at. You should be able to complete pages 1-3 of this worksheet. For example, if you are comfortable with parametrizing lines and circles, but a bit shaky on parametrizing helices, you can start with exercise 4.

What you choose to do with these notes is entirely up to you, but the reason for having this review session is 3-fold: to review curve parametrization, to be prepared for surface parametrization, and to show you one possible way to study the material in preparation for the final examination.

You can see on the worksheet that I've tried to
  • group related topics together,
  • review what the definitions are,
  • understand what the formulas mean and how to use them,
  • compute simple problems,
  • then look at sucessively harder problems, taking one small step at a time.

    Finally, after you've prepared your study notes, you need to go back and look at the broader picture, seeing similarities between topics, and studying how they relate to each other.

    Each one of you need to figure out what you personally need to do in order to learn, but if you need a template to start with, you can use the worksheet as a jump off point.

    • [08-Apr-2014]

    Lecture 27 notes (16.4, Green's Theorem) (updated 09-Apr)

    [07-Apr-2014]

    Lecture 26 notes (16.3, Conservative vector fields) (updated 08-Apr)

    [02-Apr-2014]

    Lecture 25 notes (16.2, Line integrals over vector fields) (updated 04-Apr)

    [31-Mar-2014]

    Lecture 24 notes (16.1, Line integrals over scalar fields) (updated 02-Apr)

    [31-Mar-2014]

    Midterm 2 solutions.

    [31-Mar-2014]

    Lecture 23 notes (15.8, Change of Variables in multiple integrals) (updated 31-Mar)

    [24-Mar-2014]

    Agenda for Wednesday:
    - Finish the example from the Lecture 22 notes.
    - Look at some of the Practice Problems. If there are particular problems you want me to go over, please let me know.

    Reminder: I have regular office hours Wednesday 1-2pm, and I have an extra hour Wednesday 4-5pm in DRL 3C2. We have the space of a small classroom, so it will run as an informal recitation. I hope to see some of you there.

    [20-Mar-2014]

    Announcements: For the week of March 24 - March 28, my office hours will be held at the following times:

    Monday March 24: 3-4pm in DRL 3N4C
    Wednesday March 26: 1-2pm in DRL 3N4C
    (and an extra hour on Wednesday) 4-5pm in DRL 3C2

    [20-Mar-2014]

    Announcements: Your second in-class midterm is on Friday March 28.

    The midterm covers all material from the sections 14.1-14.8, 15.1-15.5, 15.7.
    It will consist of multiple choice questions and open answer questions.
    You may bring one sheet of notes on 8.5"x11" paper, handwritten, two-sided. No other aids are allowed.
    Remember to bring your Penn ID.

    Here are many Practice Problems to help you study for the midterm. These questions are taken from old exams, and are a good indication of the level of difficulty of the problems you can expect to see on your test.

    Your TAs will host a Review Session on Thursday March 27 from 6--8pm in DRL A6. They will go over some of the questions on the Practice Problems sheet.

    [20-Mar-2014]

    Lecture 22 notes (15.7, Triple Integrals in Cylindrical and Spherical Coordinates) (updated 26-Mar)

    [17-Mar-2014]

    Lecture 21 notes (15.5, Triple Integrals) (updated 21-Mar)

    I came across a cute article today on a new paper that attempts to encode the stock market by using a high-dimension geometric object coined as the stockmarkethedron. The author claims that, by computing the volume of the object, one can predict the behaviour of the market with some probability.

    [14-Mar-2014]

    Lecture 20 notes (15.4, Double Integrals in polar coordinates) (updated 17-Mar)

    [05-Mar-2014]

    Lecture 19 notes (15.2, 15.3 More Double Integrals) (updated 07-Mar)

    [03-Mar-2014]

    Lecture 18 notes (15.1 Double Integrals) (updated 05-Mar)

    [28-Feb-2014]

    Lecture 17 notes (14.8 Lagrange's Method of Optimization) (updated 05-Mar)

    [26-Feb-2014]

    Lecture 16 notes (14.7 Finding Maxima and Minima) (updated 03-Mar)

    [24-Feb-2014]

    Lecture 15 notes (14.6 Tangent Planes, etc) (updated 26-Feb)

    [21-Feb-2014]

    Lecture 14 notes (14.5 Directional Derivative) (updated 24-Feb)

    [19-Feb-2014]

    Lecture 13 notes (14.4 Chain Rule) (updated 21-Feb)

    [18-Feb-2014]

    Midterm 1 solutions.

    [17-Feb-2014]

    Lecture 12 notes (14.3 Partial derivatives) (updated 19-Feb)

    [15-Feb-2014]

    Lecture 11 notes (14.2 Limits and Continuity) (updated 17-Feb)

    [06-Feb-2014]

    Announcements: Your first in-class midterm is on Friday February 14.

    The midterm covers all material from the sections 11.6, 12.1-12.6, 13.1-13.6.
    It will consist of seven questions, including multiple choice questions and open answer questions.
    You may bring one sheet of notes on 8.5"x11" paper, handwritten, two-sided. No other aids are allowed.
    Remember to bring your Penn ID.

    Here are many Practice Problems to help you study for the midterm. These questions are taken from old exams and midterms, and are a good indication of the kinds of problems you can expect to see on your test.
    Note: In Problem 16, use g = 32 ft/s^2.

    Your TAs will host a Review Session on Thursday February 13 from 5--7pm in DRL A2. They will go over some of the questions on the Practice Problems sheet.

    [07-Feb-2014]

    Lecture 10 notes (12.6 Quadric Surfaces, 14.1 Functions of Several Variables) (updated 10-Feb)

    Fold your own hyperbolic parabola (scroll down the page for instructions).

    [05-Feb-2014]

    Lecture 9 notes (13.6 Acceleration, 11.6 Conics) (updated 07-Feb)

    A strange fact I learned recently: The Olympic Flame is traditionally lit at Olympia, Greece, using a parabolic reflector concentrating sunlight, and is then transported to the venue of the Games. Parabolic mirrors are one of many shapes for a burning-glass.

    [03-Feb-2014]

    Announcements: HW 3 has been amended; it includes Sections 12.5, 13.1 - 13.4.

    Lecture 8 notes (13.5 Acceleration) (updated 05-Feb)

    (I have moved the material on motion in polar coordinates to Friday's lecture.)

    [02-Feb-2014]

    Lecture 7 notes (13.3 Arclength, 13.4 Curvature) (updated 03-Feb)

    A cycloid animation. The cycloid is the solution to the Brachistochrone Problem dating from the late 1600's.

    [29-Jan-2014]

    Lecture 6 notes (13.2 Projectile Motion) (updated 31-Jan)

    Real world applications of projectile motion: human cannonballs

    [24-Jan-2014]

    Announcements: My office hours for this week only, will be held Thursday January 30 4pm -- 6pm.

    Lecture 5 notes (13.1 Curves in space, 13.3 Arclength) (updated 29-Jan)

    [24-Jan-2014]

    Lecture 4 notes (12.5 Planes and Lines) (updated 27-Jan)

    [20-Jan-2014]

    Announcements: My office hours for this week will be held Thursday January 23, 1pm -- 3pm.

    Lecture 3 notes (12.3 Dot Product, 12.4 Cross Product) (updated 24-Jan)

    [15-Jan-2014]

    Lecture 2 notes (12.2 Vectors) (updated 20-Jan)

    [14-Jan-2014]

    Lecture 1 notes (12.1 3-Space) (updated 15-Jan)

    [29-Dec-2013]

    This space serves as a Class Blog. Lecture Summaries and Course Announcements will be posted here. Check frequently!