Math 115 Calculus of Functions of One Variable II

Semester: Fall 2014

Find x.
Lecture 03 (12725)
Inst : Dr. Asher Auel
asher * auel AT yale * edu
Time : Mon Wed Fri 11:35 am - 12:25 pm
Loct : LOM 214
Office : LOM 210
Phone : (203) 432-4187
Office
hours : 		Mon 01:30 - 02:30
Thu 11:00 - 12:00
Text : Calculus, Early Transcendentals, 7e: Math 115
James Stewart
ISBN-13 1-111-95350-3.
Course syllabus and homework schedule.
This will be a flipped classroom. Watch the videos on Coursera.
Bring an internet-enabled device to class for Learning Catalytics.

Description of course: This course is about integral calculus and infinite series. You should already be familiar with differential calculus. The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two objects form the basis for nearly all mathematical formulas in science. The rules by which we can compute derivatives and integrals of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. Using calculus, we want you to learn how to model situations in order to solve problems. The second half of the course is a careful investigation of infinite sequences and series, culminating with Taylor's theorem and applications to physics.

Pedagogy: Math 115 is now taught as a flipped classroom. You might be interested to learn about the method and history behind this approach. What does it mean for you? Before coming to class each day, you watch some short videos (10-12 minutes) and do 4 or 5 prep problems on-line at Coursera. Then the classroom experience can be better tailored to suit your needs.

Homework 15%
Midterm exam 1 (01 Oct)   25%
Midterm exam 2 (12 Nov)   25%
Final exam (15 Dec) 35%
Grades: Your final grades will be based on homework (including the weekly problem sets, on-line prep problems, and in-class Learning Catalytics participation), two midterm exams, and a final exam. While more emphasis is placed on exams than on weekly homework in computing your final grade, completing your homework on a weekly basis is the most sure way to success on the exams.
Group work, honestly: Working with other people on mathematics is highly encouraged and fun. You may work with anyone (e.g., other students in your section, in the course, not in the course, tutors, bums on the street, ...) on your weekly problem sets. If done right, you'll learn the material better and more efficiently working in groups. The golden rule is:
Work with anyone on solving your problem sets,
but write up your final draft by yourself.
Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends, see the guidelines below. Mathematical writing is very idiosyncratic - we will be able to tell if papers have been copied - just don't do it! You will not learn by copying solutions from others! Also, if you work with people on a particular assignment, you must list your collaborators on the top of the first page. This makes the process fun, transparent, and honest.

You are not allowed to work with anyone while taking the on-line prep questions.




Policies

(or otherwise the small print)

Homework: Weekly problem sets will be due at the beginning of lecture on Friday and will be posted on Classes*v2 at least the week before being due.

On-line prep problems related to the videos must be completed by 3 am before each class.

Late or improperly submitted problems sets or prep problems will not be accepted. Period. If you know in advance that you will be unable to submit your homework at the correct time and place, you must make special arrangements ahead of time (e.g., sickness, religious holidays, or university related trip) and get a dean's excuse.

Consider the pieces of paper you turn in as a final copy: written neatly and straight across the page, on clean paper, with nice margins and lots of space, stapled together, and well organized.

Your lowest problem set score and lowest 15% of on-line prep problem scores will be dropped from your final grade calculations.

There will be in-class participation credit assigned to Learning Catalytics (LC) activity participation. You will have to create a LC account with the code provided. To get credit, you must bring your internet enabled device to class and complete the activity. There will be no make up opportunities for LC activities, even if your phone runs out of batteries during class.

Exams/quizzes: Both mid-terms will take place 7:00 - 8:30 pm at a location to be decided. The final exam will be take place 7:00 - 10:30 pm on Monday, December 15th, 2014, in a place to be decided by the registrar. No notes and no devices of any kind are allowed during exams. Make-up exams will only be scheduled with a dean's excuse.




Problem set guidelines: Generally, a problem set problem in any math course will consist of two parts: the creative part and the write-up.

  • The creative part: This is when you "solve" the problem. You stare at it, poke at it, and work on it until you understand what's being asked, and then try different ideas until you find something that works. This part is fun to do with your friends; you can do it on the back of a napkin. If you're having trouble, even in understanding what the problem's asking, use the resources available to you: my office hours, teaching assistants' office hours, weekly tutoring sessions, etc. Ask for help as early as you can! This part should all be done on "scratch paper."

  • The write-up: Now that everything about the problem is clear in your mind, you go off by yourself and write up a coherent, succinct, and nicely written solution on clean sheets of paper. Consider this your final draft, just as in any other course. This part you should definitely NOT do with your friends.