Calculus of One and Several Variables

Course Description and Grading Breakdown

This course will introduce the mathematical method through (One Variable) Calculus, with which the Caltech freshmen have reasonable familiarity, at least for doing calculations (assuming various results as black boxes). The typical high school courses, and the AP tests themselves, are woefully inadequate in explaining, or testing, why things work and how to justify one’s propositions. In Ma 1a, the underlying concepts will be stressed, as well as the need for checking the hypotheses precisely as to where the results apply. A main focus will be on the writing of complete proofs so the case one is making is ironclad and unassailable. Learning to think precisely and rationally will come in handy in life, regardless of which subject one majors in.

The first nine topics below, and as much as possible of the tenth topic, will be treated during the Fall quarter:

(1) Mathematical Induction and the real number system

(2) Sequences and Series

(3) Continuous Functions

(4) Differential Calculus

(5) Integral Calculus

(6) Polynomial Approximations

(7) L’Hôpital’s rule for 0=0

(8) Improper Integrals

(9) Complex Numbers

(10) Integral Tests, Abel summation for series

There will be weekly homework assignments, as well as a Midterm and a Final examination, each of the Take Home variety lasting three hours. The final grade (of P or F) will depend on a composite of these factors. To be precise, the homework will be worth 40 percent, while the final and midterm will each be worth 30 percent. No one will be excused from the final exam.


Course Meeting Time and Location
Lectures
Monday, Wednesday and Friday
10:00 - 10:55
Baxter Lecture Hall (BAX)

Recitations 
Thursday
029:00 - 9:55 am B111 DWN  Konrad Pilch
039:00 - 9:55 am103 DWN Daniel Siebel
049:00 - 9:55 am 119 DWN  Hélène Rochais
05 10:00 - 10:55 amB111 DWN  Konrad Pilch
0610:00 - 10:55 am 103 DWN  Daniel Siebel
0710:00 - 10:55 am 119 DWN  Ryan (Gene) Yoo
08 1:00 - 1:55 pm 119 DWN  Siqi He
09 1:00 - 1:55 pm B122 GTS  Todd Norton
10 2:00 - 2:55 pm B111 DWN  Todd Norton
11 2:00 - 2:55 pm  102 STL Alex McDonald

If you would like to switch your recitation section, please email Meagan with your preferred recitation time.


Course Instructor Contact Information and Office Hours
256 West Bridge

TA Contact Information and Office Hours
Todd Norton (Head TA)     Office Hours: Todd will not hold office hours on Dec 3.  Instead there will be a midterm review session from 6-8 pm in E Bridge 201. 
Siqi He                                                   Sundays, 6-7 pm                  Downs B111
Alex McDonald                                        Saturdays, 12-1 pm              Downs B111
Konrad Pilch                                           Thursdays, 5-6 pm               Downs B111
                                                        and Sundays, 5-6 pm                Downs B111
Helene Rochais                                       Fridays, 2-3 pm                    Downs 107   (Please note Helene's office hours are in 107, not B111)
Daniel Siebel                                          Fridays, 4-6 pm                    Downs B111
Ryan Yoo                                                Wednesdays, 2-3 pm             Downs B111  


Course Ombuds
Thank you to the following students for volunteering to represent your class at the Ombuds meeting. If you have any feedback about the class, please reach out to one of your representatives. If you don't have a representative for your house, please feel free to contact any of the Ombudspeople or become one yourself by contacting Meagan.
 HouseOmbudsperson 
AveryDavid Zheng
Blacker 
DabneyCole Brabec, Arushi Gupta & Riana Karim
FlemingAmy Wang
Lloyd Ankush Hommerich-Dutt, Alycia Lee & Christine Yu
PageJames Wei
RickettsEric Moreno 
Ruddock 

Course Schedule

 DateTopic 
 09/25/17Chapter 0 Notes
 09/28/17Chapter 1 Notes
 10/24/17Chapter 2 Notes
 10/09/17Chapter 3 Notes
 10/11/17Chapter 9 Notes
 10/23/17Chapter 4 Notes
 11/03/17Chapter 5 Notes
 11/08/17Chapter 6 Notes
 11/27/17Chapter 7 Notes
 11/27/17Chapter 8 Notes



Course Policies
HomeworkHomework is due Sundays by 12 Midnight, just before the advent of Monday, and will be posted on the course web site on Tuesday before noon during the previous week; for example, the first HW will be due on Oct.1 (by midnight) and the problem set will be posted on Sep. 26. All problems may be done in collaboration with others. However, each student must write down the solution in his/her own individual way and there should be no two identical solutions to any problem. Do not consult the solution sets from previous years in working this year’s problems. At most one late homework set will be accepted throughout the quarter, and only at your TA’s discretion, if arrangements have been made in advance with your TA, and if the work is less than a week late. Beyond this, late homework will NOT be accepted, except with a letter from the Infirmary or from the Dean (or Associate Dean). Every week, graded homework can be picked up from the TA during the recitation on Thursday.

RecitationsPlease go to the recitations. Each week, a portion of the recitation will be dedicated to introducing some computational (or even theoretical) aspect which the Instructor will not have time to present in class. In general, get to know your TA and bug him/her to death (figuratively speaking) with your questions, and try to fill in all the holes in your understanding. Don’t wait till the midterm to start doing that!

Assignments
Homework Dropbox Location - The drop boxes are located on the first floor of Downs, across from the elevator, between rooms 113 and 119.  Deposit all completed homework assignments into the dropbox.

 Date PostedAssignment Due Date  Solutions
 09/25/2017Homework Set 1 10/01/2017Homework 1 Solutions
 10/02/2017   Homework Set 2 10/08/2017
Homework 2 Solutions
 10/11/2017Homework Set 3 (final) 10/15/2017Homework 3 Solutions
 10/17/2017Homework Set 4 10/22/2017Homework 4 Solutions
 to be postedHomework Set 5 Not to be turned inHomework 5 Solutions
 10/30/2017Homework Set 6  11/05/2017  Homework 6 Solutions
 11/06/2017Homework Set 7 11/12/2017Homework 7 Solutions
 11/13/2017Homework Set 8 11/19/2017Homework 8 Solutions
 11/20/2017
Homework Set 9 -- Last Set to hand in! 11/28/2017 by 11:59 p.m. Homework 9 Solutions
 11/27/2017Homework 10 Not to be turned inHomework 10 Solutions




Midterm and Final Exam
Midterm is available here. The password has been emailed to you. If you have any issues accessing the file, please let Meagan know. It is due on Sunday October 29th at midnight.  Turn it in to your section's drop box in Downs, just like homework assignments.

It is a take-home exam.  You are allowed to spend 4 hours working on the exam.  Your 4 hours start the moment you open the exam.  Do not look at the exam until you are ready to begin.  You must work 4 consecutive hours: for example, 4 pm - 8 pm.  You may not break up the 4 hours, such as 4pm - 6 pm and then 7 pm - 9 pm.  (Obviously bathroom breaks and such are allowed.)  You must write your solutions up in a "blue book."  You may not contact any TA while taking the exam to ask a question: ask your TA any questions you may have BEFORE starting the exam.

There will be a midterm review session on Friday, October 27 from 8 pm - 10 pm in  142 Keck.  I realize not everyone is able to attend so here are my notes. (Please email Todd to report any typos you find!)  You are allowed to consult these notes while working on the exam, but Prof. Ramakrishnan's course notes are the authoritative source: if you find any discrepancy go with the professor's notes (and report the discrepancy to Todd).

The midterm solutions are available here.  Please observe that each problem was worth 24 points.  Problems 1a, 1b, 3a, 3b, 4a, 4b, 5a, 5b were each worth 12 points.  Problem 2a was worth 16 points, problem 2b was worth 8 points.  Your grade was computed by taking the best 4 of 5 problem scores, and not the best 8 of 10 part a/b scores (so your grade could have been composed of Problems 1,2,4,5 but your grade could not have been composed of 1a, 1b, 2a, 3a, 4a, 4b, 5a, 5b).  There were 4 extra points added to each exam to bring the total to 100 points.

The Final Exam is available here. The password has been emailed to you. If you have any issues accessing the file, please let Meagan know. It is due on Thursday December 7 at 10 am. Turn it into your section's drop box in Downs. It is a take-home exam.  You are allowed to spend 4 hours working on the exam.  Your 4 hours start the moment you open the exam.  Do not look at the exam until you are ready to begin.  You must work 4 consecutive hours: for example, 4 pm - 8 pm.  You may not break up the 4 hours, such as 4pm - 6 pm and then 7 pm - 9 pm.  (Obviously bathroom breaks and such are allowed.)  You must write your solutions up in a "blue book."  You may not contact any TA while taking the exam to ask a question: ask your TA any questions you may have BEFORE starting the exam.

There will be a final exam review session on Sunday, December 3 from 6-8 pm in East Bridge, Room 201.  My notes are here (Please email Todd to report any typos you find!)  You are allowed to consult these notes while working on the exam, but Prof. Ramakrishnan's course notes are the authoritative source: if you find any discrepancy go with the professor's notes (and report the discrepancy to Todd).


The final exam has been graded and returned.  Each problem was worth 25 points.  The best 4 problems were used to calculate your score.  In Problem 4 the unnumbered part was worth 10 points, 4a was worth 5 points, and 4b was worth 10 points.


Grading questions/complaints: Because we grade such a large number of exams so quickly, we aren't able to leave detailed feedback next to each problem.  We try to address the most common errors in the above solutions, so check there FIRST to see if your grading question is addressed.  If it is not, follow this procedure:

1. Take a photograph of the specific part of a problem you have a question on (such as 4a).  Make sure you have all your solution to that part in the picture, not just part of your solution.
2. Email tnorton@caltech.edu with the following subject line:

    Ma1a Final Exam Question: Problem X, (part a or b)

    Briefly explain your question
    
3. Send a separate email for each part of each problem you have a question about.

Please keep in mind that each part of each problem was graded by a different TA.  A TA can only review the score of a problem that he/she graded.  If you use the subject line I suggested above, I can more quickly direct your question to the TA who graded that problem.  Please allow them a couple days to respond as they may receive many questions.

ALL QUESTIONS MUST BE EMAILED TO TODD BY THE END OF MONDAY, DEC 11. This is to allow the TAs enough time to address your question before final grades are due.


Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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Caltech Math,
Sep 25, 2017, 2:12 PM
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Pamela Fong,
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Pamela Fong,
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Pamela Fong,
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Thomas Norton,
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Thomas Norton,
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Pamela Fong,
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