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 Yoo
08 1:00 - 1:55 pm 107 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: Sundays, 7-9 pm    Location: TBD
Siqi He                                                   Sundays, 6-7 pm                   TBD
Alex McDonald                                        Saturdays, 12-1 pm              TBD
Konrad Pilch                                           Thursdays, 4-6 pm                TBD
Helene Rochais                                       Fridays, 2-3 pm                    TBD
Daniel Siebel                                          Fridays, 4-6 pm                    TBD
Ryan Yoo                                                Wednesdays, 2-3 pm             TBD  



Course Schedule
 DateTopic 
 9/25/17 Chapter 0 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

 Date PostedAssignment Due Date 
 9/25/2017 Homework Set 1 10/1/2017
   



Midterm and Final Exam



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
Ċ
Thomas Norton,
Sep 25, 2017, 4:06 PM
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Caltech Math,
Sep 22, 2017, 11:57 AM