Calculus of One and Several Variables

Course Description

This course will introduce the mathematical method through (One Variable) Calculus.  By the mathematical method, what we primarily mean is the ability to express one's self with absolute precision, and then to use logical proofs to establish that certain precise statements are universally true.  We assume that the Caltech freshman has reasonable familiarity with single variable calculus as a computational endeavor, and in this course we emphasize explanations of why things work and how to justify one's propositions.  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.  It will emerge that when we do this, we actually know more than the standard computational aspects of single variable calculus and that we can answer questions which are new to us and come up naturally once all the terms in Calculus are carefully defined and the definitions used.  Some of these questions are also quite natural from the point of view of the scientist and engineer.

The topics listed below will be treated during the Fall quarter:

    Mathematical induction and the real number system.

    Sequences and Series

    Continuous Functions

    Differential Calculus

    Integral Calculus

    Polynomial Approximations

    L'Hopital's rule for 0/0

    Improper Integrals

    Integral Tests, Abel summation for series

    Complex Numbers


Course Meeting Time and Location
Lecture
Monday, Wednesday and Friday
10:00 - 10:55 am
Baxter Lecture Hall

Recitation
All recitations take place on Thursday
 Section  Time  Location  TA
 2 9:00 - 9:55 am 387 Linde   Pooya Vahidi Ferdowsi
 3 9:00 - 9:55 am 103 DWN   Andrei Shubin
 4 9:00 - 9:55 am 119 DWN   Lingfei Yi
 5 10:00 - 10:55 am B127 GCL   Pooya Vahidi Ferdowsi
 6 10:00 - 10:55 am 142 KCK   Konrad Pilch
 7 10:00 - 10:55 am  119 DWN  Lingfei Yi
 8 1:00 - 1:55 pm B122 GCL   Tamir Hemo
 9 1:00 - 1:55 pm 119 DWN   Josh Lieber
 10 2:00 - 2:55 pm 387 Linde   Josh Lieber


TA Contact Information and Office Hours
 TA Time Location
 Tamir Hemo Wednesdays 18:00 - 19:00 387 Linde
 Konrad Pilch Thursdays 17:00 - 18:00 187 Linde
 Pooya Vahidi Ferdowsi Fridays 18:00 - 20:00 387 Linde
 Lingfei Yi Saturdays 18:00 - 20:00 387 Linde
 Josh Lieber Sundays 14:00 -16:00 387 Linde
 Andrei Shubin Sundays 16:00 -17:00 387 Linde

Wednesdays 18:00 - 19:00 in 387 Linde
Thursdays 17:00 - 18:00 in 187 Linde
Fridays 18:00 - 20:00  in 387 Linde
Saturdays 18:00 - 20:00 in 387 Linde
Sundays 14:00 -17:00  in 387 Linde

Course Administrator
156 Linde Hall
626-395-4336

Instructor and Office Hours
277 Linde Hall
F: 3-5 pm

Course Ombudspersons
 House/Residence Ombuds Contact (all are @caltech.edu)
 AveryLin Lin Lee llee3 
 BechtelMark Ellismellis 
 BlackerMadeline Gardner mgardner 
 DabneyMegan Tjandrasuwita mtjandra 
 Fleming  Meena Hari mhari
 LloydJannie Yu 
Myra Cheng 
jannie
myracheng 
 PageAntonia Liu 
Sarah Zou
antonia
szou 
 RickettsShubh Agrawal
Ayooluwa Odemuyiwa
shubh
aodemuyi 
 RuddockNicholas Chang
Jack Nguyen
Max Stickels
 
 nchang
jtnguyen
mstickel



Notes: written by D.Ramakrishnan
                (with figures by M.Mnatsakanian)

 Date Chapter
Sep. 26, 2018
                      0
Oct. 06, 2018
                  Equiv. Reln.
Oct.07,2018
                       1
Oct.09,2018                       2
Oct.14,2018
                       3
Oct.27,2018
                       4
Nov.04,2018                       5
Nov.11,2018
                       6
Nov.18,2018
                       7
Nov.26,2018
                       8
Oct.16,2018
                       9


Course Policies
Everyone will be allowed to submit one HW solution set late, but he/she/they will need to arrange it with the relevant TA, and abide by when it is required by the TA to be turned in.


Assignments
 Date Posted Assignment  Due Date  Solutions 
 Oct 1, 2018 Set 1  Oct 8, 2018, 9:01 am  Set 1 
Oct 9, 2018
Set 2
Oct 15, 2018, 9:01 am
Set 2
Oct 16, 2018
Set 3
Oct 22, 2018, 9:01 am
Set 3
Oct 23, 2018
Set 4
Oct 29, 2018, 9:01 am
Set 4 
Oct 29, 2018
Set 5
Need not be turned in!
Set 5
Nov 06, 2018 
Set 6
Nov 12, 2018,9:01 am
Set 6 
Nov 13, 2018
Set 7
Nov 19, 2018,9:01 am
Set 7
Nov 20, 2018
 Set 8
Nov 26, 2018,9:01 am
Set 8
Nov 28, 2018
Set 9
Dec 3, 2018,9:01 a
Set 9
Dec 4, 2018
Set 10
Need not be turned in!
Set 10


Midterm and Final Exam
The midterm exam is available here. The password was emailed to you. If you have issues accessing the exam, please contact Meagan. The exam will be due on Monday November 5th at 9:01 am. 
Midterm review with Josh Lieber - Saturday November 3rd, 7 - 9 pm in B127 GCL (Building #26).
The solutions for the midterm exam are now available here.

The final exam is available here. The password was emailed to you. If you have issues accessing the exam, please contact Meagan. The exam is due on Wednesday December 12th at 9:00 am.

Collaboration Table
  Homework Exams
You may consult:    
Course textbook (including answers in the back) YES YES
Other books YES NO
Solution manuals NO NO
Internet YES NO
Your notes (taken in class) YES YES
Class notes of others YES NO
Your hand copies of class notes of others YES YES
Photocopies of class notes of others YES NO
Electronic copies of class notes of others YES NO
Course handouts YES YES
Your returned homework / exams YES YES
Solutions to homework / exams (posted on webpage) YES YES
Homework / exams of previous years NO NO
Solutions to homework / exams of previous years NO NO
Emails from TAs YES NO
You may:

Discuss problems with others YES NO
Look at communal materials while writing up solutions YES NO
Look at individual written work of others NO NO
Post about problems online NO NO
For computational aids, you may use:

Calculators YES* NO
Computers YES* 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.

Ċ
Dinakar Ramakrishnan,
Sep 26, 2018, 3:09 PM
Ċ
Dinakar Ramakrishnan,
Oct 7, 2018, 7:44 AM
Ċ
Caltech Math,
Oct 12, 2018, 2:51 PM
Ċ
Dinakar Ramakrishnan,
Oct 14, 2018, 6:34 PM
Ċ
Dinakar Ramakrishnan,
Oct 27, 2018, 4:32 PM
Ċ
Dinakar Ramakrishnan,
Nov 4, 2018, 3:46 PM
Ċ
Caltech Math,
Nov 13, 2018, 2:26 PM
Ċ
Dinakar Ramakrishnan,
Nov 21, 2018, 8:35 AM
Ċ
Dinakar Ramakrishnan,
Nov 26, 2018, 5:20 PM
Ċ
Dinakar Ramakrishnan,
Oct 16, 2018, 1:06 PM
Ċ
Dinakar Ramakrishnan,
Oct 1, 2018, 4:15 PM
Ċ
Dinakar Ramakrishnan,
Dec 5, 2018, 2:50 PM
Ċ
Dinakar Ramakrishnan,
Oct 12, 2018, 11:36 AM
Ċ
Dinakar Ramakrishnan,
Oct 16, 2018, 2:38 PM
Ċ
Dinakar Ramakrishnan,
Oct 23, 2018, 3:07 PM
Ċ
Dinakar Ramakrishnan,
Nov 7, 2018, 4:45 PM
Ċ
Dinakar Ramakrishnan,
Nov 13, 2018, 2:07 PM
Ċ
Dinakar Ramakrishnan,
Nov 19, 2018, 1:30 PM
Ċ
Dinakar Ramakrishnan,
Nov 28, 2018, 6:03 PM
Ċ
Dinakar Ramakrishnan,
Dec 5, 2018, 2:50 PM
Ċ
Dinakar Ramakrishnan,
Oct 29, 2018, 11:42 AM
Ċ
Dinakar Ramakrishnan,
Oct 31, 2018, 6:11 PM
Ċ
Pooya Vahidi,
Nov 6, 2018, 11:32 AM
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Pooya Vahidi,
Oct 15, 2018, 1:42 AM
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Pooya Vahidi,
Oct 18, 2018, 3:06 PM
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Pooya Vahidi,
Oct 30, 2018, 11:37 AM
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Pooya Vahidi,
Nov 1, 2018, 9:56 PM
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Pooya Vahidi,
Nov 16, 2018, 1:39 PM
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Pooya Vahidi,
Nov 27, 2018, 5:39 PM
Ċ
Pooya Vahidi,
Dec 5, 2018, 3:21 PM
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Pooya Vahidi,
Dec 5, 2018, 3:16 PM
Ċ
Dinakar Ramakrishnan,
Oct 7, 2018, 7:40 AM