### Calculus of One and Several Variables and Linear Algebra

This course will introduce the mathematical method through (One Variable) Calculus.
By the mathematical method, what we primarily mean is the ability to express oneself with
absolute precision, employ critical thinking to approach the problem with the available tools,
show clearly the relevant calculations, and then to use logical proofs to establish that certain
precise statements are true - in a given context or universally, as the case may be.
We assume that Caltech freshmen have a 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

The Real numbers, and the preponderance of rational numbers

Sequences and Series

Continuous Functions

Differential Calculus

Integral Calculus

Polynomial Approximations

L'Hopital's rule for 0/0

Improper Integrals

Complex Numbers and functions

Integral Tests, Abel summation for series

The course will be graded on a pass/fail system, based on the

Final composite score,

with the following breakdown:

60% HW sets, 20% each for Midterm and Final

Midterm Composite score:

60% HW (first four sets), 40% Midterm Exam score

A+  97-100
A    90-96
A-   86-89
B    83-86
B    69-82
B-   65-68
C+  61-64
C    54-60
D    50-53
F       1-49

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

Course Text
CALCULUS, volume 1 (second edition), by Tom Apostol

Course Instructor Contact Information and Office Hours

277 Linde Hall
Office Hours: Friday 3-5pm

TA Contact Information and Office Hours

 Sect # Recitation Day and time Location TA Office hours information 2 Thursdays @ 9:00 am 310 LINDE Lingfei Yi lyi@caltech.edu Th 7-8pm Linde 259 3 Thursdays @ 10:00 am 310 LINDE Victor Zhangvzzhang@caltech.edu Th 11am-12pm and Th 3:30-4:30pm Linde 287 or 3rd floor Linde outside recitation classroom 4 Thursdays @ 10:00 am 142 KCK Luciena Xiaoxxiao@caltech.edu Fri 2-3pm Linde 302 5 Thursdays @1:00 pm 387 Linde Victor Zhangvzzhang@caltech.edu Th 11am-12pm and Th 3:30-4:30pm Linde 287 or 3rd floor Linde outside recitation classroom 6 Thursdays @ 1:00 pm B180 BBB(Beckman Behavioral Bld) Ruide (Frid) Furffu@caltech.edu Fri 8-9pm Linde 3rd floor common area 7 Thursdays @ 2:00 pm 387 LINDE Konrad Pilchkpilch@caltech.edu Fri 5-7pm Linde 302 8 Wednesdays @ 7:00 pm 310 LINDE Konrad Pilchkpilch@caltech.edu Fri 5-7pm Linde 302 9 Thursdays @ 9:00 am 255 LINDE Jiaxin Zhangzhangjx@caltech.edu Wed 2-3pm Linde 183 10 Thursdays @ 2:00 pm 119 DWN Yongzhe (Allen) Zhangyongzhe@caltech.edu Sunday 4-5pm Linde 183(no office hours last 2 weeks of term) 11 Wednesdays @ 7:00 pm 255 LINDE Kushal Banerjeekushalb@caltech.edu Fri 7-8 Linde 153, 187

Lecture Notes

 Date Chapter 10/1/2019 0 9/27/2019 0a 10/4/2019 1 10/8/2019 2 10/20/2019 3 10/29/2019 4 11/5/2019 5 11/10/2019 6 11/18/2019 7 11/21/2019 8 10/29/2019 9 12/3/2019

Course Policies

Late work: Each student can turn in at most one homework late without penalty. You must contact the TA of your assigned section number and notify them beforehand in order to use this policy. Otherwise, there will be a heavy penalty for late work but we will still grade it. Late work can only be accepted up to 1 week after the original due date, when solutions will be posted. Exceptions are given only with note from the Health Service or the Dean. This policy will be strictly enforced.

Final deadline for all late work: All outstanding work must be turned in before or with the final exam, because the graders leave for the winter break and be unable to grade.

Section Recitations: Any student can attend any section or office hour, regardless of the assigned section number. But the earliest opportunity to collect graded work is during the recitation for your assigned section number, when the TA hands it out. Afterwards it will be put in the drop box.

Homework 1, 3, 6, 8: Problem 1 - Victor, Problem 2 - Lingfei, Problem 3 - Kushal, Problem 4 - Frid
Homework 2, 4, 7, 9: Problem 1 - Konrad, Problem 2 - Luciena, Problem 3 - Jiaxin, Problem 4 - Allen
Some homeworks have a problem 5, whenever this is the case, Konrad is grading it.
EXCEPTIONS:
HW7 and HW8: Lueicena and Lingfei are switching grading duties
HW9: Jiaxin is grading for Allen

Final Exam:
2. Victor, Kushal, Luciena, Frid
3. Lingfei
4a: Luciena
4b: Jiaxin
5. Kushal, Frid

Assignments
 Date Posted Assignment Due Date 10/2/2019 HW 1 Oct. 7, 2019 10/8/2019 HW 2 Oct. 14, 2019 10/16/2019 HW 3 Oct. 21, 2019 10/21/2019 HW 4 Oct. 28, 2019 10/30/2019 HW 5 Needn't be   turned in! 11/6/2019 HW 6 Nov. 11, 2019 11/13/2019 HW 7 Nov. 18, 2019 11/18/2019 HW 8 Nov. 25, 2019 11/25/2019 HW 9 Dec. 3, 2019 11/27/2019 HW 10 Needn't be turned in !

Midterm and Final Exam

The midterm is due on Tuesday, November 5 at 10:01 AM, and is available here. Please check your email for accessing the file linked to this course page.

The midterm review session is 3pm Sunday Nov 3 in Linde 387. It is aimed to last 90 minutes.

The final exam is due Wednesday, Dec 11 at 10:01 am, and is available here. Grading will begin soon after the due time.

The final review session is 3pm Sunday Dec 8, in Bridge 201. It is aimed to last 90 minutes.

Collaboration Table
HomeworkExams
You may consult:
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
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
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