Calculus of One and Several Variables

Course Description and Grading Breakdown

40% Homework, 30% Midterm, 30% Final

The two main aims for the course are:
    - Becoming familiar with mathematical reasoning, and writing rigorous proofs.
    - Learning to do explicit calculations.

Both aims will be pursued in the context of Calculus: analysis of integration and differentiation of functions, along with closely related topics.

The following topics will be covered, roughly in order:
  • Mathematical Induction
  • Completeness
  • Functions
  • Integral for Step Functions
  • Integral for More General Functions
  • Applications of Integration
  • Limits
  • Continuity
  • Intermediate Value Theorem
  • Inversion
  • Extreme Value Theorem
  • Integrability Theorem
  • Mean - Value Theorem for Integrals
  • Derivatives
  • Implicit Differentiation
  • Extreme Values
  • Mean - Value Theorem for Derivatives
  • Curve Sketching
  • Fundamental Theorem of Calculus
  • Integration by Substitution
  • Integration by Parts
  • Logarithm
  • Exponential Function
  • Integration by Partial Fractions
  • Taylor Series (This topic will be mainly covered in Math 1d)



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

Recitation
Thursday 
7:30 - 8:55 pm
387 Linde


Course Instructor Contact Information and Office Hours

256 Linde Hall
e-mail (instructor's first name)@caltech.edu
Office Hours: Mondays 1-2pm, or by appointment
    

TA Contact Information and Office Hours:

Luciena Xiao:
e-mail: xxiao at caltech.edu
Office Hours: Sundays 3-4pm, or by appointment
Office Hours Location: 302 Linde Hall


Course Schedule and Textbook

Apostol, Tom M., Calculus, Volume 1, 1991, Wiley, ISBN:  0-471-00005-1.

A day-by-day list of topics covered will be posted here during the course:

 DateTopic 
  
  


Lecture Notes:

Class notes are in brief summary form.



Course Policies

Late work will not be accepted except for: 
1) Medical reasons (requiring a note from the Health Center) 
2) Serious personal difficulties (requiring a note from the Dean's Office)




Assignments

Weekly assignments will be posted online on Mondays, and will be due the following Monday. 

You may discuss the problems with classmates, and are indeed encouraged to do so. However, you must write up your own solutions separately.

You may use theorems from the textbook, but you must refer to them clearly. 

The schedule according to which the homework, midterm, and final will be posted/due is as follows.

 Date PostedAssignment Due Date  Solutions Average  Standard Deviation
 Oct 1         HW1 Oct 8 HW1 43.9/5511.7 
 Oct. 7 HW2  Oct 15 HW2 73/10016.5 
 Oct 15 HW3  Oct 22    
 HW3 74.6/10016.5 
 Oct 22 HW4 Oct 29
 HW4 54.5/10022.6 
 Oct 29 Midterm  Nov 5
 MidSol 72/100
 Nov 5 HW5  Nov 12  HW5 79/10020 
 Nov 12 HW6  Nov 19 HW6 95/10021 
 Nov 19 HW7 Nov 26 HW7 87/10012.5 
 Nov 26 HW8  Dec 3 HW8 78.6/10014.4 
 Dec. 7 Final  Dec. 14   


Midterm and Final Exam

The midterm will take place during the fifth week, according to the schedule above. 

The midterm is available here. The password has been emailed to you. For issues accessing the file, please contact Meagan. The exam is due at 4 pm on Monday November 5th. 

The final will be available to the students on the last day of the course, and due a week later. There will be a practice final posted one week earlier.


Here are also the Solutions to the practice final.

The final is available here. The password has been emailed to you. For issues accessing the file, please contact Meagan. The exam is due at 4 pm on Friday December 14th. 



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.

Ċ
Luciena Xiao,
Oct 8, 2018, 4:15 PM
Ċ
hw1.pdf
(105k)
Zavosh Amir-Khosravi,
Oct 2, 2018, 10:11 PM
Ċ
Luciena Xiao,
Oct 18, 2018, 6:04 PM
Ċ
hw2.pdf
(107k)
Zavosh Amir-Khosravi,
Oct 9, 2018, 7:34 AM
Ċ
Luciena Xiao,
Oct 23, 2018, 3:14 PM
Ċ
hw3.pdf
(122k)
Zavosh Amir-Khosravi,
Oct 19, 2018, 11:43 AM
Ċ
Luciena Xiao,
Nov 1, 2018, 9:13 PM
Ċ
hw4.pdf
(102k)
Zavosh Amir-Khosravi,
Oct 29, 2018, 11:15 AM
Ċ
Luciena Xiao,
Nov 12, 2018, 4:02 PM
Ċ
hw5.pdf
(22k)
Zavosh Amir-Khosravi,
Nov 5, 2018, 1:01 PM
Ċ
Luciena Xiao,
Nov 19, 2018, 4:10 PM
Ċ
hw6.pdf
(29k)
Zavosh Amir-Khosravi,
Nov 12, 2018, 12:00 PM
Ċ
Luciena Xiao,
Nov 26, 2018, 4:42 PM
Ċ
hw7.pdf
(131k)
Zavosh Amir-Khosravi,
Nov 24, 2018, 11:18 PM
Ċ
Luciena Xiao,
Dec 3, 2018, 4:48 PM
Ċ
hw8.pdf
(99k)
Zavosh Amir-Khosravi,
Nov 26, 2018, 9:40 PM
Ċ
Zavosh Amir-Khosravi,
Nov 11, 2018, 3:27 AM
Ċ
Zavosh Amir-Khosravi,
Dec 7, 2018, 5:36 PM
Ċ
Zavosh Amir-Khosravi,
Dec 3, 2018, 7:33 PM
Ċ
Zavosh Amir-Khosravi,
Oct 29, 2018, 11:23 PM