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Course

Calculus I - Math UN1101 - Section 001 and 002.
Fall 2019.
Columbia University.

Lectures

Classroom 203 Mathematics.
Section 001: Mo, We 10:10am-11:25am.
Section 002: Mo, We 2:40pm-3:55pm.

Instructor

Name: Daniele Alessandrini.
Contact: daniele.alessandrini@gmail.com.

Office hours: Mo, We 11:30am-12:30pm.
Office: 624 Mathematics.
NOTE: Sometimes it happens that there are too many students at the office hours, and it is not possible to stay in my office. In this case, we will go to room 528 Mathematics. If I am not in my office during office hours, try to look for me in 528. Notice that this is not the Math Lounge, we will go to a normal classroom.

Help Room

The Help Room is a place for students to seek assistance with material that comes up in the course. The room is staffed by graduate students and undergraduate teaching assistants. The relevant Help Room for this course is at 502 Milstein Center, on the Barnard campus. You can go to the Help Room at any time when it is open, see here for the schedule.

TAs

The TAs grade the assignments and can answer questions from students. They serve in the Help Room at 502 Milstein Center on the Barnard Campus.

Name email Help Room
Yang An alanmilleran@gmail.com Fr 9am-12am
Michelle Chen xc2413@columbia.edu Mo 12pm-2pm
Lori Leu ll3256@columbia.edu Th 12pm-2pm

Syllabus

The Syllabus for this course.

Content

Required text

Calculus: Early Transcendentals, 8th edition, by James Stewart (CENAGE Learning). The book is available at the Columbia bookstore.

Course Outline

In this course we will describe some basic ideas and techniques that lie at the foundation of all pure and applied mathematics. We will discuss about functions and their limits, dervatives and integrals. We will focus on their meaning, significance, applications and methods of computation. We will use the first six chapters of the course textbook (Calculus, Early Transcendentals, by Stewart).

Lectures

Date Topic Textbook Reference
19/09/04 Basics about functions Section 1.1
19/09/09 Even/odd, increasing/decreasing functions, polynomials Section 1.1, 1.2
19/09/11 Rational functions, combination of functions, powers with real exponents Section 1.2, 1.3, 1.4
19/09/16 Power functions, exponential functions, trigonometric functions Section 1.2, 1.4, Appendix D
19/09/18 1-1 functions, inverse function, logarithms, inverse trigonometric functions Section 1.5
19/09/23 Examples of equations
19/09/25 One-Sided Limits Section 2.2, 2.3
19/09/30 Limit laws Section 2.3
19/10/02 First Midterm
19/10/07 Limits at infinity Section 2.6
19/10/09 Continuous functions Section 2.5
19/10/14 Derivatives Section 2.1, 2.7, 2.8, 3.1
19/10/16 Differentiation Rules Section 3.2, 3.3, 3.4
19/10/21 Differentiation Rules, Velocity, Rate of change Section 2.1, 2.7
19/10/23 Second derivatives, Absolute maxima and minima Section 2.8, 4.1
19/10/28 Rolle's Thm, Mean Value Thm Section 4.2
19/10/30 Increasing/Decreasing functions, Graph sketching Section 4.3, 4.5
19/11/04 Holiday
19/11/06 Concavity, second derivative, local maxima and minima Section 4.3
19/11/11 L'Hospital Rule, Optimization Problems Section 4.4, 4.7
19/11/13 Integrals as signed areas
19/11/18 Second Midterm
19/11/20 The fundamental theorem of calculus Section 5.3
19/11/25 Substitution rule Section 5.5
19/11/27 Holiday
19/12/02 Areas between curves, correction of midterm Section 6.1
19/12/04 Computing volumes with integrals Section 6.2
19/12/09 Review lecture
Prerequisite

There are no formal pre-requisites; anyway, an understanding of pre-calculus will be assumed. This includes high school mathematics.

Resources

If your pre-calculus is weak, the textbook has some review material in Appendix A and B. Moreover, the section "Principles of problem solving", at the end of Chapter 1 can also be helpful.

Also, you can consider the website Khan Academy, it has plenty of useful instruction material freely available.

Assignments

Exersice sheets

The assignments will be published here in form of exercise sheets every Wednesday night, starting from Wednesday September 11. There is one week time to submit the written solutions.

Handing in

Written assignments will be due on Wednesdays at 11pm in one of the collection boxes on the fourth floor of the Mathematics Hall, beginning on September 18. Assignments will not be accepted in electronic form; only a physical copy in the collection box will be accepted. We encourage collaboration on assignments, but all solutions must be written up by you alone in your own words.

Late hand in

We will accept late assignment, but we deduct 15% of the points for every day of lateness. If you submit your assignment after Wednesday 11pm, please make a scan or a good quality picture of it. AFTER you have put your assignment in the collection box, please send an email to all the three TAs to notify them that you have handed-in a late assignment. Please, include the scan or picture of your assignment in the email, in case the TA is not able to get your solutions from the collection box at that time. Notice that handing-in a physical copy of the assignment in the collection box is still required, and must be done BEFORE sending the email.

Exams

Midterm exams

There will be midterm exams in class on Wednesday October 2nd and on Monday November 18.

Final exam

The final exam is currently projected for Wednesday December 18. For Section 001, 9am– Noon; for Section 002, 1:10-4pm. The date will be confirmed in November.

Exam details

You must plan to take the midterm and final exams at the scheduled time, so please make your travel plans accordingly. Besides students with disabilities having prior arrangements with ODS, the only exceptions will be for those with an incapacitating illness, a serious family emergency, or situations of comparable gravity. In the first case you will need a note from a doctor; in the other cases you will need a note from your advising dean. Incompletes can be granted only by your advising dean and only in the circumstances mentioned above. Anyone guilty of academic dishonesty, such as cheating on an exam or helping someone else to cheat, will fail the course and faces further academic discipline.

The day of the exam

  • For the midterms, we have very litle time, hence we have to try and start the exam as soon as possible (ideally at 10:10am or 2:40pm sharp). So please, try to enter in the room some minutes before this time, sit quickly, and put all the non-relevant objects inside your backpack.
  • You must leave an empty seat between every two students. We will use the seats in the first column from the left (from the point of view of the students), then the third column, the fifth, and so on. Please, don't sit in an even column.
  • Bring your University Id with you, I will check your identity during the exam. If for some reason you don't have a University Id, please let me know before the exam, and bring some other id with photo.
  • Bring two black or blue pens. Don't write in colors different from black or blue, we need the other colors for grading. It is not possible to ask for a pen to your colleagues during the exam.
  • You can bring a sheet of paper with handwritten notes. The sheet can be two sided, but it cannot be printed.
  • All electronic devices must be switched off and put into your backpack before entering in the exam room. You cannot touch your phone during the entire duration of the exam.
  • During the exam, you have with you only your two pens, your sheet with handwritten notes and your University Id. All the other objects are in your backpack.
  • At the beginning of the exam, I will distribute the questions. You will write your answers in the sheets of paper where the questions are printed. If you need additional paper to write your answer or your computations, I will give it to you. You cannot use your own paper.
  • When you receive the questions, write your name and Columbia Id on the first page. Don't turn the pages until I finish to distribute the questions to everybody.
  • It will not be possible to leave the room for using the restrooms in the first and in the last 20 minutes of the exam. In the middle part of the exam, it will be possible to use the restrooms, but please ask for permission to leave, and wait for your turn, because there can be only one student out at a time.

Grading

Assignments 10%, midterms 25%, final 40%.