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Course

Calculus I - Math UN1101 - Section 001.
Fall 2021.
Columbia University.

Lectures

Classroom: Room 203 Mathematics.
Mo, We 10:10am-11:25am.

Instructor

Name: Daniele Alessandrini.
Contact: daniele.alessandrini@gmail.com.
Office: 624 Mathematics.

Office hours: Tentative schedule: Mo 11:30am-12:30pm Room 507 Mathematics, We 9am-10am Room 622 Mathematics.

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. You can ask them questions in Ed Discussion or by email, and they serve in the Help Room at 502 Milstein Center on the Barnard Campus, where you can meet them to ask your questions. You can find their email addresses on Courseworks at the Syllabus page.

Name Help Room Schedule
Baiqing Zhu Wed 3-6pm
Yuanbo Li Tue 9-10am, Fr 9-10am
Hreedi Dev Tue 3-4pm, Thu 12-1pm

Syllabus

The Syllabus for this course.

Content

Required text

Calculus: Early Transcendentals, 9th edition, by James Stewart (CENAGE Learning). The book is available at the Columbia bookstore. If you have the 8th edition or an earlier edition that is probably fine too.

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).

  1. Functions (Chapter 1).
    • Polynomials and rational functions.
    • Roots.
    • Exponential and logarithm.
    • Trigonometric functions.
  2. Limits (Chapter 2).
    • Computation of limits.
    • Continuous functions.
    • Increasing and decreasing functions.
  3. Derivatives.
    • Introduction to derivatives (Chapter 2).
    • Differentiation rules (Chapter 3).
    • Maxima and minima (Chapter 4).
    • Concavity (Chapter 4).
  4. Integrals.
    • Computation of integrals (Chapter 5).
    • Applications of integrals (Chapter 6).

Lectures

Date No Topic Textbook Reference
21/09/13 01 Introduction; Prerequisites: Real numbers and radicals. n/a
21/09/15 02 Prerequisites: Equations and inequalities. n/a
21/09/20 03 Prerequisites: Simultaneous inequalities and Equations with parameters. n/a
21/09/22 04 Functions, Graphs, Range. Sec. 1.1.
21/09/27 05 Increasing, decreasing and 1-1 functions. Inverse fuctions. Section 1.1, 1.5.
21/09/29 06 Equations and inverse fuctions. Root functions. Section 1.2, 1.5.
21/10/04 07 Change of variables. Exponential and logarithm. Section 1.4, 1.5.
21/10/06 First Midterm. n/a
21/10/11 08 Trigonometric functions and equations. Appendix D.
21/10/13 09 Trigonometric equations. Introduction to Limits. Appendix D. Section 2.2, 2.6.
21/10/18 10 Limit laws. Section 2.3, 2.6.
21/10/20 11 Limit laws. Section 2.3, 2.6.
21/10/25 12 Continuous functions. Section 2.5.
21/10/27 13 Intermediate Value Theorem. Introduction to Derivatives. Section 2.5, 2.7.
21/11/01 Holiday. n/a
21/11/03 14 Derivatives, Derivatives of rational functions, Graphing functions. Section 2.8, 3.1, 3.2, 4.3.
21/11/08 15 Differentiation rules. Section 3.1, 3.2, 3.3, 3.4, 3.6.
21/11/10 16 Differentiable functions, graphing functions. Section 4.5.
21/11/15 17 Absolute and local maxima and minima. Section 4.1
21/11/17 Second Midterm. n/a
21/11/22 18 L'Hospital Rule, Second derivative, concavity. Section 4.3, 4.4.
21/11/24 Holiday. n/a
21/11/29 19 Integrals. The fundamental theorem of calculus. Section 5.3.
21/12/01 20 Integrals. Substitution Rule. Section 5.3, 5.5.
21/12/06 21 Substitution and Integration by parts. Area between curves. Section 5.5, 7.1, 6.1.
21/12/08 22 Area between curves. Computation of volumes. Section 6.1, 6.2.
21/12/13 23 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.

You can also consider the book Precalculus, Mathematics for calculus, by Stewart, Redlin, Watson. This book is not required, and not important for most students. It is useful only if you have gaps in your background knowledge.

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

Homework

Homework sheets

The homework will be published online in form of homework sheets every Wednesday night. You have 6 days time to submit the written solutions.

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Date Number Topic Submit by Grader Answers
21/09/15 01 Prerequisites 21/09/21 Baiqing Answers 1
21/09/22 02 Equations and Functions 21/09/28 Yuanbo Answers 2
21/09/29 03 Inverse Function 21/10/05 Hreedi Answers 3
21/10/06 04 Exponential functions 21/10/12 Yuanbo Answers 4
20/10/13 05 Trigonometric functions and Limits 21/10/19 Baiqing Answers 5
21/10/20 06 Limits 21/10/26 Hreedi Answers 6
21/10/27 07 Continuous functions 21/11/02 Baiqing Answers 7
21/11/03 08 Derivatives 21/11/09 Hreedi Answers 8
21/11/10 09 Graphing functions 21/11/16 Yuanbo Answers 9
21/11/17 10 Maxima and Minima 21/11/23 Hreedi Answers 10
21/11/24 11 Concavity 21/11/30 Baiqing Answers 11
21/12/01 12 Integrals 21/12/07 Yuanbo Answers 12
21/12/08 13 Integrals and applications not graded Answers 13
21/12/13 Mock Exam not graded Answers Mock Exam

Submission

Written assignments will be due in the night between Tuesday and Wednesday, more precisely on Wednesday early morning at 5:00am. Submission is online, via Courseworks, at the Gradescope page.

Late hand in

We will accept late homework, but we deduct 10% of the points for every day of lateness.

Exams

Midterm exams

There will be midterm exams on Wednesday October 6th and on Wednesday November 17, during the usual class times.

Final exam

Final exam: Wednesday December 22nd, 9am–Noon. The exam will be online. Please, check the rules for on-line exams.

Exam dates

You must plan to take the midterm and final exams at the scheduled time, so please make your plans accordingly. Besides students with disabilities having prior arrangements with DS or CARDS, the only exceptions will be for those with an incapacitating illness, a serious family emergency, or situations of comparable gravity. In this case you will need to ask your advising dean to send me a note. If your advising dean approves your reason for skipping a midterm, I will use the grade of your final exam as grade for your midterm. For the final exam, we will organize a make-up exam in January, at the beginning of the Spring semester. Incompletes can be granted only by your advising dean and only in the circumstances mentioned above.

Academic dishonesty

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.

Grading

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