Instructor: Nathan Chen Office: 609
Lecture 1 (Call number 10630): Mon/Wed 11:40am-12:55pm
Lecture 2 (Call number 10631): Mon/Wed 1:10am-2:25pm
Office hours: Monday 4:30-5:30pm ET and Friday 10-11am ET.
Email: nathanchen@math.columbia.edu
Textbook: OpenStax, Calculus Volume 1 (nearly identical to James Stewart, Calculus: Early Transcendentals). Available online as a pdf: https://openstax.org/details/books/calculus-volume-1
Here is the syllabus.
TAs: Tuan, Saloni, Amal, Ella, Chuwen.
TA office hours are in 502 Milstein Center (Barnard campus). This link has a schedule with their hours.
First class: September 6, 2023. Last class: December 11, 2023. Notes.
Lecture 1: 9/6/2023. Review of functions, range/domain. Prerequisites: Law of exponents, radicals, equations, graphs. Sections 1.1 and 1.2.
Lecture 2: 9/11/2023. Trigonometric functions, inverse functions, 1-1. Prerequisites: evaluating the unit circle, radians vs degrees. Sections 1.3 and 1.4.
Lecture 3: 9/13/2023. Inverse functions, inverse trig, 1-1. Prerequisites: evaluating the unit circle, radians vs degrees. Sections 1.3 and 1.4.
Lecture 4: 9/18/2023. Exponential and logarithm functions (skip hyperbolic functions). Sections 1.4 and 1.5.
Lecture 5: 9/20/2023. Motivation for limits: tangent problem and derivatives, area problem and integrals. Limits of functions. Sections 2.1 and 2.2.
Lecture 6: 9/25/2023. Limit laws, one-sided limits, squeeze theorem. Section 2.3.
Lecture 7: 9/27/2023. Continuity, discontinuities, asymptotes, intermediate value theorem. Section 2.4.
Lecture 8: 10/2/2023. Definition of a derivative. Sections 3.1, 3.2.
Lecture 9: 10/4/2023. Review. PDF of some practice problems.
Midterm 1: 10/9/2023. Solutions
Lecture 10: 10/11/2023. Derivative as a function and differentiation rules (sum/difference, product, quotient). Section 3.3.
Lecture 11: 10/16/2023. Derivatives as rates of change, derivatives of trig functions. Sections 3.4, 3.5.
Lecture 12: 10/18/2023. The chain rule and implicit differentiation (especially for inverse trig functions). Sections 3.6, 3.8.
Lecture 13: 10/23/2023. Derivatives of exponential and logarithm functions. Section 3.9.
Lecture 14: 10/25/2023. Related rates. Section 4.1.
Lecture 15: 10/30/2023. Maxima/minima, critical points, mean value theorem. Sections 4.3, 4.4.
Lecture 16: 11/1/2023. Second derivatives, concavity, inflection points. Section 4.5.
No lecture: 11/6/2023. Academic holiday.
Lecture 18: 11/08/2023. Optimization. Section 4.7.
SATURDAY REVIEW. 11/11/2023 at 11am ET. Location: Uris Hall 142. Here is a PDF of some practice problems.
Midterm 2: 11/13/2023. Solutions
Lecture 19: 11/15/2023. Limits at infinity and asymptotes. Sections 4.6.
Lecture 20: 11/20/2023. L'Hôpital's Rule, antiderivatives. Sections 4.8 and 4.9.
Thanksgiving: 11/22/2023. No lecture.
Lecture 21: 11/27/2023. Approximating area, definite integrals. Sections 5.1, 5.2.
Lecture 22: 11/29/2023. Fundamental theorem of calculus. Sections 5.3 and 5.4.
Lecture 23: 12/4/2023. Integration using substitution. Sections 5.5 and 5.6.
Lecture 24: 12/6/2023. Area between curves. Section 6.1.
Lecture 25: 12/11/2023. Review. Here is a PDF of some practice problems.
Lecture 26: 12/18/2023. Final exam.
Homework exercises will be published online every Wednesday night and the solutions will be due 6 days later. More precisely, the deadline for submitting homework is Wednesday early morning at 4am ET even though the listed dates are on Tuesdays. Homework solutions are here.
Homework 0. (DO NOT TURN IN) Section 1.1: 9, 10, 16, 20, 21, 47 (try to graph 16, 20, 21). Section 1.2: 64, 66, 70, 72, 86 (try plugging in x = 1), 91. Section 1.3: 115, 117, 119, 124, 127.
Homework 1. Due 9/19/2023. PDF
Homework 2. Due 9/26/2023. PDF
Homework 3. Due 10/3/2023. PDF
Homework 4. Due 10/17/2023. PDF
Homework 5. Due 10/24/2023. PDF
Homework 6. Due 11/1/2023. PDF
Homework 7. Due 11/7/2023. PDF
Homework 8. Due 11/28/2023. PDF
Homework 9. Due 12/8/2023. PDF