Day and Time: TR 11:40 am - 12:55 pm
Location: 417 Mathematics
Instructor: Pak-Hin Lee
Email: phlee "at" math.columbia.edu
Office Hours Location: 622 Mathematics
Office Hours: Wednesdays 4:30 pm to 6:30 pm
Teaching Assistants: Abhiram Gaddam (UNI: ag3651), Jonnathan Baquero (UNI: jeb2260)
Help Room: 502 Milstein
Help Room Hours:
Textbook: James Stewart, Calculus: Early Transcendentals, 8th Edition
(More information about the textbook is available here. Please make sure you have access to the corrrect edition when working on the homework problems.)
WebAssign: The class key for this section is columbia 7726 4963.
(More information about WebAssign is available here.)
Course Description: Techniques and applications of integration. Differential equations. Parametric equations. Infinite sequences and series. Taylor's theorem. (Chapters 6 to 11 of Stewart.)
Prerequisites: Calculus I. (Chapters 1 to 5 of Stewart.)
Important Dates: For more details, please refer to the academic calendar.
Homework: There will be weekly homework consisting of a WebAssign component and a written problem set (15% each), due generally every Thursday at 1 pm.
Examinations: There will be two midterms (20% each) and one final (30%) held in class. The topics to be covered in each exam will be announced later. The use of books, notes, cell phones, calculators, or other electronic devices is not permitted in any of the exams. If you have a conflict with any of the exam dates, you must contact me at least one week in advance for alternative arrangements. In case of medical or family emergency, you must contact me as soon as possible and provide a note from your doctor or dean.
Plagiarism: Any work plagiarized from outside sources or between classmates will receive no credit and potentially result in disciplinary actions.
Canvas: All course materials (homework, solutions, etc.) and grades will be posted on Canvas, with links on this webpage. Important announcements will also be sent out via Canvas.
Help Room: The Help Room is open 10 am to 6 pm Mondays through Thursdays, and 10 am to 4 pm on Fridays. The full schedule is available here. Feel free to seek help from any TA's who are on duty.
WebAssign: WebAssign is required in this section. Please refer to the information here. I recommend that you take advantage of the Personal Study Plan for additional practice problems.
Disability Services: In order to receive disability-related academic accommodations, students must first be registered with the Disability Services (DS). More information on the DS registration process is available online here. Registered students must present an accommodation letter to the instructor before exam or other accommodations can be provided. Students who have, or think they may have, a disability are invited to contact DS for a confidential discussion.
Tutoring Services: Information is available here.
The following is subject to change as the course moves along.
Date | Topics | Reading | Homework | |
Lecture 1 | Jan 22 (Tue) | Introduction; Review of integration | §5.1, 5.2 | Homework 1 due on Jan 31 (Thu): WebAssign; §5.3: 61, 78; §5.5: 92, 93 (Solutions) |
Lecture 2 | Jan 24 (Thu) | Review of the Fundamental Theorem of Calculus; The substitution rule | §5.3 - 5.5 | |
Lecture 3 | Jan 29 (Tue) | Integration by parts | §7.1 | Homework 2 due on Feb 7 (Thu): WebAssign; §7.1: 48; §7.2: 20, 31, 50 (Solutions) |
Lecture 4 | Jan 31 (Thu) | Reduction formulae; Trigonometric integrals | §7.1, 7.2, App. D | |
Lecture 5 | Feb 5 (Tue) | Trigonometric integrals; Trigonometric substitution (strategy) | §7.2, 7.3 | Homework 3 due on Feb 14 (Thu): WebAssign; §7.3: 18, 36 (no need to graph); §7.4: 21, 74 (Solutions) |
Lecture 6 | Feb 7 (Thu) | Trigonometric substitution (examples); Introduction to partial fractions | §7.3, 7.4 | |
Lecture 7 | Feb 12 (Tue) | Integration of rational functions by partial fractions (linear factors) | §7.4, Notes | |
Lecture 8 | Feb 14 (Thu) | Improper integrals | §7.8 | Homework 4 due on Feb 26 (Tue): WebAssign; §7.4: 35; §7.8: 52, 56, 57, 61 (Solutions) |
Lecture 9 | Feb 19 (Tue) | Improper integrals; Review | §7.8, 7.5 | |
Lecture 10 | Feb 21 (Thu) | Midterm Exam 1 (Solutions; Statistics) | Announcement; Practice Exam and Solutions | |
Lecture 11 | Feb 26 (Tue) | Sequences | §11.1 | Homework 5 (with hint) due on Mar 7 (Thu): WebAssign; §11.1: 52, 69, 79, 80 (Solutions) |
Lecture 12 | Feb 28 (Thu) | Sequences | §11.1 | |
Lecture 13 | Mar 5 (Tue) | Series | §11.2 | Homework 6 (with hint) due on Mar 15 (Fri): WebAssign; §11.2: 48, 75; §11.3: 32, 40 (Solutions) |
Lecture 14 | Mar 7 (Thu) | Series | §11.2 | |
Lecture 15 | Mar 12 (Tue) | Integral test; Statement of comparison test | §11.3, 11.4 | |
Lecture 16 | Mar 14 (Thu) | Comparison tests; Alternating series | §11.4, 11.5 | Homework 7 (with special policy and hint) due on Apr 2 (Tue): WebAssign; §11.4: 44; §11.5: 32; §11.6: 38, 40 (Solutions) |
No class | Mar 19 (Tue) | Spring Recess | ||
Mar 21 (Thu) | ||||
Lecture 17 | Mar 26 (Tue) | Absolute convergence; Ratio and root tests (covered by Yihang Zhu) | §11.6 | |
Lecture 18 | Mar 28 (Thu) | Power series (covered by Yihang Zhu) | §11.8 | Homework 8 (with hint) due on Apr 9 (Tue): WebAssign; §11.8: 22, 31, 37; §11.9: 42(b) (Solutions) |
Lecture 19 | Apr 2 (Tue) | Functions as power series; Introduction to Taylor series | §11.9, 11.10 | |
Lecture 20 | Apr 4 (Thu) | Taylor and Maclaurin series | §11.10 | Homework 9 due on Apr 18 (Thu): WebAssign; §11.10: 80, 82; Review (P.785): 38, 39 (Solutions) |
Lecture 21 | Apr 9 (Tue) | Review; Strategy for testing series | §11.7 | |
Lecture 22 | Apr 11 (Thu) | Midterm Exam 2 (Solutions; Statistics) | Announcement; Practice Exam and Solutions | |
Lecture 23 | Apr 16 (Tue) | Areas between curves; Volumes | §6.1, 6.2 | Homework 10 (with hint) due on Apr 25 (Thu): WebAssign; §6.2: 63, 72; §6.3: 48(b) (Solutions) |
Lecture 24 | Apr 18 (Thu) | Volumes by disks and washers; Volumes by cylindrical shells (introduction) | §6.2, 6.3 | |
Lecture 25 | Apr 23 (Tue) | Volumes by cylindrical shells | §6.3 | |
Lecture 26 | Apr 25 (Thu) | Parametric curves; Tangents of parametric curves | §10.1, 10.2 | Homework 11 (with instructions and hint) due on May 3 (Fri): WebAssign; see attachment on Canvas (Solutions) |
Lecture 27 | Apr 30 (Tue) | Calculus with parametric curves (arc lengths and surface areas); Introduction to differential equations | §10.2, 9.1 | |
Lecture 28 | May 2 (Thu) | Separable equations; Linear equations | §9.3, 9.5 | Homework 12 (with hint) due on May 10 (Fri): WebAssign; §9.4: 22 (except part (c)); §9.5: 26 (Solutions) |
May 9 (Thu) | Review | |||
May 16 (Thu) | Final Exam (4:10 pm - 7:00 pm) | Announcement; Practice Exam and Solutions |
Last updated: May 11, 2019.
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