Location 407 Mathematics Building
Office Hours T 4–4:30 pm, Th 2–2:30 pm and 4–4:30 pm in 408 Math, or by appointment
E-mail cmmwong [at] math [dot] university-name [dot] edu
Teaching Assistant Rui Ding. Help Room Hours: W 10 am–12 pm in 333 Milbank
Textbook Calculus: Early Transcendentals, 8th edition by James Stewart, with WebAssign. The cheapest option to purchase the text, for $121 (multiple-term access) or $82 (single-term access) is from the WebAssign website, after creating an account and enrolling in the class there. If you would like to read a physical book, a package consisting of a loose-leaf book and access to WebAssign is also available from the publisher for $142.95.
Prerequisites No formal prerequisites; an understanding of pre-calculus will be assumed.
Main topics covered Limits of functions. Derivatives, differentiation rules, and applications of differention. Integrals and applications.
Grading The final grade will be computed from the following components:
- Homework – 30%;
- Mid-term exam 1 – 20%;
- Mid-term exam 2 – 20%;
- Final exam – 30%.
Homework This section requires students to use WebAssign, an on-line system integrated with the course textbook. You must purchase the access to the WebAssign system. See "textbook" above. (Some other sections do not require the use of WebAssign.) Late homework will not be accepted, but the two lowest scores will be dropped.
Students with disabilities 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 at www.health.columbia.edu/ods. 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.
Missed exams If you have a conflict with any of the exam dates, you must contact me ahead of time so we can make arrangements. (At least a week ahead is preferable.) If you are unable to take the exam because of a medical problem, you must go to the health center and get a note from them – and contact me as soon as you can.
Getting help Here are some places where you can get help.
- Office hours. My office hours are a great opportunity for you to clear up concepts that you may not have perfectly understood. Do use them!
- Help room. The mathematics help room, at Milbank 333, is open from 10 am to 10 pm, Monday through Thursday, and between 10 am and 4 pm on Friday. The TAs there will be able to help you with any problem you might have, especially with computation.
- Tutoring. Many graduate students offer tutoring services on a private, one-on-one basis. If you are interested, send an e-mail to tutoring20145@math.columbia.edu. In addition, the individual schools (e.g. Columbia College, Barnard, School of General Studies) also offer tutoring services. For more information, see the official webpage.
Other advice You should
- Read the material to be covered before each class. Make notes of things that confuse you.
- Ask a lot of questions during class. Active participation will help ensure you learn the material well. Almost always, students ask too few questions and allow things to go over their head for fear of looking silly or disrupting the class. Don't! If you are asking too many questions (or the wrong ones), I will let you know, but that is highly unlikely.
- Review the material covered on the same day after each class. This will help you retain whatever you have learned during class in your long-term memory.
- Start attempting the homework early. All too often, students rush into the help room a few hours before the problem set is due, hoping that the TAs will do their homework for them. Do not let this happen! The WebAssign problems are designed to give you an opportunity to practise; even if somebody does all the problems for you, you will not do well on the exams.
- Get help as soon as you need it. Do not wait. As soon as you are confused about something, come to office hours or go to the help room within a day or two. If you wait, you will be lost.
- Practise, practise, practise! This is the one and only one way to learn calculus well. Keep a list of hard problems to practise for your exams.
Schedule The following schedule is tentative and may be modified as the course progresses. Please read the relevant textbook sections before the lecture.
| Date | Material | Textbook | Announcements |
|---|---|---|---|
| 01/19 | Introduction. Review of functions. Trigonometric functions. New functions from old. | §1.1–1.3 | |
| 01/21 | Inverse functions. Exponential and logarithmic functions. | §1.4, 1.5 | |
| 01/26 | Informal definition of limits. | §2.1, 2.2 | |
| 01/28 | Limit laws. Squeeze theorem. | §2.3 | Read §2.4 also. 01/29: Last day of add/drop period. |
| 02/02 | Continuity. Asymptotes. | §2.5, 2.6 | |
| 02/04 | Definition of derivatives. Derivative as a function. | §2.7, 2.8 | |
| 02/09 | Derivatives of polynomials and exponential functions. | §3.1 | |
| 02/11 | Product and quotient rules. | §3.2 | |
| 02/16 | Derivatives of trigonometric functions. | §3.3 | Mid-Term Exam 1 will cover §1.1–1.5, 2.1–2.3, 2.5–2.8, 3.1–3.3. |
| 02/18 | Mid-Term Exam 1 |
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| 02/23 | Chain rule. | §3.4 | Last day to drop class. |
| 02/25 | Implicit differentiation. | §3.5 | |
| 03/01 | Derivatives of logarithmic functions. Applications. | §3.6–3.8 | |
| 03/03 | Related rates. | §3.9 | |
| 03/08 | Linear approximation. | §3.10 | |
| 03/10 | L'Hospital's rule. | §4.4 | |
| 03/15 | Spring Recess |
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| 03/17 | Spring Recess |
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| 03/22 | Maximum and minimum values. Mean value theorem. | §4.1, 4.2 | |
| 03/24 | Second derivatives. Convexity. Second derivative test. | §4.3 | Last day to pass/fail. |
| 03/29 | Curve sketching. | §4.5 | Mid-Term Exam 2 will cover §3.4–3.10, 4,1–4.5. |
| 03/31 | Mid-Term Exam 2 |
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| 04/05 | Optimization problems. | §4.7 | |
| 04/07 | Newton's method. | §4.8 | |
| 04/12 | Antiderivatives. | §4.9 | |
| 04/14 | Areas and distances. The definite integral. | §5.1, 5.2 | |
| 04/19 | The fundamental theorem of calculus. Indefinite integrals. The net change theorem. | §5.3, 5.4 | |
| 04/21 | The substitution rule. | §5.5 | |
| 04/26 | Areas between curves. Average value of a function. | §6.1, 6.5 | |
| 04/28 | Review session. | ||