We'll cover the theory and applications of differential calculus and get a glimpse into the world of integral calculus and the fundamental theorem of calculus, an amazing result that connects differential and integral calculus in a surprising and very useful way.
You can contact me by email at rizzardo@math.columbia.edu .
My office is in math 408.
Office hours will be on Monday, 5:30 to 6:30 (room 528) and on Thursday, 5 to 6 (room tba-meet in 408).
If you cannot come to office hours you can write me an email and schedule an appointment. For help on your homework questions you can go to the Help room .
The TA for this class is Nikitha Yereddi, ny2137@columbia.edu. Her help room hours are on Thursday, 10am-12pm.
Here you can find a list of the students enrolled in this class .
Monday and Wednesday, 4:10-5:25 pm
Room 417
James Stewart, Calculus (Early Transcendentals), 6th edition published by Thomson Brooks/Cole.
It is available at the Columbia bookstore. It is also available online, probably at lower prices. Many of Stewart's other books look similar, so check carefully that you have chosen the correct text if you order online. This class will cover chapters 1 through 6. There is a table below that shows which sections in the text correspond to each lecture. You are encouraged to read the relevant sections before coming to class.
Workload: There is much to be done in a relatively short period of time, so please try to keep up. Please ask questions if you have them! Set aside enough time in your schedule to keep up with your reading, studying, and homework.
Homework: I will assign homework during most class meetings. Homework is due on Tuesday by 4pm in the drop-off box on the fourth floor. I do not accept late homework, but I will drop your lowest homework score.
To receive full credit for a solution, it is not enough for you to simply write down the correct answer. You must also show all relevant work in an organized fashion. Include explanatory words or phrases if it is not completely obvious how one step leads to the next, so that any other calculus student would be able to read your solution and understand how you obtained your answer. Circle or otherwise clearly indicate your final answer, and include units (meters, seconds, square feet, etc.), if applicable. Please staple your homework!!
You can come to office hours for help or just ask questions after class. Additional help is available every day, beginning September 14, at the help room in room 333 of Milbank Hall on the Barnard campus. Here is the schedule .
Quizzes: Often at the beginning of class there will be a brief (5 to 10 minute) quiz covering material from previous class meetings. If you are late and you miss a quiz, you will receive a zero for that quiz. The quizzes are designed to give you immediate feedback about your understanding of the crucial ideas from the course. If you attend class, pay attention, ask questions, and are diligent about reviewing your notes, reading the book, starting your homework assignments early, and coming to me or to the help room when you need help, you will probably do well on the quizzes. If you find yourself struggling on the quizzes, it's a sign that you need to change your study habits immediately. I do not give makeup quizzes for any reason, but I will drop your lowest quiz score.
Webwork: This is an online homework system to supplement written homework. The advantage of Webwork is that you will get immediate feedback on your answers and so it's a great tool to practice your skills. There is no penalty for the number of times you get an answer wrong before getting the right answer (but you'll find guessing is much more time-consuming that actually solving the problems). You will receive an email with all of the instructions on how to use it and the login information. For technical problems with Webwork, please contact the webwork T.A., Thomas Peters tpeters@math.columbia.edu . I will add a 10% to your Webwork score when computing your grade (e.g. 90% becomes 100%, 80% becomes 90%, 100% stays 100%).
Attention for Barnard students: the Webwork emails get sent to your @columbia.edu email.
Grading Scheme: Grades will be determined approximately as follows:
| Midterm exams | 20% each |
| Final Exam | 30% |
| Quizzes | 5% |
| Webwork | 5% |
| Homework | 20% |
| Day | Sections | Material | HW | Recommended (not to be handed in) | Due date |
|---|---|---|---|---|---|
| 9/9 | Chapter 1 | Review of functions | 1.1 #5,6,20,21,28,38,44,68 1.2 #4,7,16 | Take the diagnostic tests at the beginning of the book | September 17 Solutions |
| 9/14 | Chapter 1 | More review | 1.1 #23 1.3 #35,42,46 1.5 #13,15,25(except for (d)) 1.6 #22,53,71 | 1.3 #17,31-35,37,41,47 1.5 #26 1.6 #3-11,17,59,60,61 |
September 22 Solutions |
| 9/16 | 2.1,2.2 | Limits of functions | 1.6 #35,38 2.1 #3 2.2 #7,12,14 | 2.2 #1-3,13,15 | |
| 9/21 | 2.3 | Limit laws | 2.2 #8 2.3 #6,10,22,24,37,38,40,41 | 2.3 pick a few(or all of them!) among 3-9 and 11-30, plus 36,42,45,58 | September 29 Solutions |
| 9/23 | 2.4 | The epsilon-delta definition of limit | 2.4 #3,16,26,38 | 2.4 #1,2,4,15,19,20 | |
| 9/28 | 2.5 | Continuity | 2.5 #12,14,37,41,42 | 2.5 #17,18,21,36,38 | October 6 Solutions |
| 9/30 | 2.6,2.7,2.8 | Limits at infinity, Rates of change, the derivative Quiz 1!! and Solutions | 2.5 #47,48 2.6 #18,22,26,28,35 | 2.6 #15-36,39-44,49-52,56 | |
| 10/5 | 3.1 | Derivatives of polynomials and exponentials | 2.8 #3,20,21,36 3.1 #20,28,30,34,49,52 | 2.8 #19-29,35-38,50 3.1 #3-31,33,45,46,51-56,71,75 Check this out: e, as we defined it today, is an irrational number! These guys computed the first two million digits of it. A fun (but hard) exercise on intermediate value theorem |
October 13 Solutions |
| 10/7 | Midterm 1 solutions | Study suggestions | Sample questions Solutions to Sample questions Solutions to the chapter 2 review exercises |
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| 10/12 | 3.2,3.3 | The product and quotient rules, Trigonometric functions | 3.2 #5,24,28,44 3.3 #10,12,16,34,44,48 |
3.2 #1-32,49,50 3.3 #1-24,30,32-34,39-48 |
October 20 Solutions |
| 10/14 | 3.4,3.5 | The Chain rule Implicit differentiation | 3.4 #10,12,31,40,44 3.5 #29,30,40,46,52,66 (for 66: notice that (12,3) is not a point on the curve) | 3.4 #1-54,59-64,67-72,75,76,94 3.5 #5-20,25-30,32(a) and (b),33-36,39-42,45-54,65 From the New York times: Key House Panel Votes to Regulate Derivatives |
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| 10/19 | 3.6,3.7 | Logarithmic functions Applications | 3.6 #4,24,39,42,50 3.7 #8,9 3.8 #3 | 3.6 #2-34,37-50 3.7 #21 3.8 #11 (just because it's cool) it doesn't hurt to practice some more for the chain rule... |
October 27 Solutions |
| 10/21 | 3.9,3.10 | Related rates Linear approximation Quiz 2: Solutions | 3.8 #18(a) 3.9 #4,12,16,22 | 3.9 #7,8,11-14,23,30,38,44 | |
| 10/26 | 4.4 | Linear approximation L'Hospital's Rule | 3.10 #6 (no need to graph, just find the linear approximation),24,44 (use linear approx in each case) 4.4 #7,10,26,40,47,50 | 3.10 #1-5,23-28,32(a),43 4.4 practice on all of 5-52 until you feel confident plus 69,70,71 |
November 5 4pm Solutions Solution for the infinity^0 exercise |
| 10/28 | 4.1 | L'Hospital's rule: indeterminate powers Extrema of functions Quiz 3: Solutions | 4.4 #54,60,61 4.1 #8,14,34,36 Plus don't forget the following: Justify, as we did in class, that infinity^0 is an indeterminate form 1.6 #33,34,36,39,46 | 4.4 #53-64 4.1 #7-13,29-44 |
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| 11/4 | 4.2 | Mean Value Theorem | 4.1 #50,60,62 4.2 #6,18,19,20 chapter 3-review: true-false (explain why!) 1-12 3.9 #5,17,19 3.5 #14,17,26 Study well the theorems we saw in class today (Fermat's, Rolle, Mean Value theorem) and make sure you understand them. Feedback form (better late than never) | 4.1 #47-62,76,78 4.2 #1-4,5,17-22,36(hard) |
November 10 Solutions |
| 11/9 | 4.3,4.5 | Curve Sketching. Quiz 4: Solutions In the discussion of feedback forms, we decided the following: -I will try to improve my handwriting -I will assign a few extra odd review problems from old sections | 4.2 #12,24 4.3 #10,14,24,32,40,42 3.4 #27,31,39,41 | 4.2 #23,25 4.3 #7,8,9-18,25-30,33-44,69-70(hard) |
November 17 Solutions |
| 11/11 | 4.5 | Curve Sketching, review | 4.5 #12,14,26,42,50 4.4 #31,37,49,53 | 4.5 practice on 1-52 until you feel confident; look at the examples in the book! |
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| 11/16 | 4.7 | Optimization Problems | 4.7 #14,19,24,32,44,46,72 (I find this last one a little disgusting but maybe our pre-med students will be interested) | 4.7 #5,6,11,12,17,19,21,33,36,50,63(that's harder!but cool!) | November 24 Solutions |
| 11/18 | Solutions | Study suggestions |
Sample questions Solutions to the sample questions |
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| 11/23 | 5.1,5.2 | Areas, the definite integral | 5.1 #16,20,22 5.2 #18,23,34,48 4.4 #25,53,61 | 5.1 #1-5,15,21 5.2 #1,17,19,34,37,38,40,41 |
December 1 Solutions |
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| 11/30 | 5.3 | The fundamental theorem of Calculus | 5.2#36,38,50 5.3 #14,18,53,54 | 5.2 #33-40 5.3 #7-18,53-56 |
December 8 Solutions |
| 12/2 | 5.3,4.9 | The Fundamental Theorem of Calculus, Antiderivatives | 4.9 #12,18,39,44,50,52,73 5.3 #22,36,40,42(break the integral in two parts),63 5.4 #6,12,58 | 4.9 #1-20,23-46,49,75,76 5.3 practice on integrals! #19-42,58,72,74 |
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| 12/4 | 5.5 | Make-up class Room 417 The substitution rule This is a very important method to compute integrals, so don't miss this class!! | 5.5 #14,24,30,42,54,60,66,67,82 | 5.5 practice on substitutions as much as you can on #1-70, plus #75,78,81 | |
| 12/7 | 6.1 | Areas between curves | chapter 5-review true-false 1-15 (explain why!) and #17,29,32,38,61,64 6.1 #18,19,20,32,48,49 chapter 3-review exercises #31,37,57,61,75 (if the tangent line has slope m the normal line has slope -1/m) | 6.1 #1-4,5-28,45,53 | December 15 Solutions |
| 12/9 | 6.2,6.3 | Volumes Quiz 5: Solutions | 6.2 #14,17,20,26,34,44,52,54,56 6.3 #10,16,24,25,39 | 6.2 #1-18,19-30,31-36,50,53 6.3 #3-7,9-14,21-26,37-42 Some practice on optimization |
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| 12/14 | everything | Review Quiz 6: Solutions | --- | Study suggestions Sample questions Solution to the sample questions a mistake has been corrected in exercise 5. also, the area of the trapezoid was supposed to be maximized and not minimized. let me know if you find other mistakes, thank you. | - |
| 12/21 | 4:10pm to 7pm in room 417 |
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