Math 109, Calculus II (Math, Phys. Sci., and Eng.), Spring 2017
Instructor: Xudong Zheng
Office: 313 Krieger Hall
Lectures: MWF 10:00 - 10:50 Bloomberg 272
Office Hours: 9 - 10 am on Tuesdays and Thursdays
Textbook: Single Variable Calculus: Early Transcendentals, 8th Ed. James Stewart
- May 14. Below is how the letter grades were designated.
A+: score of 90 and above
A: 83 to 90 (top 35% of the class)
A-: 80 to 83 (top 50% of the class)
B+: 75 to 80
B: 70 to 75
B-: 65 to 70 (top 89% of the class)
C+: 60 to 65
C: 55 to 60
C-: 50 to 55 (top 100% of the class)
- May 8. The keys to HW 10 are available.
- May 7. The keys to the practice final, keys and rubrics for Mid-term 2 are available.
- May 2. The final exam of the previous semester is available for practice under "Handouts".
If you are seeking for extra time or there is scheduling conflict for the final exam, please inform me as soon as possible.
The regular time final exam will be on Wednesday, May 10th from 9 am - 12 pm at Bloomberg 272.
I plan to spend the remaining two lectures to review via examples. Please bring your questions as well.
- Apr. 21. HW 10 is available.
- Apr. 20. In Mid-term 2, I graded problem 2, and here is my idea. First of all, in the middle of the exam I wrote on the board that it would not be ok if you use a p-series argument. This is because the convergence of a p-series was concluded using the improper integral, and you will be running into a circular argument. So I basically gave 5 points for free if by any chance I see a "lim" symbol on your work indicating that you are doing an improper ingegral. The most common mistake I found: the improper integral has to be done differently depending whether p is equal to 1 or not, because if p = 1, the anti-derivative does not look like of the same form as when p not equal to 1. Hence the case p = 1 has to be argued separately. If you missed the p = 1 case (even if your conclusion is correct), you got at most 15 points. For the best solution, please see Example 1 and 4 combined from Section 7.8 of the textbook.
- Apr. 12. HW 9 and Practice Exam 2 (under Handouts) are available. There is also a handout on limits of algebraic functions.
- 1. Christopher Kauffman T 3:00 - 3:50 (email@example.com) Maryland 202 (Office Hour: Monday 5-6 pm)
- 2. Daniel Fuentes-Keuthan T 4:30 - 5:20 (firstname.lastname@example.org) Maryland 202 (Office Hour: Tuesday 3-4 pm)
- 3. Apurv Nakade Th 1:30 - 2:20 (email@example.com) Croft Hall G02 (Office Hour: Wednesday 3-4 pm)
- 4. Apurv Nakade Th 3:00 - 3:50 (firstname.lastname@example.org) Maryland 202
- 5. Christopher Kauffman T 1:30 - 2:20 (email@example.com) Bloomberg 272
Midterm 1: March 3, Friday. Covering to 10.2.
Midterm 2: April 19, Wednesday. Covering from Midterm 1 to 11.7.
Final Exam: May 10, Wednesday, 9-12 noon.
Brief description: The goal of MATH 109 is to continue the study of calculus on the real line, which you started in Calculus I, with a focus on integration, the basics of differential equations, as well as sequences and series.
This course covers chapters 7, 9-11 in the textbook.
The following components contribute to your total grades. Grades will be regularly updated in Blackboard.
Missed exams: There will be no make-ups on exams.
- Homework assignments 4% each, 40% total
- Mid-term exams 10% each, 20% total
- Final exam 40%
Lecture Notes: Hand-written notes will be posted here after each lecture.
- January 30, Integration by parts
- February 1 and 3, Integrals of trigonometric functions I
- February 6, Integrals of trigonometric functions II
- February 8, Trig substitutions
- February 10, Integrals of rational functions I
- February 13, Integrals of rational functions II
- February 15, Initial value problems and direction fields
- February 17, Separable equations
- February 20, The logistic population growth model
- February 22, Linear equations
- February 24, Parametric curves
- February 27, Parametric curves
- March 6, Polar coordinates
- March 8, Calculus in polar coordinates
- March 13, Improper integrals I, II
- March 15, Sequences I, definition
- March 17 and 27, Sequences II, convergence, definition and criteria
- March 29, Series
- March 31, Series II, integral and comparison tests
- April 3, Series III, limiting comparison
- April 5, Series IV, alternating series
- April 7, Series V, remainder estimations
- April 10, Series VI, absolute convergence, ratio test
- April 12, Series VII, root test
- April 14, Power series I
- April 17, 21, Power series II
- April 24, Representing functions as power series
- April 26, Taylor series I
- April 28, Taylor series II
- May 1, Applications of Taylor series
- Review in the last week
Homework: Homework assignments will be posted on the course website regularly. Check the due dates in the syllabus. You are encouraged to do your homework in groups. You are required, however, to write up your homework on your own. There will be five problems from each homework set to be graded. The grades reflect both your analytical and reasoning skills on the graded problems and the completeness of the entire set. Problems marked with an asterisk are challenging, hence not required (5 graded problems will not include any such). Your TA and I will be more than happy to discuss about those challenging problems.
- How to write up homework solutions. Please see here and here for some examples from Professor Richard Brown's page.
- Always staple your homework in order.
- Assure your full name recognizable on the first page.
- Cut or tear along the perforations of your spiral or ring binded nootbook.
- Homework 1 (due Feb 7 or 9, in recitation.) Key and Rubric
- Homework 2 (due Feb 14 or 16, in recitation.) Key and Rubric
- Homework 3 (due Feb 21 or 23, in recitation.) Key and Rubric
- Homework 4 (due Mar 7 or 9, in recitation.) Key and Rubric
- Homework 5 (due Mar 14 or 16, in recitation.) Key and Rubric
- Homework 6 (due Mar 28 or 30, in recitation.) Key and Rubric
- Homework 7 (due Apr 4 or 6, in recitation.) Key and Rubric
- Homework 8 (due Apr 11 or 13, in recitation.) Key and Rubric
- Homework 9 (due Apr 25 or 27, in recitation.) Key and Rubric
- Homework 10 (due May 2 or 4, in recitation.) Key and Rubric
PILOT Learning: A peer-led team learning program that supports our students in the gateway science courses. PILOT Learning has been supporting students at JHU since 2008 and 97% of students would recommend PILOT to others. Students enrolled in PILOT are placed into groups of classmates and lead by a peer leader who has taken the course before and received an A or better. Each PILOT group meets for 2 hours per week for the entire semester to work on problem-sets that compliment homework problems and concepts that are taught in lecture. The peer leader (PILOT Leader) works as a facilitator who helps guide them through the problem but encourages conversations and collaborations from the group to spearhead the problem-solving.
Help Room: 213 Kreiger Hall. The hours are 9am - 9pm on Monday through Thursday, and 9am - 5pm on Friday. This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course. It is staffed by graduate students and advanced undergraduates.
- WolframAlpha. A thorough online tool for computational and graphic tasks.
- MIT OpenCourseWare. The link here directs to the course "Single Variable Calculus", which together with subsequent courses there provide some comprehensive suppliments to us. Check out the videos of the lectures there.
- Mar. 26. HW 7 is available.
- Mar. 22. I post an example of the precise definition of a limit of a sequence under "Handouts".
- Mar. 17. Happy Spring Break! Having trouble with the precise definition of a limit? You are not alone! If the textbook does not satisfy you, try something like this: The Formal Limit Definition: Getting the Intuition Behind It. Or you can find a lot more online by yourselves!
- Mar. 16. This is a response to some of the comments I saw so far from the survey. This is also the occasion where I clarify my standpoint.
- First of all, about your study strategy. It's not easy to overcome the inertia that mathematics courses would not have reading assignments comparing with sociology, psychology, political science, etc where reading assignments are by default. This might be the case for Calculus I, but no longer for Calculus II onward. Rather, in reality the textbook might be your best friend for your success in this course. This is simply because I can only partially cover what you are supposed to learn for the benefit of the majority of the audience so that I do not crash my lecturing speed. What I anticipated is that you learn much much more from each other and from your own reading through the semester than you learn from me. Eventually mathematics is very much social in nature, in the sense that open discussion between you and me, your friends, and your TA is absolutely necessary. On the other hand, my position, quoting from a senior colleague:" I don't want them to see me as the source of their knowledge. I aspire that they attain some degree of self-reliance, to use the textbook as a valuable and important resource for their learning."
- Second, about the fairness of the exam and the homework. You commented about the grading because you care about your grades. Who don't? The best way to resolve any disputes about "unfair" grading of homework/exam is to talk to your TA or myself directly. On the other hand, I think fairness is a plural notion applying to the entire class. For me to be "fair" means to be consistent towards everyone so that there is no single individual being discriminated against. One can only say being treated unfairly if this person has compared the outcome with peers seeing different results. In that case, I will give the points back to you. That's for sure.
- Third, about your motivation in the subject. Why did you choose this course? You can simply say that this course is required for your major. But unless you want to major in mathematics, have you thought about why the university poses this mandate for you to learn something that you will rarely see again in the rest of your life? Here is my answer. It is only my personal opinion rather a reflection of the school's orientation. To me mathematics is one of the fundamental subjects in human civilization parallel to philosophy, literature, and music. It is such an ancient, sacred, and pure subject. A student's mathematical literacy is an integral part of one's knowledge. You might become a surgeon eventually, but the university still makes philosophy courses available to you. Likewise, mathematics. In that sense, the university expects everyone to know some high level mathematics. However, mathematics is never the popular subject. I would be surprised if a lot of you end up majoring in mathematics. The purpose of this course is not to let you memorize many things, instead is to train your analytical thinking skill. Precision is the goal and the keyword. Choosing your courses is like choosing an instrument to play in an orchestra, and mathematics is never one of those string instruments. Rather, mathematics might be the triangle. Once you pick it up, only through the most rigorous training can you make the tone with the desired absolute clarity. I don't doubt everyone can hit the triangle. But if all you have are ten notes throughout a 50-minute symphony, what a percussionist is required to do is to hit the ten notes at the exact moments where they are supposed to be.
- Fourth, about your interest in the subject. Honestly, calculus is not a very interesting subject. Among more than 25 mathematics courses I took in my undergraduate years calculus probably ranks 23-25 (the bottom three are Calculus I, II, and III). But if you do not know what the Fibonacci sequence/the golden ratio is, have you looked it up? It is fair to say there is no royal road through mathematics. So you wanna play basketball in the NBA? Have you started practicing 1000 3-pointers everyday? Surviving in the NBA is much tougher than getting to the glorious moment of being drafted, according to Steph Curry. Likewise, attending Hopkins.
- Mar. 15. Please review the "precise definition of limit" of a function. We will assume your familiarity of this concept to study the limit of a sequence on Friday.
- Mar. 14. HW 6 is available. A mid-semseter survey is available in Blackboard under "Course Content" on the left column. Your participation to it is very important to me. Thanks!
- Mar. 7. The key and rubric for Mid-term 1 is posted under Handouts. Here is how question 2 graded. Essentially we saw two correct approaches (I am not saying there are only two ways of solving this problem, but I only saw two ways from YOUR solutions which could lead to a reasonable answer). One is to first complete the square. This was my original solution, which I felt the most natural. If the completion of the square is written correctly, this part worths 10 points; if I can recognize that you tried to complete the square but it is incorrect then you get at most 7 points IN TOTAL. If you tried to complete the square and got more than 10 points but not perfect, then there would be minor algebraic mistake(s). The second way is to substitute x by 2(\sin \theta)^2 (or 2(\cos \theta)^2). I think this is very very brilliant. After a few steps of simplifications, you would end up integrating something like (\sin \theta)^2 (\cos \theta)^2 (up to a scalar of 8). You got 10 points up to this step. The remaining 10 points went to this trig integral. Afterall, if you got less than 10 points, you certainly have missed the main track at an early stage in your solution.
- Mar. 6. HW 5 is available.
- Feb. 27. The time and locations for mid-term 1 with special accommodations should be arranged by the Office of Student Disability Services upon your requests. The venue for mid-term 1 for those who are not seeking special accommodations is our classroom: Bloomberg 272.
- Feb. 24. The mid-term 1 for the previous semester is available here under Handouts for practice. Please note that the materials were slightly different (more on Chap. 10, less on Chap. 7), whereas the level of difficulty remains about the same.
- Feb. 20. Rubrics and keys for Assignment 2 are available.
- Feb. 16. Assignment 4 is available. Note that the due dates are in the week following Mid-term Exam 1, but it covers up to the exam. So it is a very good source for the preparation for the exam; and you are encouraged to work out a majority of the problems before the exam.
- Feb. 10. Answer key and rubric for Assignment 1, and Assignment 3 are available. The lecture notes for today is much more theoretical than the lecture, so read the section in the textbook first and understand as much as you can from there then move on to the notes. Also please read section 8.1 of the textbook; it is not contained in our syllabus but we need it in Chapter 10. I have included three problems from here in Assignment 3.
- Feb. 7. My office hours are changed to Tuesdays and Thursdays 9-10 am. HW 2 is available.
- Feb. 6. There is a handout available down this page.
- Feb. 3. I am happy to make appointments via emails if there are conflicts with my office hours.
- Feb. 1. There is a student in this class who requires the services of a note taker. This is an opportunity to share notes through the Student Disability Services Office. If you are interested in performing this service, please register as a notetaker with Student Disability Services via the following URL: https://andes.accessiblelearning.com/JHU
- For any enrollment inquiries please contact Sabrina Raymond (firstname.lastname@example.org)