Math 107 Calculus II (Biological and Social Sciences)

Spring 2017

Skip down to course schedule and announcements.



Course Information


  • Vitaly Lorman
  • Email: vlorman(at)math(dot)jhu(dot)edu
  • Office hours: Mondays and Wednesdays 3–4 in Krieger 204 (or in my office, Krieger 202) or by appointment.


  • MWF 10:00–10:50 (Sections 1 and 4) in Remsen 101
  • MWF 11:00–11:50 (Sections 5, 6, 7, 8) in Remsen 101


Calculus for Biology and Medicine (3rd Edition) Claudia Neuhauser, Prentice Hall




Time TA Room Office Hours
1 Tuesdays at  1:30pm Jin Zhou (jzhou39) Krieger 205 Wednesday, 4-6 (in Krieger 211)
4 Thursdays at  4:30 pm Shengwen Wang (swang126) Maryland 309 Thursday, 12-2 (in Krieger 201)
5 Thursdays at  3pm Shengwen Wang (swang126) Bloomberg 278 Thursday, 12-2 (in Krieger 201)
6 Tuesdays at  4:30pm Kalyani Kansal ( kkansal2) Bloomber 176 Monday 3-4 p.m. (in Krieger 211)
7 Tuesdays at  3pm Jin Zhou (jzhou39) Bloomberg 272 Wednesday, 4-6 (in Krieger 201)
8 Thursdays at  1:30pm Bowei Zhao ( bzhao7) Maryland 217 Wednesday 3-4:30 (in Krieger 201)


Course objectives

The sequel to 106 Calculus I for the Biological and Social Sciences, this course will continue to develop the tools of calculus. We will start by reviewing and further expanding our ability to compute integrals. From there, we will put our knowledge of calculus to work in solving differential equations, which are ubiquitous in both mathematics and the sciences. We will then take a long detour through linear algebra (the study of systems of linear equations), which in addition to being useful in its own right, will put us in good shape to study systems of differential equations later in the course. We will also spend some time studying functions of many variables and generalize some of the tools of Calculus I to the context of many variables. Finally, we will conclude the class with a study of probability and statistics. One of the most satisfying things about this class will be seeing how the many tools we develop interact with each other. All of the topics we study are essential tools in many subjects in the sciences, and we will make connections to them where possible.


Homework will be posted each Tuesday in the course schedule below and will be due in section the next Tuesday or Thursday (depending when you have section). You will receive the graded homework back in the following week's section. Sufficient practice in the homework is essential to master the material, so you are recommended to try to complete every assignment. You are allowed to work together and ask for help on the homework; however, you MUST write your own solutions. Copying is not acceptable.

You will be graded not only on your final answer, but also on the work that shows the process of how you obtained the answer. Richard Brown wrote a superb note on how to properly write up homework for this class, so that the writing process of the homework becomes a learning process, and also so that your reader can follow your thought process. The examples he gives are from math 106, so they should be familiar to you.

You must staple your homework, write your name and section number on it clearly, and write legibly. If your homework is too messy or illegible, the grader may choose not to grade it and may decide to take points off if the homework is not stapled.

No late homework will be accepted. On the other hand, you may miss up to one homework assignment without grade penalty, as the lowest homework score will be dropped from the final grade calculation. If you absolutely cannot make class, make sure someone hands in the homework for you, or make arrangements with the TA directly to get it in before the due date.


There will be two in-class midterm examinations and a final exam. The midterms will be conducted during your usual lecture times.

  • Midterm 1: Monday, March 6 (Week 6)
  • Midterm 2: Friday, April 21 (Week 11)
  • Final: Wednesday, May 10 (Finals week)

There will be no make-up exams. For excused absences, the grade for a missed exam will be a weighted average of the grades for all subsequent exams. Unexcused absences count as a 0. Documentation of illness etc. must be obtained from the Office of Academic Advising.

Class Attendance

I will not formally take attendance; however, you are encouraged to come to lectures. By attending lecture you will get a sense of what I consider important and that should help you know what to focus on studying for the exams. We will briefly talk about what to expect on each exam the class period before it takes place, so it is in your best interest to be there. If you have to miss class, you do not need to tell me; my best advice is to get notes and find out what you missed out on in class from someone who attended.

Class Rules

No cell phones and no computers, except for note taking.

Grading Scheme

The course grade will be determined as follows:

  • Homework: 15%
  • Midterm Exams: 25% each
  • Final Exam: 35%

Academic support

Your TAs and I will have weekly office hours (posted above). These are a great place to go to ask questions. Another resource available to you is the PILOT Learning program—-see the webpage with information about academic support and tutoring. Furthermore, there is a Math Help Room in Krieger 213, open M-Th 9-9 and F 9-5 and staffed by math TAs from various classes.

Special Aid

Students with disabilities or those who may need special arrangements within this course must first register with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accomodations please remind me at least 7 days before each of the midterms or final exam by email.

On collaboration and academic honesty

As mentioned above, while you are welcome to work on homework problems together, you must write up the solutions on your own. Before consulting with classmates on homework problems, I strongly advise you to first attempt the problems yourself. Getting stuck on homework problems is frustrating, but it is essential to learning the material. This is an experience everyone has, at every stage of their mathematical development, and it is the only way forward. Get stuck, ask questions, try again, ask more questions. This can be frustrating, but remind yourself that it is a normal part of the learning process. Before you consult with others, give yourselves a chance to get stuck first. And afterwards, write up the solutions on your own to be sure that you really understand it. In talking with others, we often trick ourselves that we really understand (myself included)—being able to write something up on our own is the true test of understanding.

Here is a thought experiment. Say it is 2 a.m. the night before an assignment is due and you are stuck on a homework problem with many more left to go (try to start early so that this doesn't happen!). Copying from a classmate is not the answer. You will be left not understanding the material, and this will hurt you in the long run when it comes time to take the exams (a significantly bigger part of your grade) or when you have to use what we learn later in your academic career. Instead, take 10-15 more minutes to clearly write down as much of the solution you have. Then write a sentence (or two or three) explaining where you are stuck. Perhaps you don't understand a certain definition, or you don't understand how to use a result from class. Write this up, and be as specific as you can—that way at least you understand what you don't understand and can ask about it later. Besides being dishonest and harming the academic environment we are trying to cultivate, copying precludes any actual understanding from happening! Work together and never be afraid to ask questions. Needing help is completely reasonable, and asking for help is encouraged. Cheating is unreasonable and inexcusable.


Course Schedule

The tentative lecture schedule and homework assignments will be updated as we go. It is highly recommended that you read the relevant sections of the book before and/or after each lecture.

Topics Sections Homework
Week 1:
Jan 30, Feb 1,3

Review, methods of integration, partial fractions § 7.3 and older stuff Review sections 7.1 and 7.2. Read 7.3.

Homework 1 (due in section 2/7 or 2/9)

Solutions to graded problems
Week 2:
Feb 6, 8, 10

Finish up partial fractions, improper integrals, start differential equations § 7.3, 7.4, 8.1 Homework 2

Homework 2 (due in section 2/14 or 2/16)

Solutions to graded problems
Week 3:
Feb 9, 11, 13

Solving differential equations, equilibria and their stability
§ 8.1, 8.2

Homework 3

Homework 3 (due in section 2/21 or 2/23)

Solutions to graded problems
Week 4:
Feb 20, 22, 24

Systems of linear equations, matrices, eigenvalues and eigenvectors § 9.1, 9.2, 9.3

Homework 4

Homework 4 (due in section 2/28 or 3/2)

Solutions to graded problems
Week 5:
Feb 27, Mar 1, 3

Eigenvalues and eigenvectors, vectors and higher dimensions § 9.3, 9.4

No homework—study for the midterm next week! Here is a study guide.

Week 6:
March 6, 8, 10

Midterm 1 on Monday (3/6)

Limits and continuity, partial derivatives
10.1, 10.2 Homework 5

Homework 5 (due in section 3/14 or 3/16)

Solutions to graded problems

Also, here is the midterm, which you may need to complete your homework.

Here are the Midterm 1 solutions
Week 7:
March 9, 11, 13

Partial derivatives, tangent planes, linearization

§ 10.3, 10.4

Homework 6

Homework 6 (due in section 3/28 or 3/30)

Solutions to graded problems

March 20-26

Week 8:
March 27, 29, 31

Chain rule, directional derivatives, applications: optimization in many variables, start systems of differential equations § 10.5, 10.6, 11.1

Homework 7

Homework 7 (due in section 4/4 or 4/6)

Solutions to graded problems

Week 9:
April 3, 5, 7

Systems of linear differential equations and applications § 11.1 Homework 8

Homework 8 (due in section 4/11 or 4/13)

Solutions to graded problems

Week 10:
April 10, 12, 14

Finish up systems of differential equations (applications), counting and beginning probability § 11.2, 12.1, 12.2

Homework 9 (shorter)

Homework 9 (due in section 4/18 or 4/20)

Solutions to graded problems

Week 11:
April 17, 19, 21

Midterm 2 on Friday (4/21)

Probability, start conditional probability
§ 12.2, 12.3 Homework 10 (shorter)

Homework 10 (due in section 4/25 or 4/27)

Solutions to graded problems

Here is Midterm 2, and here are the Midterm 2 solutions.

Week 12:
April 24, 26, 28

Conditional probability and discrete random variables and discrete distributions § 12.3, 12.4 Homework 11

Homework 11 (due in lecture on 5/5)

Solutions to graded problems

Week 13:
May 1, 3, 5

Discrete random variables, review § 12.4 NO HOMEWORK. Review old homework and notes. I didn't assign any homework on what we did this week, but please review your notes from class.
FINAL EXAM Wednesday May 10th, 9am -- 12noon in Remsen 1 (a floor below our usual room)


(5/5) Here are some other practice exams from previous versions of this course: Practice Final 2 (and solutions, also skip 10(b)), Practice Final 3 (from S15, no solutions available, skip problem 6. We also didn't really emphasize number 9). You are also welcome to look through the archive of old exams linked to below, although many of them don't cover the same exact material, so following the study guide and doing problems from the book may be more helpful. Finally, I've posted solutions to our second midterm (up above in the table).

(5/2)Here is a study guide for the final exam. Here is a practice exam. Here are solutions.

(4/16) Due to differences in schedules and order of material covered, I have not been able to find exams from old courses that match exactly what will be on our exam. If you are still interested in looking at old exams, here is a large collection. You can use the guide to midterm 2 (below) to help you find relevant problems. Don't forget about old homework assignments and the relevant sections of the book as great places to find more practice problems!
(4/13) Midterm 2 is next Friday (10/21). Here is a study guide to the exam. I will post some old practice exams this weekend, although they may not be completely accurate representations of what will be on our exam.
(3/1) Here are some old exams where you can find some problems to practice for Midterm 1:
Fall 2016 Midterm 1, skip problem 5, includes solutions.
Fall 2012 Midterm 1, skip problem 5, includes solutions.
Fall 2012 Midterm 1 practice, skip last page.
Fall 2015 Midterm 1, skip problem 6 and all problems 11 and onward.
Spring 2014 Midterm 1, skip all probability questions.

(2/28) Midterm 1 is this upcoming Monday, March 6. Here is a study guide to the exam. I will also hold an extra office hour on Friday from 12 to 1.

(1/31) Welcome! Homework 1 has now been posted, due in section next week. (Future HWs will always be posted on Tuesdays and due in section the following week.)