Math 106 Calculus I (Bio)

Spring 2018

Skip down to course schedule and announcements.



Course Information


  • Mona Merling
  • Email: mmerling(at)math(dot)jhu(dot)edu
  • Office hours: Wednesdays 3–4 at Krieger 311 or by appointment.


  • MWF 10:00–10:50 at Shaffer 301


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




Time TA Room Office Hours
1 Tuesdays at  1:30pm Daniel Fuentes (dfuente6) Maryland 202 Tuesdays 3-4pm, Krieger 200
2 Thursdays at  3pm Zehua Zhao (zzhao25) Maryland 309 Thursdays 4-5pm, Krieger 201



Homework will be posted each Friday in the course schedule below and will be due at the beginning of class the next Friday. 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 our class, math 106.

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 he 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 two homework assignments without grade penalty, as the lowest two homework scores 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 to him before the due date.


There will be two in-class midterm examinations and a final exam.

  • Midterm 1: Monday, March 5 (week 6) during class time
  • Midterm 2: Monday, April 9 (week 11) during class time
  • Final: Wednesday, May 9 (finals week), 9am-12pm

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. I will give short quizzes once in a while -- these will never be handed in; they are supposed to provide practice for the exams. Also, 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%
Here is a note on grading.

Academic support

Check out the PILOT Learning program, and the webpage with information about academic support and tutoring. Furthermore, there is a math helproom in Krieger 213, and you are encouraged to make the best use of it.

Special Aid

Students with disabilities or other special needs who require classroom accommodations must first be registered with the disability coordinator in the Office of Academic Advising.  To arrange for testing accommodations the request must be submitted to the instructor at least 7 days (including the weekend) before each of the midterms or final exam.  You may make this request during office hours, after class or by sending an email to the instructor.

JHU Ethics Statement

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the "Statement on Ethics" at the Ethics Board website for more information.


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 DUE
Week 1:
Jan 29, 31, Feb 2

Review of precalculus.
Sets, subsets of real numbers, inequalities, lines, circles, trigonometry, definition of functions

§ 1.1.1-1.1.4, 1.2.1. Homework 1

§1.1: exercises 6, 10, 34, 42, 54, 58, 62, 66, 70, 71

(For exercise 62 please review how to complete squares if you forgot)

§1.2: exercises 2, 4, 6.

Solutions to graded problems (provided by Daniel)
Week 2:
Feb 5,7,9

More precalculus review.
Functions, ways of combining functions, function composition, and inverse functions.
Polynomial functions, rational functions, power functions, trig functions.
§ 1.2.1.-1.2.4., 1.2.6., 1.2.8., 1.3.1.

In order to see where some of the functions we have reviewed show up in practice, please read the following examples form the book:
§ 1.2.2. Example 4,
§ 1.2.3. Example 6,
§ 1.2.4. Example 7.
Homework 2

§ 1.2.: exercises 10, 12, 16, 18, 20, 32, 46, 52, 71, 74

(For some of these exercises, the book says to use a graphing calculator. I think you should try to figure out as much of the graph as you can without, and then check your answer with a graphing calculator or if you don't have one, you can use the online tool Mathematica offers: here is a link, you can play around with plugging functions in there. But use this as a backup to see if your graph is correct after you've thought about it and have an idea of how it should look like.)

§ 1.3.: exercises 2, 8, 19, 32.

(For these questions, you are told not to use a graphing calculator, and you should think of transformations to graphs you know to get the graphs in the first three questions here.)

Solutions to graded problems, part 1

Solutions to graded problems, part 1
(provided by Zehua)
Week 3:
Feb 12, 14, 16

Exponential and logarithmic functions, population growth in discrete time, recursions, sequences, limits of sequences. § 1.2.5., 1.2.7., 2.1, 2.2.

Optional reading: 2.3.1. (on a population growth model that is more realistic and does not grow to infinity)
2.3.4. (on the Fibonacci sequence and the golden mean)
Homework 3

Exercise 1: Do the exercise from this note

§ 1.2.: exercises 57, 82, 84

§ 2.1.: exercises 18, 28, 42, 56

§ 2.2.: exercises 10, 30, 36, 53, 56, 62, 65, 67, 72, 76, 78, 80, 82, 110.

Solutions to extra problem and to exercise 2.2.(67) (provided by Mona)

Solutions to other graded problems
(provided by Daniel)
Week 4
Feb 19,21,23

Intuitive definition of limit, formal definition of limit, limit laws, continuity. § 3.1., 3.6., 3.2.

Homework 4

NOT to hand in: try some of problems 1-32 from § 3.1.1. that ask you to plug in values of the given functions into a calculator to get an idea of what the limit should be.

Exercises to hand in:

§ 3.1.: exercises 38, 42, 43, 46, 50 ,54

§ 3.6.: exercises 1, 8, 10, 18

§ 3.2.: exercises 6, 8, 10, 12, 13, 22, 24, 26, 27, 30, 40, 42, 43, 46, 48

Solutions to graded problems
(provided by Zehua)
Week 5:
Feb 26, 28, March 2

Continuity, limits at infinity § 3.2, 3.3., 3.6.

Here is the practice problem set (same as the one posted below under announcements.)
Here are solutions to the practice problem set.
NO HOMEWORK DUE 03/09! Hooray!

Relax after the exam.

Note that there is no homework due next Friday.
Week 6
Mar 5, 7, 9

Midterm 1 on Monday

Sandwich theorem, trigonometric limits, intermediate value theorem.
§ 3.4., 3.5.

Homework 5

§ 3.4. exercises 2, 3, 4, 8, 10, 12, 14, 18, 20, 21

§ 3.5. exercises 2, 4, 7, 8, 9, 13, 14, 15

Solutions to graded problems
(provided by Daniel)
Week 7
Mar 12, 14, 16

Definition of derivative, diffenrentiability and continuity, rules for differentiation § 4.1., 4.2., 4.3.

In class we discussed instantaneous rate of change for population growth as a possible application of derivatives. You can read in 4.1.2. about other examples of functions whose instantaneous rates of change are used in applications.
Homework 6

Exercise 1: Using the limit law for sums and the definition of derivative, show that the law (f+g)'=f'+g' holds.

§ 4.1. exercises 22, 26, 36, 49, 53, 56, 68

§ 4.2. exercises 10, 12, 20, 26, 32, 40, 44, 54, 58, 68, 80

§ 4.3. exercises 12, 28, 32, 62, 68, 78, 86

Solutions to graded problems
(provided by Zehua)
03/30 (Friday after spring break)
Week 8

Week 9
Mar 26, 28, 30

Higher Derivatives, chain Rule, implicit differentiation and related rates, derivatives of trigonometric functions, exponential functions and inverse functions (in particular logarithmic functions), logarithmic differentiation. § 4.4. 4.5, 4.6., 4.7.

Read the proof of the chain rule on page 164 in your textbook.
Homework 7

§ 4.4. exercises 8, 14, 16, 40, 44, 54, 59(a), 80, 86

§ 4.5. exercises 16, 28, 34, 61, 62, 70

§ 4.6. exercises 4, 16, 20, 38, 52, 64

§ 4.7. exercises 4, 22, 28, 34, 40, 60, 68, 71, 72

This homework is on the longer side, but note that you will not have any homework to hand in the following week after the exam. It's good to practice as much as you can this week. Please start early, so you can identify where you have trouble and can ask about it in section, office hours, help room, etc, this next week.

Solutions to graded problems
(provided by Daniel)
Week 10
Apr 2, 4, 6

Logarithmic Differentiation, extreme value theorem, finding max/min. § 4.7., 5.1.

NO HOMEWORK DUE 04/13! Hooray!

Relax after the exam, and spend the time trying to understand anything you didn't fully get on the exam.
Week 11
Apr 9, 11, 13

Midterm 2 on Monday

Fermat's theorem (criterion) for extreme values, Mean Value Theorem and consequences, monotonicity and concavity
§ 5.1., 5.2.

Read the proofs of Rolle's and the Mean Value Theorem on page 211.

Read example 2 on page 217 and example 4 on page 220 to see some applications of monotonicity and concavity to problems in bio.
Homework 8

§ 5.1. exercises 10, 12, 20, 24, 32, 34, 38, 40, 44, 50, 56

§ 5.2. exercises 4, 8, 14, 20, 23, 24, 25, 28, 30.

Solutions to graded problems
(provided by Zehua)
Week 11
Apr 16,18,20

Finding extrema, inflection points, asymptotes, graphing functions. Max min problems. § 5.3., 5.4.

Read example 4 on page 232 so that you are aware of the existence of oblique asymptotes

Read example 5 on page 241 to see a more complicated and longer application of calculus for optimization problems in bio.
Homework 9

§ 5.3. exercises 2, 8, 14, 17, 18, 22, 24, 28, 33, 36, 38, 38, 39, 42

§ 5.4. exercises 2, 8.

Solutions to graded problems
(provided by Daniel)
Week 12
Apr 23,25,27

L'Hopital for computing indeterminate limits, areas and definition of intergral § 5.5., 6.1.

Homework 10

§ 5.5. exercises 2, 6, 8, 12, 14, 20, 26, 46, 52, 60

§ 6.1. exercises 2, 31, 36, 39, 62, 71, 74, 76, 84

NOT to hand in:

§ 6.1. exercises 6, 10, 16, 18, 20, 22, 44, 46, 48, 50, 55, 56.
(do these first as practice with notation and definitions)

§ 6.2. exercises 4, 6, 12, 44, 46, 62, 70, 92, 98, 110.

NOTE: This homework will be returned by your TAs during an office hour starting at 2pm on Monday May 7. If you cannot make that, please feel to make arrangements with them to pick it up another time.

Solutions to graded problems
(provided by Zehua)
Week 13
Apr 30, May 02, 04

Integrals and areas, fundamental theorem of calculus, antiderivatives.

Read the proof of the fundamental theorem of calculus at the end of section 6.2.1. in your book.
§ 6.1., 6.2., 5.8.

FINAL EXAM Wednesday May 9th, 9am -- 12noon


Mon, Jan 29: PILOT registration will open today, Monday, January 29th and close on Friday, February 2nd and sessions will start the week of February 4th. You will get an email with registration instructions. I highly recommend you take advantage of the PILOT program

Fri, Feb 23: There will be a review session on the Fridays before each midterm. These will take place as follows:
Friday March 2: Hodson 213 at 4pm, held by Zehua
Friday April 6: Hodson 213 at 4pm, held by Daniel
These are for everyone, no matter which section you are in.

Wed, Feb 28: Here is the practice problem set for the first midterm. Please alert me if you find any errors or typos.

Please review the following: all the examples from class through today, all the homework questions, and then try the problem set on your own so that you get a sense on where you get stuck. This will be covered in the review session and later on I will also send solutions to illustrate how you are supposed to write your answers.

Work extra hard this week -- next week you will not have any homework to hand in. So work hard now and you can relax after the midterm!

Mon, Mar 5: Here are solutions to the first midterm. Please read them carefully and try to understand what you did wrong, or why your solution was incomplete wherever it was. (If you find typos or errors, please alert me.) The exams will be returned in section, and the rules about returning them are here--read these carefully. Your TA will go over the entire exam in depth in section this week.

Tue, Apr 3: Here is the practice problem set for the second midterm. Please alert me if you find any errors or typos. (Updated Wed Apr 4, 12:30pm, corrected typo in exercise 3, and updated again Wed Apr 4, 2pm, corrected typo in exercise 5, last small edit at 4:30 pm, changed the domain in 2(2) to the open interval.)

Just like last time, try this after you review examples from class and homework. The practice will be covered in the review session and I will also send you solutions.

The second exam will cover sections 3.4., 3.5. and 4.1. through and including 4.7. Of course, all this material builds on the previous material we have learned.

Wed Apr 4: Here are solutions to the practice problem set. Please only look at them after you try the problems. I tried to write out explanations, but please let me know if you have any questions anywhere. (update Sat 10:40pm, typo corrected in solution to exercise 5, answer should be 72.)

Mon Apr 6:Here are solutions to the second midterm (updated Tue Apr 10, 11:30am, corrected typo in solution to 2c). Please read them carefully and try to understand what you did wrong, or why your solution was incomplete wherever it was. (If you find typos or errors, please alert me.)

The average was 79 and the median was 82 --congratulations on such a good job! Let's work to make it even better on the final. Please study your mistakes now since similar problems with the ones from the midterms will appear on the final.

The exams will be returned in section, and the rules about returning them are the same as last time--read these carefully. Your TA will go over the entire exam in depth in section this week.

Sun Apr 29: Here are the 2 midterms, blank, so you can print them and redo them as practice: midterm 1 and midterm 2. Sun Apr 29: Your TAs will hold an extra office hour at 2pm during Monday of review period -- you can get the last homework back and any other previous homeworks you didn't pick up. You should also ask any remaining questions about homework problems. If you can't make this time, arrange with your TA to pick up your homework from them at another time that day.

There will be a review session held by me on
Tuesday May 8 2-4pm, Shaffer 100.

We will go over practice questions (which I will send to you in advance as usual).

Sat May 5: Here is a practice problem set. PLease also redo the last midterms, and review all your notes and the examples from class.

Here are solutions to the practice problem set.