Math 138: Calculus 2 with Life Science Applications

1 Overview

This is the course website for Math 138 in the Fall 2017 semester. This is where you will find general information and course policies, as well as announcements, course materials and useful links. The Canvas page for this course is located here.

2 Contact Information

Instructor: Nathan Fieldsteel

  • Email: \(\text{nathan}\ldotp\text{fieldsteel}@\text{uky}\ldotp\text{edu}\)
  • Office: Patterson Office Tower, room 767
  • Office hours:
    • Monday and Thursday, 2:00 - 3:00 in the Mathskeller.
    • Friday 1:00 - 2:00 in 767 POT.

TA: Tefjol Pllaha

  • Email: \(\text{tefjol}\ldotp\text{pllaha}@\text{uky}\ldotp\text{edu}\)
  • Office: Patterson Office Tower, room 906
  • Office hours: TBA

3 Course Information

3.1 Times and Locations

  • Lecture: MWF 11:00 - 11:50 in Whitehall Classroom Building 212.
  • Recitation 001: TR 12:30 - 1:20 in Jacobs Science Building 103.
  • Recitation 002: TR 2:00 - 2:50 in Whitehall Classroom Building 342.

3.2 Syllabus

3.2.1 Course goals

My aim in this course is to prepare you to do the following:

  • Fluently use the computational techniques of the course.
  • Write and justify solutions to mathematical problems.
  • Apply the methods of calculus to new areas or unfamiliar problems.

3.2.2 Grading

You can obtain a maximum of 500 points in this class, as follows:

Assignment Points % of final grade
Exam 1 100 20%
Exam 2 100 20%
Exam 3 100 20%
Final Exam 100 20%
Homework 50 10%
Worksheets 50 10%

Your final grade in the course will be determined using the following table:

Points percentage Final Grade
450 - 500 90 - 100% A
400 - 449 80 - 89.9% B
350 - 399 70 - 79.9% C
300 - 349 60 - 69.9% D
0 - 299 0 - 59.9% E

At the end of the semester, the minimum grade cutoff required to obtain certain letter grades might be lowered. But the cutoffs will not be raised. In other words, if there are adjustments made to the above table, they will only be beneficial to your letter grade.

3.2.3 Policies

  • Calculators

I will try to run this class so that a calculator is never required. You can bring a calculator to class if you want to, but you are unlikely to need it. You can bring a scientific calculator to exams for arithmetic, but not a graphing calculator.

  • Attendance and Absensces:

Attendance to both lecture and recitation is mandatory. You should arrive on time and stay until class ends. If you expect to be absent, you should notify me ahead of time.

S.R. defines the following as acceptable reasons for excused absences: (a) serious illness, (b) illness or death of family member, (c) University-related trips, (d) major religious holidays, and (e) other circumstances found to fit as reasonable cause for nonattendance by the professor.

You might be asked to verify that an absence is acceptable in order for it to be considered excused. Senate Rule states that faculty have the right to request appropriate verification when students claim an excused absence because of illness or death in the family. Appropriate notification of absences due to university-related trips is required prior to the absence.

If you anticipate an absence for a major religious holiday please notify me (in writing) of anticipated absences due to your observance of such holidays no later than the last day in the semester to add a class. Two weeks prior to the absence is reasonable, but should not be given any later. Information regarding major religious holidays may be obtained through the Ombud (859) 257-3737,

You are expected to withdraw from the class if more than 20% of the classes scheduled for the semester are missed (excused or unexcused), per university policy.

  • Electronic Devices:

No electronic devices are permitted during exams. If you use a laptop, tablet or other device for taking notes during lecture, you should not be using it during class for any unrelated purpose. Your TA will determine the classroom policy for recitation.

  • Make-up policies:

Per Senate Rule, if you are missing any graded work due to an excused absence you are responsible for informing me about your excused absence within one week following the period of the excused absence (except where prior notification is required); and for making up the missed work. I will give you an opportunity to make up the work and/or the exams missed due to an excused absence. If possible it will be during the semester in which the absence occurred.

In particular, if you have university excused absences, or if you have university-scheduled class conflicts with uniform examinations, you may arrange with me to take the exam at an alternate time. Generally these make-up exams will be scheduled on the day of or on the day after the regularly scheduled exam. Work-related conflicts are neither university excused absences nor university-scheduled absences.

  • Students needing accomodations:

If you have a documented disability that requires academic accommodations, please let me know as soon as possible. In order to receive accommodations in this course, you must show me a letter of accommodation from the Disability Resource Center (DRC). The DRC coordinates campus disability services available to students with disabilities. It is located on the corner of Rose Street and Huguelet Drive in the Multidisciplinary Science Building, Suite 407. You can reach them via phone at (859) 257-2754 and via email at

Their web address is

  • Accomodations for victims of violence:

By federal law, any student who is a victim of dating violence, domestic/intimate partner violence, sexual assault, or stalking (whether on or off campus) is entitled to appropriate accommodations for his or her coursework. To get help getting accommodations and other support, students who are assaulted can do any of the following:

  • Tell your instructor, who will assist you in accessing resources appropriate to your situation;
  • Call the UK VIP Center (Violence Intervention and Prevention Center) at 257-3574 or or; or walk in to the Center in Frazee Hall, lower level, between 8:30 and 5:00;
  • Call the University Counseling Center at 257-8701; 2nd floor, Frazee Hall;
  • Call Ms. Patty Bender from the UK Institutional Equity and Equal Opportunity at 257-8927 or;
  • In the case of an emergency, contact the UK Police Department at 911.
  • Students may also contact community resources 24-hours a day, including:

3.2.4 Academic Honesty

Cheating or plagiarism is a serious offense and will not be tolerated. It will be thoroughly investigated, and might lead to failure in the course or even to expulsion from the university. See (Sections 6.3.1 and 6.3.2) for information on cheating, plagiarism, and penalties.

A summary of recent changes to rules on cheating can be found at the Academic Ombud website:

3.3 Course Overview

In this course we will learn techniques for integration, differential equations, and a little bit of multivariable calculus. Differential equations model quantities which change over time, and are widely applicable in the life sciences. Techniques for integration are useful for solving differential equations.

  • Chapter 6 : Integration
    • Review
    • Applications of integration
  • Chapter 7 : Integration Techniques and Computational Methods
    • Integration by substitution
    • Definite integrals
    • Integration by parts
    • Partial fractions
    • Improper integrals
  • Chapter 8 : Differential Equations
    • Solving differential equations
    • Equilibria and stability
  • Chapter 9 : Linear Algebra and Analytic Geometry
    • Linear systems
    • Matrices
    • Linear maps, eigenvectors and eigenvalues
    • Curve fitting, least-squares approximation
  • Chapter 10 : Multivariable Calculus
    • Functions of more than one variable
    • Limits and continuity
    • Partial derivatives
    • Tangent planes, differentiability and linearization
    • Systems of difference equations
  • Chapter 11 : Systems of Differential Equations
    • Linear systems: theory
    • Nonlinear autonomous systems: theory
    • Nonlinear systems: applications

4 Course Materials

The lecture notes for this course will not be posted online. The lecture notes for this course from previous semesters can be downloaded here, under "Lecture Notes". Reading the lecture notes from previous semesters is not an adequate alternative to attending class and taking your own notes.

5 Homework

The course will have both online homework and handwritten homework. Each will account for half of your final homework grade. The online homework will cover more routine, computational aspects of the course. You can think of the online homework as a first check of your understanding. The written homework will be more conceptual, and will aim to help you understand the concepts more completely, and exist in part to check whether you are writing clearly and demonstrating conceptual understanding. Written homework problems will almost always be problems from the text book, and will often be motivated by problems in the life sciences.

5.1 Online Homework

The online homework will be accessible at the following link:

Your username is your LinkBlue ID (use capital letters) and your password is your student ID number.

For (most of) the online problems, you can make any number of attempts before the deadline, and the system will tell you whether or not your answer is correct.

Once the assignments have closed, correct answers to the problems can be viewed. Some of the problems also have a step-by-step solution, but some do not. If you want to see step-by-step work for a problem that does not provide it, you should can ask about it in office hours

5.2 Written Homework

Written homework will be submitted to the TA during TA sections. It must follow these guidelines:

  1. All pages must be stapled together with a single staple in the top left corner.
  2. Pages should not have "notebook fringe", and should be standard-size sheets of paper.
  3. Problems must be done in numerical order, must be clearly labelled, and must start at the left margin.

You may lose one point for each guideline that is not followed.

5.3 Homework Schedule

The homework schedule below will be updated throughout the semester. The online homeworks will usually be due by the end of the day on Tuesdays or Fridays, and I will usually set them to close one hour past midnight.

Section Problems Due Date
§ 6.3 # 17, 19, 21, 23, 31 Aug 31 Recitation
§ 7.1 Homework1: Online Closes Sept 6 at 1:00 am
§ 7.2 Homework2: Online Closes Sept 9 at 1:00 am
§ 7.3 Homework3: Online Closes Sept 13 at 1:00 am
§ 7.4 Homework4: Online Closes Sept 16 at 1:00 am
Chapter 7 Review Problems # 1 - 6, 12 - 15, 23 - 26, 40 - 44 Sept 19 Recitation
§ 8.1 Homework5: Online Closes Sept 23 at 1:00 am
§ 8.2 Homework6: Online Closes Sept 27 at 1:00 am
§ 9.1 Homework7: Online Closes Oct 9 at 1:00 am
§ 9.2 Homework8: Online Closes Oct 17 at 1:00 am
Exam 2 Review Problems § 8.1: 11, 13, 15, 22. § 8.2: 1-4. § 9 review: 1, 2, 5, 6, 7. Oct 17 Recitation
§ 9.3 Online  
§ 10.1 Online  
§ 10.2 Online  
§ 10.3 Online  
§ 10.4 Online  
§ 11.1 Online  
§ 11.2 Online  
§ 11.3 Online  
§ 11.4 Online  

6 Schedule of Topics

This is a schedule of topics for the semester. It may change slightly, depending on time constraints and other factors.

Day Section Topic
Week 1    
Wednesday, August 23 § 6.3 Review of integration. Applications of integration
Thursday, August 24 § 6.3 Recitation Worksheet 1
Friday, August 25 § 6.3 Applications of integration
Week 2    
Monday, August 28 § 7.1 The substitution rule
Tuesday, August 29   Recitation Worksheet 2
Wednesday, August 30 § 7.2 Integration by parts and practicing integration
Thursday, August 31   Recitation Worksheet 3
Friday, September 1 § 7.2 Integration by parts and practicing integration
Week 3    
Monday, September 4 No Class Labor Day
Tuesday, September 5    
Wednesday, September 6 § 7.3 Rational Functions and partial fractions
Thursday, September 7    
Friday, September 8 § 7.3 Rational Functions and partial fractions
Week 4    
Monday, September 11 § 7.4 Improper Integrals
Tuesday, Septermber 12    
Wednesday, September 13 § 7.4 Improper Integrals
Thursday, Septermber 14    
Friday, September 15 § 7.4 Improper Integrals
Week 5    
Monday, September 18   Review and regroup
Tuesday, September 19   Exam 1
Wednesday, September 20 § 8.1 Solving differential equations
Thursday, Septermber 21    
Friday, September 22 § 8.1 Solving differential equations
Week 6    
Monday, September 25 § 8.1 Solving differential equations
Tuesday, September 26    
Wednesday, September 27 Handout Direction fields and \(\texttt{WolframAlpha}\)
Thursday, September 28    
Friday, September 29 Handout Direction fields and \(\texttt{WolframAlpha}\)
Week 7    
Monday, October 2 § 8.2 Equilibria and stability
Tuesday, October 3    
Wednesday, October 4 § 8.2 Linear systems
Thursday, October 5    
Friday, October 6 § 9.1 Linear systems
Week 8    
Monday, October 9 § 9.1 Matrices
Tuesday, October 10    
Wednesday, October 11 § 9.2 Matrices - Determinants
Thursday, October 12    
Friday, October 13 § 9.2 Linear functions
Week 9    
Monday, October 16   Review and regroup
Tuesday, October 17   Exam 2
Wednesday, October 18 § 9.3 Linear maps, eigenvectors and eigenvalues
Thursday, October 19    
Friday, October 20 § 9.3 Linear maps, eigenvectors and eigenvalues
Week 10    
Monday, October 23 § 9.3 Linear maps, eigenvectors and eigenvalues
Tuesday, October 24    
Wednesday, October 25 Handout Fibonacci numbers, a population model, and matrix powers
Thursday, October 26    
Friday, October 27 Handout Curve fitting, least-squares approximation
Week 11    
Monday, October 30   Curve fitting, least-squares approximation
Tuesday, October 31    
Wednesday, November 1 § 10.1 Functions of two or more variables
Thursday, November 2    
Friday, November 3 § 10.2 Limits and continuity
Week 12    
Monday, November 6 § 10.3 Partial derivatives
Tuesday, November 7    
Wednesday, November 8 § 10.3 Partial derivatives
Thursday, November 9    
Friday, November 10 § 10.4 Tangent planes, differentiability, and linearization
Week 13    
Monday, November 13 § 10.4 Tangent planes, differentiability, and linearization
Tuesday, November 14   Exam 3
Wednesday, November 15 § 10.5 Vector valued functions
Thursday, November 16    
Friday, November 17 § 11.1 Linear systems - theory
Week 14    
Monday, November 20 § 11.1 Linear systems - theory
Tuesday, November 21    
Wednesday, November 22 No Class Thanksgiving Break
Thursday, November 23    
Friday, November 24 No Class  
Week 15    
Monday, November 27 § 11.1 Linear systems - theory
Tuesday, November 28    
Wednesday, November 29 § 11.1 Linear systems - theory
Thursday, November 30    
Friday, December 1 § 11.2 Linear systems - applications
Week 16    
Monday, December 4 § 11.3 Nonlinear autonomous systems - theory
Tuesday, December 5    
Wednesday, December 6 § 11.3 Nonlinear autonomous systems - theory
Thursday, December 7    
Friday, December 8 § 11.4 Nonlinear systems - applications
Monday, December 11   Final Exam

7 Textbook

The textbook for this course is Calculus for Biology and Medicine (3rd edition) by Claudia Neuhauser (ISBN 978-0-321-64468-8). The book can be purchased from the UK Bookstore, Kennedy Bookstore, Wildcat Textbooks, or online.

We are aiming to cover chapters 6 through 11. We will cover methods for evaluating integrals, differential equations, and an introduction to multivariable calculus.

8 Exams

There will be three midterm exams and a final exam. Each exam is worth 100 points, and each exam is worth 20% of your final grade. You must bring a photo ID to each exam. You may use a scientific calculator, but not a programmable or graphic calculator. No cell phone use is permitted during an exam.

8.2 Exam times and locations

The midterm exams will be held on September \(19^{th}\), October \(17^{th}\) and November \(14^{th}\), from 5:00 - 7:00 pm. All of these dates are Tuesdays.

The final Exam for this course will be held on Monday, December \(11^{th}\) from 8:30 pm to 10:30 pm.

All of the midterm exams and the final exam will be held in KAS 213.

8.3 Exam materials

  • Exam 1 will cover:
    • § 6.3 Applications of Integration
    • § 7.1 Substitution
    • § 7.2 Integration by Parts
    • § 7.3 Rational Functions and Partial Fractions
    • § 7.4 Improper Integrals
  • Exam 2 will cover:
    • § 8.1 Solving Differential Equations
    • § 8.2 Equilibria and Their Stability
    • § 9.1 Linear Systems
    • § 9.2 Matrices, Matrix Algebra, Determinants
  • Exam 3 will cover:
    • § 9.3 Linear Maps, Eigenvectors and Eigenvalues
    • § 10.1 Functions of Two or More Independent Variables
    • § 10.2 Limits and Continuity
    • § 10.3 Partial Derivatives
    • § 10.4 Tangent Planes, Differentiability and Linearization
  • The final exam is comprehensive. It will cover:
    • All material from the three previous exams.
    • § 11.1 Linear Systems: Theory
    • § 11.2 Linear Systems: Applications
    • § 11.3 Nonlinear Autonomous Systems: Theory
    • § 11.4 Nonlinear Autonomous Systems: Applications

8.4 Alternate exams

Students who have university excused absences or who have university-scheduled class conflicts with uniform examinations may take an Alternate Exam. In order for me to set up a time and location for the alternate exam, you must let me know about your conflict at least one week before the schduled exam time.

8.5 Old Exams

Midterm and final exams given in previous versions of this course are available and can be downloaded here, under "Old Exams".

Be advised that these past exams were written by different professors with different classes, different plans and different expectations. While these exams are a useful study guide, you should not necessarily expect that they are perfect preparation for the exams I will write this semester.

9 Tutoring

If you find yourself struggling in the course, it is important to seek help immediately. Talk to your instructor or your TA as soon as possible.

There is math tutoring available in The Mathskeller, in the basement of Whitehall Classroom Building. I will be in The Mathskeller on Mondays and Wednesdays from 2:00 - 3:00, but you can go at any time. In addition, peer tutoring is available through The Study,