David Darmon

MA 115, Pre-Calculus Modeling for the Biological Sciences, Section 03

Fall 2019

Section 03: Wednesday and Friday, 10:05 AM – 11:25 AM, Howard Hall 308

Here's the official description:

Provides a development of an understanding of linear, exponential, logarithmic, polynomial and trigonometric functions related to biological phenomena. The development is from an algebraic, graphical and modelling perspective. In addition, the solutions of equations and inequalities related to these functions are studied. Use of related technology is included.

This course covers the prerequisites necessary to develop and use mathematical models as they appear in the biological sciences. It is centered around the concept of a function: a way to map from one set of things to another. We will develop the language of functions, which requires knowledge of its vocabulary and grammar. We begin with a refresher on algebra, including variables, arithmetic with variables, expressions, equations and inequalities, and functions and their graphs. We then cover the elementary functions: polynomial, exponential, logarithmic, and trigonometric. We will consider these functions in context, both historical and scientific, emphasizing why they were invented in the first place and where you are likely to find them in biological models. We finish the class with a taste of more advanced topics, including systems of linear equations and sequences and summations.


MA 101 passed with a grade of C- or higher or Math Placement Level 3 or 4.


Dr. David Darmon ddarmon [at] monmouth.edu
Howard Hall 241

Topics, Notes, Readings

This is currently a tentative listing of topics, in order.

Review of algebra: Integer exponents as shorthand for repeated multiplication or division. Radicals. Rational exponents as another notation for radicals. What does it mean for two expressions to be equal? Inequalities. The coordinate plane. Plotting graphs of equations in the coordinate plane.
Polynomial functions: Three viewpoints of a function: tables, graphs, equations. Linear polynomials. Quadratic polynomials. General polynomials.
Exponential and logarithmic functions: Exponentiation as repeated multiplication. The exponential function. Contrasting the exponential function with a monomial function. The natural exponent. The logarithm as the inverse of the exponential function. Rules for manipulating expressions involving logarithms.
Trigonometric functions: The unit circle. Sine, cosine, and tangent. Harmonic motion. Periodic behavior.
Systems of linear equations: Moving from equality in a single equation to equality in a group (system) of equations. Systems of two linear equations. Types of solutions for systems of two linear equations. Solving systems of linear equations by substituting, eliminating, or graphing. Systems of more than two linear equations.
Sequences and summation: Sequences as functions of counting numbers. Recursive sequences. Difference equations. "Sigma" notation as shorthand for summing a sequence. Arithmetic sequences. Geometric sequences.
See the end for the current lecture schedule, subject to revision. Lecture notes will be linked there, as available.

Course Mechanics

Office Hours

Tuesday,   03:00–04:00 PM Howard Hall 241
Thursday, 10:00–11:00 AM Howard Hall 241
Thursday, 01:30–02:30 PM Howard Hall 241
Friday,     09:00–10:00 AM Howard Hall 241

If you want help with WebAssign, please bring your laptop.

If you cannot make the scheduled office hours, please e-mail me about making an appointment.

Grading Policy

Your final grade will be determined by:
50% for 4 in-class exams (12.5% each)
20% for a cumulative final exam
15% for in-class quizzes
15% for homework problem sets

Extra Credit

In addition to the main categories above, there are two opportunities for extra credit:

+5% for use of Anki (Instructions)
+5% for post-class reflections (Instructions)

Note: These are the only opportunities for extra credit in this course.


Quizzes will be given during the first 10 minutes of a Wednesday class session. Quizzes will not be every week: I will announce quizzes at least one class session before they will occur. If you miss a quiz your grade will be zero for that quiz. Your lowest two quiz grades of the semester will be dropped.


Homework will be assigned at the end of every class meeting, and listed on WebAssign. Homework assignments are due at the beginning of the next class meeting. See this Quick Start Guide provided by WebAssign for details on setting up your account. The class key for this course is below.

Class Key: MONMOUTH 9524 7388


Required. If you expect to miss 2-3 sessions of the course, you should take the course during another semester.

Examination Absences

If you miss an examination your grade will be zero for that exam. If you know you will be absent for an exam you must let me know at least one week in advance to schedule a make-up exam.


The required textbook is:

Collaboration, Cheating, and Plagiarism

All submitted work should be your own. You are welcome and encouraged to consult with others while working on an assignment, including other students in the class and tutors in the Mathematics Learning Center. However, whenever you have had assistance with a problem, you must state so at the beginning of the problem solution. Unless this mechanism is abused, there will be no reduction in credit for using and reporting such assistance. This policy applies to both individual and group work. In group work, you only need to acknowledge help from outside the group. This policy does not apply to examinations.

Statement on Special Accommodations

Students with disabilities who need special accommodations for this class are encouraged to meet with me or the appropriate disability service provider on campus as soon as possible. In order to receive accommodations, students must be registered with the appropriate disability service provider on campus as set forth in the student handbook and must follow the University procedure for self-disclosure, which is stated in the University Guide to Services and Accommodations for Students with Disabilities. Students will not be afforded any special accommodations for academic work completed prior to the disclosure of the disability, nor will they be afforded any special accommodations prior to the completion of the documentation process with the appropriate disability office.


As stated in the Extra Credit section, you will have the opportunity to use Anki for spaced retrieval practice throughout the semester. Anki is open-source, free (as in both gratis and libre) software. You can download Anki to your personal computer from this link. If you have ever used flashcards, then Anki should be fairly intuitive. If you would like more details you can find Anki's User Manual here.


Subject to revision. Assignments and solutions will all be linked here, as they are available. All readings are from the textbook by Stewart et al., unless otherwise noted.
September 4, Lecture 1:
Topics: Exponents and Radicals. Algebraic Expressions.
Sections: 1.2, 1.3
Learning Objectives
September 6, Lecture 2:
Topics: Rational Expressions. Equations.
Sections: 1.4, 1.5
Learning Objectives
September 11, Lecture 3:
Topics: Inequalities. The Coordinate Plane; Graphs of Equations; Circles.
Sections: 1.8, 1.9
Learning Objectives
September 13, Lecture 4:
Topics: Lab.
Sections: Lab
Due: September 18 at 10:05 AM
Lab 1 Handout
Lab 1 Excel File
Screenshots for Lab 1
September 18, Lecture 5:
Topics: Review.
Sections: Review
Exam 1 Study Guide
September 20, Lecture 6:
Topics: Exam.
Sections: Exam
September 25, Lecture 7:
Topics: Functions. Average Rate of Change of a Function. Linear Functions and Models.
Sections: 2.1, 2.4, 2.5
Learning Objectives
Desmos Demo for Average Rate of Change of a Function
Desmos Demos for Linear Functions: Standard Form, Point-Slope Form, Two-Point Form
September 27, Lecture 8:
Topics: Quadratic Functions and Models.
Sections: 3.1
Learning Objectives
Desmos Demos for Quadratic Functions: Non-Standard Form, Standard Form
October 2, Lecture 9:
Topics: Polynomial Functions and Their Graphs.
Sections: 3.2
Learning Objectives
October 4, Lecture 10:
Topics: Review.
Sections: Review
Exam 2 Study Guide
October 9, Lecture 11:
Topics: Exam.
Sections: Exam
October 11, Lecture 12:
Topics: Exponential Functions. The Natural Exponential Function.
Sections: 4.1, 4.2
Learning Objectives
Desmos Demo of Approximating Irrational Exponents with Rational Exponents
Desmos Demo of Graphs of Exponential Functions (Basic)
Desmos Demo of Graphs of Exponential Functions (Transformations)
October 16, Lecture 13:
Topics: Logarithmic Functions. Laws of Logarithms.
Sections: 4.3, 4.4
Learning Objectives
Desmos Demo of the Relationship Between Exponential and Logarithmic Functions
October 18, Lecture 14:
Topics: Modeling with Exponential Functions.
Sections: 4.6
Learning Objectives
October 23, Lecture 15:
Topics: Review.
Sections: Review
Exam 3 Study Guide
October 25, Lecture 16:
Topics: Exam.
Sections: Exam
Link to Lab 2
October 30, Lecture 17:
Topics: The Unit Circle.
Sections: 5.1
Learning Objectives
Unit Circle Demo
November 1, Lecture 18:
Topics: Trigonometric Functions of Real Numbers.
Sections: 5.2
Learning Objectives
November 6, Lecture 19:
Topics: Trigonometric Graphs. More Trigonometric Graphs.
Sections: 5.3, 5.4
Learning Objectives
Sine, Cosine, and the Unit Circle Demo
Transformations of Sine and Cosine Demo
Tangent and Cotangent Demo
Cosecant and Secant Demo
November 8, Lecture 20:
Topics: Modeling Harmonic Motion.
Sections: 5.6
Learning Objectives
Spring-Mass Demo
Sound Wave Demo
Tone Generator
November 13, Lecture 21:
Topics: Review.
Sections: Review
Exam 4 Study Guide
November 15, Lecture 22:
Topics: Exam.
Sections: Exam
November 20, Lecture 23:
Topics: Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables.
Sections: 10.1, 10.2
Learning Objectives
November 22, Lecture 24:
Topics: Sequences and Summation Notation.
Sections: 12.1
Learning Objectives
Graphing Sequences Demo
December 4, Lecture 25:
Topics: Arithmetic Sequences. Geometric Sequences.
Sections: 12.2, 12.3
Learning Objectives
December 6, Lecture 26:
Topics: Review for Final.
Sections: Review for Final
Final Exam Study Guide
December 11, Final Exam:
Time: 8:30 AM - 11:20 AM
Location: Howard Hall 308 (HH 308)