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 |

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.

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.

- 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

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.

**Class Key:** `MONMOUTH 9524 7388`

The **required** textbook is:

- James Stewart, Lothar Redlin, and Saleem Watson,
*Precalculus: Mathematics for Calculus*, 7th edition (Cengage Learning, 2015, ISBN: 9781305701618). Link to University Store

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.

- 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)