Business Calculus for Life Sciences: Syllabus and Course Overview

Course Overview

Introduction to Business Calculus for Life Sciences

This course, Mathematics 2321: Calculus for Life Sciences I, is designed to serve the needs of students in the life sciences. The curriculum focuses on fundamental calculus concepts and their applications, particularly as they relate to biological and life science contexts. The course emphasizes understanding derivatives, integrals, and their applications, as well as the use of mathematical models to analyze real-world phenomena.

• Instructor: Dr. Elizabeth Roan

• Meeting Times: MW 2:00pm–3:20pm

• Location: College of Education 04008

• Prerequisite: Mathematics ACT score of at least 24 (SAT 520) or MATH 1315 with a grade of “C” or higher

Main Topics

Core Calculus Concepts

The course covers the following main topics, with a focus on applications in the life sciences:

• Derivatives as Rates of Change: Understanding how derivatives represent rates of change, often computed as a limit of ratios.

• Integrals as Sums: Viewing integrals as the sum of quantities, computed as a limit of Riemann sums.

• Graphs and Functions: Analyzing and interpreting various types of functions, including exponential and logarithmic functions, in biological contexts.

• Exponents and Logarithms: Exploring their properties and applications, especially in modeling growth and decay.

• Sequences and Summation: Introduction to sequences, series, and summation notation as they apply to scientific data.

• Applications: Applying calculus concepts to real-world problems in the life sciences, such as population dynamics, rates of reaction, and resource optimization.

Learning Outcomes

Mathematical Competencies

Upon successful completion of the course, students will be able to:

• Interpret key mathematical concepts and apply appropriate quantitative tools to everyday experiences in the life sciences.

• Demonstrate critical thinking by analyzing, innovating, and evaluating scientific information.

• Communicate mathematical ideas effectively through written, oral, and visual means.

• Manipulate and analyze data using empirical and quantitative skills.

Key Definitions and Concepts

Derivatives

• Definition: The derivative of a function at a point measures the instantaneous rate of change of the function with respect to its variable.

• Formula:

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Application: In biology, derivatives can represent rates such as population growth or decay, velocity, or rates of reaction.

Integrals

• Definition: The integral of a function over an interval gives the accumulated sum, such as area under a curve or total quantity.

• Formula (Definite Integral):

$\int_a^b f(x)\,dx$

• Application: Used to calculate total population, accumulated resources, or total change over time.

Exponential and Logarithmic Functions

• Exponential Function: $f(x) = a e^{bx}$

• Logarithmic Function: $f(x) = \log_a(x)$

• Application: Modeling population growth, radioactive decay, and pH in biological systems.

Sequences and Summation

• Sequence: An ordered list of numbers, often representing data points or measurements over time.

• Summation Notation: $\sum_{i=1}^n a_i$

• Application: Used in calculating total quantities from discrete data sets.

Course Structure and Assessment

Grading Policy

Grades are determined by a combination of homework, written assignments, exams, and participation. The breakdown is as follows:

Category	Percentage	Grade
WebAssign Homework	20%	90–100% = A
Written Homework	15%	80–89% = B
Exams (2)	20% (each)	70–79% = C
Final Exam	25%	60–69% = D
Extra Credit	??	Below 60% = F

Assignments and Exams

• WebAssign Homework: Online assignments via MyMathLab, with the lowest scores dropped at the end of the semester.

• Written Homework: Weekly assignments focusing on conceptual understanding and problem-solving.

• Exams: Two in-class exams and a comprehensive final exam. No make-ups without sufficient documentation.

• Test Corrections: Opportunity to reflect and correct mistakes for partial credit.

Course Materials

Textbook

• Title: Calculus with Applications by Lial, Greenwell, Ritchie (12th edition)

• ISBN: 9780135187193

• Access: E-book comes with MyMathLab code

Other Required Materials

• Access to MyMathLab for homework

• Physical or digital binder for notes

• Graphing tools (e.g., Desmos) for homework (not permitted on exams)

• Scientific calculator (no computer algebra systems or smart devices on exams)

Communication and Support

Instructor Communication

• Use Canvas and university email for all course-related communication.

• Check Canvas regularly for announcements, assignments, and updates.

• Office hours available for additional support and questions.

Additional Support Resources

• Student Help Centers, tutoring, and academic support services are available.

• Accommodations for students with disabilities can be arranged through Disability Services.

• Resources for food security and wellbeing are provided by the university.

Important Policies

Attendance and Participation

• Regular attendance is expected; participation enhances learning and community.

• Absence notifications and documentation procedures are outlined for excused absences.

Academic Integrity

• Collaboration is encouraged on homework, but all submitted work must be your own.

• Cheating or plagiarism will result in disciplinary action according to university policy.

Inclusivity and Civility

• Respectful and inclusive classroom environment is expected at all times.

• University policies on civility, emergency management, and religious observances apply.

Summary Table: Main Course Components

Component	Description
Derivatives	Rates of change, limit of ratios, applications in life sciences
Integrals	Accumulated sums, Riemann sums, area under curves
Exponents & Logarithms	Growth/decay models, scientific notation
Sequences & Summation	Discrete data analysis, summation notation
Applications	Population dynamics, resource optimization, rates of reaction

Example Application

• Population Growth Model: The exponential growth of a population can be modeled by the function $P(t) = P_0 e^{rt}$, where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is time.

• Rate of Change: The derivative $\frac{dP}{dt} = rP$ gives the instantaneous rate of population change at time $t$.