Syllabus for Math 124
Joseph
Mahaffy
Professor, Mathematical Biology

Lectures: MW 16:0017:15 in GMCS 333 
Office phone: 6195943743 
Office Hours: MW 1313:50,
15:2015:50,17:2017:50

Fax: 6195946746 
Office location: GMCS 593 
Email: jmahaffy@mail.sdsu.edu 
Derek Moree
Graduate Assistant 
Lab: Friday in GMCS 421

Office phone: 619594xxxx 
Office Hours: T1011, Th 24 GMCS 421 or 422

Fax: 6195946746 

Email: dmoree@sdsu.edu 
Textbook:
Joseph Mahaffy and Alexandra
ChavezRoss, Calculus: A Modeling
approach for the Life Sciences (Volumes 1 and 2),
Pearson Custom Publishing, 2009.
Lecture Notes
are available online.
A Lab
Manual is being developed with much of
the first part completed and online.
Prerequisite: Satisfaction
of the ELM requirement (Entry Level Math) and IA
examination, or MATH 141 with a grade of C or better.
Students should have good knowledge of
High School Algebra and do reasonably well on the Algebra
SelfTest given at the beginning of the course. Recently
the Mathematics Department has begun testing the ALEKS
system, which is likely to become the admission standard
for this course (and Math 150). Students should score 74
or better from ALEKS
to enter Math 124.
Course Catalog Description:
Basic concepts of calculus with life science applications.
Topics from differential and integral calculus and an
introduction to elementary differential equations.
Computer applications to biological problems. Not open to
students with credit in Mathematics 121 and 122, or 150.
Student Learning Outcomes:
At the end of this course students will be able to:
 Model biological problems with basic functions:
linear, polynomial, exponential, logarithmic, and
trigonometric.
 Understand the fundamental concepts of differential
and integral calculus.
 Apply methods from discrete and continuous dynamical
systems to solve problems from biology.
 Use Excel, Word, and Maple software to study the
dynamics of a variety of biological problems, including
population dynamics, physiological processes, and
ecological models.
 Read and analyze graphs fitting real biological data.
 Create quality computer lab reports with scientific
standards on both the graphs and the writing.
Course Objectives and
Expectations on Students:
This course is a 4 unit course designed for students who
are majoring in life sciences, particularly in biology. It
is also for students wishing to satisfy SDSU’s mathematics
requirement for General Education.
Biological sciences are rapidly expanding with an
increased need for more quantitative analysis of the data.
Mathematics and computers are becoming more important to
the life science work force. The main objective of this
course is to provide student basic calculus skills to
develop mathematical models for biological sciences, to
help analyze data from life sciences, and to use
mathematics software for solving life science problems.
The students are expected to appreciate the usefulness of
differential and integral calculus and differential
equations to relate the mathematics of life science
problems in their real life.
Scope and Purpose of the Course:
This course is an engaging introduction to differential
and integral calculus and differential equations for life
sciences. It will introduce students to the basic
concepts and methods of differential and integral calculus
and applications to life sciences. The central themes of
the course will be functions as mathematical models for
life science problems, and determination and analysis of
these functions by using differentiation and integration
tools and computer software. For example, logarithmic and
exponential functions can be used to model population
growth; the temperature of a female human body has a
diurnal cycle with the maximum and minimum temperature of
a day found from a polynomial or trigonometric function;
the buildup of toxicity in the bodies of growing children
exposed to lead can be modeled by a differential equation,
which is solved using integration. Quantitative
description and analysis of these life science examples by
using calculus will be taught in the course.
The course is intended to help students develop basic
calculus thinking and problemsolving strategies that can
be applied to life science problems. By emphasizing
mathematical methods of applications, this course will
engage students in logical thinking, problem solving, and
basic skills of data analysis and modeling in life
sciences.
We will normally cover the topics: functions and models,
least squares method, limits andcontinuity, concept of a
derivative, methods and rules of differentiation, graphing
functions, optimization, differential equations and their
solutions, integration, area and the fundamental theorem
of calculus, and use of computer software. Although you
will be challenged, the overriding theme of the course is
to gain the basic calculus skills that are essential to
today’s life science workforce and researchers.
This Course Addresses GE (General
Education) Requirement
This is a GE course. It addresses the GE requirement
from three perspectives: (1) construct mathematical models
for life sciences, analyze biological data, and
communicate mathematical arguments, (2) apply differential
and integral calculus an ddifferential equation skills to
real world problems, and (3) illustrate relevance of
mathematical concepts across boundaries of various
disciplines.
Course Assessment
and Grading
 Lecture Material is 70%
of grade:
 Lecture participation (I>Clicker) (7% of
Lecture grade)
 50% of participation grade is answering 75% of
posed questions
 50% of participation grade is based on correct
answers of select questions
 Two lowest scores are dropped over the
semester
 Homework with WeBWorK (9% of Lecture grade)
 Quizzes, Exams, and Final ((84% of Lecture
grade))
 Quizzes on HW every Lab (end), except when
taking Algebra Quiz or a Lab Exam (14% of
Lecture grade)
 3 Exams (each 14% of Lecture grade) and Final
(28% of Lecture grade)
 Scientific Calculator only  Quizzes, Exams,
and Final
 One 3x5 notecard for Quizzes or Exams and
three 3x5 notecards for Final
 Lab Work is 30% of
grade:
 1314 Lab assignments  Lowest Lab score is
dropped
 Lab attendance is mandatory
(unless you receive an excused absence)
 3 Lab Quizzes worth twice a regular Lab assignment
 Open notes, Computer (except email), No Cell
Phones
The grade divisions are typically 85100
is an A, 7385
is a B, 6273
is a C, 5062
is a D, and below 50
is an F with + or 
assigned near the boundary (within 3%). Because the HW can
be done with outside help or technology and the Computer
Lab grade can reflect work done by others, then if these
scores are disproportionately high
compared to Quiz, Exam, and Final scores, then the
instructor reserves the right to lower a grade.
(Yes, there is some subjectivity in the
final grade based on instructor experience.) The
instructor considers the comprehensive final exam
especially important in deciding the final grade, as this
exam reflects what a student has learned in the course. Anyone
receiving a score less than 50% on the Final is unlikely
to obtain a grade higher than a C. Simlarly,
a high performance on the final may be used to increase a
student's grade above the typical grade divisions noted
above.
Accommodation Of Disability:
Students with disabilities who may need academic
accommodations should notify the professor in writing
within the first two weeks of instruction. Students need
appropriate forms aproved by SDS (Calpulli Center, Suite
3101). All information will be kept confidential. Students
that need evacuation assistance during campus emergencies
should also meet with the instructor as soon as possible
to assure the health and safety of all students. If you
encounter a problem accessing anything in this course,
please contact me as soon as possible.
Classroom Behavior And Student
Code Of Conduct
 It is expected that students will conduct themselves
within the standards outlined in the student code of
conduct,
disciplinary procedure and student due process.
Disciplinary action will be taken by the instructor as
necessary. See more information at the SDSU
Student Ethical & Civic Responsibility Code.
 Students are expected to come to class in a timely
manner, prepared for the day’s work. Full participation
for the entire
class period in activities, class exercises and
discussions is required.
 Please turn off all cell phones,
pagers, etc. (except for use with the I>Clicker
response). You will be released from class with an
unexcused absence for making or accepting telephone
calls or text messages in the classroom.
 It is the student’s responsibility to make up missed
material. This includes, but is not limited to,
obtaining missed lecture notes from another student (not
from the instructor), and finding out about any
modifications of schedules or assignments announced
during class time.
 WeBWorK assignments are posted with a
specific due date. It is the student’s responsibility to
complete the assignment on time.
 Academic dishonesty will result in a
grade of zero for the assignment and will be reported to
Academic Affairs. It may result in further disciplinary
action. Academic dishonesty includes, but is not limited
to, cheating, which includes unauthorized collaboration
and plagiarism.
 Missed Exams or Lab Exams: Students will receive a
ZERO for any missed exam, except for written/documented
excuses (illness, personal/family crises, etc.).
 Even the visual presence of a Cell Phone
during an Exam will result in a ZERO
for that Exam.
 Lab assignments:
 Attendance is mandatory or
automatic 10 point deduction (unless you receive an
excused absence).
 Partners are assigned and must work with given
partner.
 Arriving 20 minutes late or missing a Lab means
working the lab alone.
 Labs due promptly by Thursday
9 PM following a given Lab unless told
otherwise.
 Lowest lab score is dropped.
 It is the student’s responsibility to back up Lab
work  No excuses accepted or extensions granted
for lost material.
Other Course Policies
 The instructor will make special arrangements for
students with documented learning disabilities and will
try to make accommodations for other unforeseen
circumstances, e.g., illness, personal/family
crises, etc. in a way that is fair to all students
enrolled in the class. Please contact the instructor
EARLY regarding special circumstances.
 Students are expected and encouraged to ask questions
in class.
 Students are expected and encouraged to make use of
office hours.
Planned Schedule
Week 1: Introduction, linear
equations, linear models, and quadratics
Lab 1: Lecture on Word and Excel
graphing
 Intersection of line and quadratic
 Linear model of crickets chirping and temperature
 Weak Acids – quadratics, square root, and pH (log10)
Week 2: Function review,
polynomials, and rational functions
Lab 2: Lecture on least squares
fitting data and introduction to Maple
 Introduction to Maple – lines, polynomials, and
rational functions intersecting and other properties
 Linear model – Concentration and absorbance (urea
concentration in animals)
 Fit quadratic to growth of yeast (logistic growth)
Week 3: Allometric models,
exponentials, natural logarithm, and begin trigonometric
functions
Lab 3: Review power law related
to linear least square fit
 Exponentials, logarithms, and power laws – relative
size of functions
 Allometric model of dogs – length, surface area, and
weight
 Island biodiversity or Alleghany forest – allometric
model
Week 4: Trigonometric functions
and discrete dynamical models
Lab 4: Lecture on Excel's
Solver and nonautonomous and linear discrete dynamical
models
 Annual length of day and average temperature with trig
functions
 Malthusian growth model for U. S. – fitting census
data
 Model for breathing – linear discrete dynamical model
Week 5: Exam 1 and Introduction
to the derivative
Lab 5: Lecture on growth and
the derivative and Lab Quiz
 Discrete and nonautonomous Malthusian growth – fitting
recent census data
 Weight and height of girls – allometric model and
growth curves
Week 6: Velocity and tangent
lines (derivative concepts) and formal definitions of
limits, continuity, and derivative, power law rule for
differentiation
Lab 6: Lecture on geometry and
graphs related to derivative
 Tangent lines and the derivative – secant lines,
limits, experiment rules of derivative
 von Bertalanffy model – length and growth of fish
 Oxygen consumption of Triatoma phyllosoma –
max and min of polynomial
Week 7: Applications of the
derivative and derivative of the exponential, logarithm,
and trigonometric functions
Lab 7: Lecture on graphing with
large data sets and using Maple for specific maxima and
minima
 Female body temperature – fertility related to max,
min, and point of inflection
 Radioactive isotopes – maxima and points of inflection
 Fourier fit to population data – using sums of trig
functions to fit pelt data
Week 8: Product, quotient, and
chain rules of differentiation
Lab 8: Review methods for
allometric modeling and finding points of inflection
 Continuous logistic growth – fitting data and finding
the point of inflection
 Tumor growth – logistic and Gompertz growth laws
 Growth of Pacific fish – von Bertalanffy model and
allometric model showing chain rule of differentiation
Week 9: Exam 2 and optimization
Lab 9: Lecture on designing
figures for optimization and Lab Quiz
 Optimal volume of box or tent volume
 Optimal foraging for seagulls
Week 10: Application to logistic
and other nonlinear discrete dynamical models
Lab 10: Review concepts of
updating functions, growth functions, and time series
simulations
 Optimal trough volumes – two troughs with varying
angles (differentiation of trig functions)
 von Bertalanffy model – length and growth of fish
 Beetle populations – fit with logistic, Ricker, and
BevertonHolt models, finding updating
Week 11: Introduction to
differential equations and linear differential
equations
Lab 11: Lecture on Maple
differential equation solvers and slope fields
 Malthusian and logistic growth models studied with
Maple slope fields
 Study different cell sizes and growths – learn the
power of Malthusian growth
 Newton’s law of cooling applied to the death of a cat
Week 12: Differential equations
and integration
Lab 12: Lecture on numerical
techniques for differential equations – Euler’s and
improved Euler’s methods
 Growth of E. coli – comparing two models
 Carbon monoxide in a room – two models for buildup of
CO
 Lead exposure in children – modeling with timevarying
differential equation
Week 13: Separation of variables
and integration by substitution
Lab 13: Lecture on Riemann sums
and numerical integration
 European population model – time varying growth
 Insect population – fit with polynomials and trig
functions and use definite integrals to find average
 Poiseuille’s law for flow of blood used with integrals
to find arterial flow
Week 14: Exam 3 and definite
integrals and Fundamental Theorem of Calculus
Lab 14: Lecture on 2D modeling
problems
 Flight of a ball in two dimensionsn
 Model for gonorrhea – SIS epidemic model
 Predatorprey model studied – fit data and simulate
with Euler’s method
Week 15: Qualitative theory of
differential equations and review
Lab Final
Comprehensive Final Exam
Tutoring: The Math Department may offer
free tutoring depending on funding. Any tutoring
information will be posted on the HW
Assignment page.
