Joseph M. Mahaffy SDSU
Math 124: Calculus for the Life Sciences Spring 2017
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Syllabus for Math 124

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Joseph Mahaffy
Professor, Mathematical Biology
Lectures: MW 16:00-17:15 in GMCS 333 Office phone: 619-594-3743

Office Hours: MW 13-13:50,

Fax: 619-594-6746
Office location: GMCS 593 E-mail:
Derek Moree
Graduate Assistant
Lab: Friday in GMCS 421
Office phone: 619-594-xxxx
Office Hours: T10-11, Th 2-4 GMCS 421 or 422
Fax: 619-594-6746


Joseph Mahaffy and Alexandra Chavez-Ross, 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 Self-Test 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:

  1. Model biological problems with basic functions: linear, polynomial, exponential, logarithmic, and trigonometric.
  2. Understand the fundamental concepts of differential and integral calculus.
  3. Apply methods from discrete and continuous dynamical systems to solve problems from biology.
  4. Use Excel, Word, and Maple software to study the dynamics of a variety of biological problems, including population dynamics, physiological processes, and ecological models.
  5. Read and analyze graphs fitting real biological data.
  6. 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 build-up 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 problem-solving 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:
    • 13-14 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 85-100 is an A, 73-85 is a B, 62-73 is a C, 50-62 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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. WeBWorK assignments are posted with a specific due date. It is the student’s responsibility to complete the assignment on time.
  6. 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.
  7. Missed Exams or Lab Exams: Students will receive a ZERO for any missed exam, except for written/documented excuses (illness, personal/family crises, etc.).
  8. Even the visual presence of a Cell Phone during an Exam will result in a ZERO for that Exam.
  9. 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

  1. Intersection of line and quadratic
  2. Linear model of crickets chirping and temperature
  3. 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

  1. Introduction to Maple – lines, polynomials, and rational functions intersecting and other properties
  2. Linear model – Concentration and absorbance (urea concentration in animals)
  3. 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

  1. Exponentials, logarithms, and power laws – relative size of functions
  2. Allometric model of dogs – length, surface area, and weight
  3. 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

  1. Annual length of day and average temperature with trig functions
  2. Malthusian growth model for U. S. – fitting census data
  3. 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

  1. Discrete and nonautonomous Malthusian growth – fitting recent census data
  2. 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

  1. Tangent lines and the derivative – secant lines, limits, experiment rules of derivative
  2. von Bertalanffy model – length and growth of fish
  3. 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

  1. Female body temperature – fertility related to max, min, and point of inflection
  2. Radioactive isotopes – maxima and points of inflection
  3. 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

  1. Continuous logistic growth – fitting data and finding the point of inflection
  2. Tumor growth – logistic and Gompertz growth laws
  3. 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

  1. Optimal volume of box or tent volume
  2. 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

  1. Optimal trough volumes – two troughs with varying angles (differentiation of trig functions)
  2. von Bertalanffy model – length and growth of fish
  3. Beetle populations – fit with logistic, Ricker, and Beverton-Holt models, finding updating

Week 11:  Introduction to differential equations and linear differential equations 

Lab 11:  Lecture on Maple differential equation solvers and slope fields

  1. Malthusian and logistic growth models studied with Maple slope fields
  2. Study different cell sizes and growths – learn the power of Malthusian growth
  3. 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

  1. Growth of E. coli – comparing two models
  2. Carbon monoxide in a room – two models for build-up of CO
  3. Lead exposure in children – modeling with time-varying differential equation

Week 13:  Separation of variables and integration by substitution  

Lab 13:  Lecture on Riemann sums and numerical integration

  1. European population model – time varying growth
  2. Insect population – fit with polynomials and trig functions and use definite integrals to find average
  3. 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

  1. Flight of a ball in two dimensionsn
  2. Model for gonorrhea – SIS epidemic model
  3. Predator-prey 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.


Copyright © 2017 Joseph M. Mahaffy.