Applications of Calculus to Biology and Medicine

Case Studies from Lake Victoria

Biology majors and pre-health students at many colleges and universities are required to take a semester of calculus but rarely do such students see authentic applications of its techniques and concepts. Applications of Calculus to Biology and Medicine: Case Studies from Lake Victoria is designed to address this issue: it prepares students to engage with the research literature in the mathematical modeling of biological systems, assuming they have had only one semester of calculus. The text includes projects, problems and exercises: the projects ask the students to engage with the research literature, problems ask the students to extend their understanding of the materials and exercises ask the students to check their understanding as they read the text. Students who successfully work their way through the text will be able to engage in a meaningful way with the research literature to the point that they would be able to make genuine contributions to the literature.

Contents:

• Background:

  • Lake Victoria
  • What is Calculus?

• Population Modeling:

  • Introduction to Population Modeling
  • Logistic Growth
  • Harvesting a Population with Logistic Growth
  • Euler's Method
  • Modeling Interlude: The Modeling Process
  • Research Interlude: Reading a Research Paper
  • Brief Introduction to Sage
  • Projects for Population Modeling

• Drug Modeling:

  • Introduction to Pharmacokinetics
  • Two Models for Lead in the Body
  • Methods of Drug Administration
  • Euler's Method for Systems of Differential Equations
  • Modeling Interlude: Sensitivity Analysis
  • Research Interlude: Writing a Research Paper
  • Projects for Pharmacokinetic Modeling

• Predator Prey Modeling:

  • Undamped Lotka-Volterra Equations
  • Damped Lotka-Volterra Equations
  • Predator Satiation
  • Isoclines
  • Species Formation
  • Top Predators
  • Modeling Interlude: Potential Problems with Models
  • Research Interlude: Making Figures
  • Projects for Predatory-Prey Models

• Infectious Disease Modeling:

  • SIR Model for Infectious Diseases
  • Malaria
  • HIV/AIDS
  • Projects for Infectious Disease Models
  • Classroom Tested Projects

Readership: Undergraduates in biomathematics, mathematical biology, mathematical modeling, applied mathematics, and dynamical systems.
Key Features:

• Project-based, while others are exercise-based
• Motivated by genuine research on the biological systems of one part of the world
• Uses Sage, a free open-source computer algebra system for the mathematical modeling