Math Insight

Thread: Math 201, Spring 2015

Topics covered in the course Math 201, BioCalculus I at the University of Portland.

  1. Background material
    1. Functions
    2. Exponentials and logarithms
  2. Discrete dynamical systems
    1. Dynamical system introduction
    2. An infectious disease model
    3. Linear models
      1. Solving linear systems
      2. Exponential growth and decay
      3. Initial bacteria growth model
      4. Penicillin clearance model
    4. Equilibria
    5. Cobwebbing and stability
    6. Controlling a rabbit population
    7. Exam
  3. The derivative
    1. Introduction to the derivative
    2. Derivatives of polynomials
    3. Derivatives of exponentials and logarithms
    4. Differentiation rules
    5. Partial derivatives
    6. Problems
  4. Applications of differentiation
    1. Linear approximation
    2. Stability of equilibria in discrete dynamical systems
    3. Logistic growth
    4. The derivative and graphing
    5. Minimization and maximization
    6. Problems
  5. Pure-time differential equations
  6. Autonomous differential equations
    1. Introduction
    2. Solution methods
      1. Solution to linear equations
      2. Graphical methods
      3. Stability of equilibria
      4. Numerical solution
    3. Bifurcations
    4. An infectious disease model
    5. Problems

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