Math Insight

Thread: University of Minnesota, Math 1241

Topics covered in the course Math 1241, Calculus and Dynamical Systems in Biology at the University of Minnesota.

  1. Background material
    1. Functions
    2. Exponentials and logarithms
    3. Modeling
    4. Gateway exam
  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. 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
  6. Two dimensional autonomous differential equations
    1. Biological models
      1. An infectious disease model
      2. Dynamics of competition
      3. Predator-prey dynamics
      4. A spiking neuron
    2. Phase plane analysis
    3. Problems