Math Insight

Thread: Math 1241, Fall 2020

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
  2. Discrete dynamical systems
    1. Gateway exam
    2. Dynamical system introduction
    3. An infectious disease model
    4. Linear models
      1. Solving linear systems
      2. Exponential growth and decay
      3. Initial bacteria growth model
      4. Penicillin clearance model
    5. Equilibria
    6. Cobwebbing and stability
    7. Controlling a rabbit population
    8. Exam
  3. The derivative
    1. Introduction to the derivative
    2. Derivatives of polynomials
    3. Derivatives of exponentials and logarithms
    4. Differentiation rules
    5. 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
    1. Introduction
    2. Graphical solution
    3. The Forward Euler algorithm
    4. Integration
    5. Riemann sums
    6. The Fundamental Theorem of Calculus
    7. Applications
    8. Problems
  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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