Calculus for Modelling

Categories: Calculus
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About Course

Have you just entered the world of infectious disease modelling? Are you ‘not a mathematician’?
Understanding a few core topics of calculus will enable you to understand a wide range of  mathematical models.

Learn the mathematical background of ordinary differential equation models with worked examples, exercises and tutor support – use the Q&A box to ask questions.

What Will You Learn?

  • The concept of differentiation and integration
  • Ordinary differential equations (ODEs)
  • The population growth ODE model with and without carrying capacity
  • Equilibrium and steady states of ODES
  • Numerical integration including Euler method
  • R packages for numerical integration
  • The predator-prey ODE model

Course Content

Differentiation I
Learn how to calculate the gradient of a straight line from first principles

Differentiation II
Learn how to differentiate a function using the definition of a derivative

Differentiation III
Introduction of the general rules of differentiation

Integration
Introduction of the principles of integration

Ordinary differential equations
What is an ordinary differential equation? Using population growth as an example

Equilibrium states of ODEs
Learn what an equilibrium state of an ODE is, using population growth with carrying capacity as an example

Numerical integration I
What is numerical integration : the Euler method

Numerical integration II
Numerical integration using deSolve and RK methods

Systems of ODEs
The predator-prey model as an introduction to systems of ODEs

Summary
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