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Calculus for modelling

Categories: Calculus
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About Course

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

About the instructor

AM
These courses aim to equip you with the confidence to apply skills in mathematical modelling and data analytics in high-quality research, based on my experience working as an infectious disease modeller at the Big Data Institute University of Oxford, London School of Hygiene and Tropical Medicine (LSHTM) and the University of Warwick. I have taught mathematical modelling, statistics and R programming to audiences ranging from undergraduate students to professionals. I have designed and led courses internationally (University of Malaya and Federal University of Bahia, Brazil) and in the UK (University of Leeds, Warwick, LSHTM). Prior to this, I completed a doctorate in mathematical modelling of infectious disease at the University of Liverpool, following a Master’s degree in applied statistics from the University of Lancaster.

Course Curriculum

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

  • Gradient at a point I
  • Gradient at a point II
  • Exercise
  • Exercise solution

Differentiation III
Introduction of the general rules of differentiation

  • General rules of differentiation

Integration
Introduction of the principles of integration

  • Introduction
  • Excercise
  • Exercise solution
  • Separation of variables

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

  • Introduction
  • Population growth ODE
  • Population growth solution
  • Population growth solution II

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

  • Introduction
  • Population growth with carrying capacity
  • Population growth model equilibrium states
  • Population growth model equilibrium states II

Numerical integration I
What is numerical integration : the Euler method

  • Introduction
  • Euler method I
  • Euler method II
  • Comparison to analytical solution

Numerical integration II
Numerical integration using deSolve and RK methods

  • Runge-Kutta methods
  • Using deSolve I
  • Using deSolve II
  • Exercise
  • Exercise solution

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

  • Introduction
  • Predator-prey model
  • Predator-prey model II
  • Exercise
  • Exercise solution

Course feedback
Help to improve the course with your feedback

  • Form
  • Review

Student Ratings & Reviews

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PG
4 months ago
This is a good course!