Juan Patiño-Echeverría
Auckland, New Zealand
Teaching
Tools and interactive applets for use in lectures and/or self-study. All run directly in the browser — no software installation needed.
Differential equations
Phase plane explorer ↗
Interactive vector fields and trajectories for nonlinear ODE systems. Includes RK4 integration, nullclines, and preset systems (pendulum, Van der Pol, Lotka-Volterra, Duffing, and more). Adjustable equations, view window, and arrow style.
Interactive vector fields and trajectories for nonlinear ODE systems. Includes RK4 integration, nullclines, and preset systems (pendulum, Van der Pol, Lotka-Volterra, Duffing, and more). Adjustable equations, view window, and arrow style.
Lecture notes
Methods in Applied Mathematics (MATHS 362)
Lecture notes on asymptotic methods: asymptotic expansions, regular and singular perturbation problems, and matched asymptotic expansions for algebraic and differential equations.
Open PDF ↗
Lecture notes on asymptotic methods: asymptotic expansions, regular and singular perturbation problems, and matched asymptotic expansions for algebraic and differential equations.
Open PDF ↗
Mathematical Modelling (MATHS 765)
Course notes on the modelling process: dimensional analysis and the Buckingham Pi theorem, nondimensionalisation, and dominant balance in the construction of models.
Open PDF ↗
Course notes on the modelling process: dimensional analysis and the Buckingham Pi theorem, nondimensionalisation, and dominant balance in the construction of models.
Open PDF ↗