Nonlinear Differential Equation Course
This course equips you with essential techniques for tackling nonlinear differential equations via population dynamics models. Explore stability analysis, bifurcation phenomena, and numerical simulations using Euler and Runge-Kutta methods. Develop the ability to construct precise ODE models and deliver clear, professional reports—perfect for mathematicians aiming to apply advanced concepts in real-world scenarios.

from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
Gain practical skills to examine equilibria, stability, and bifurcations in scalar nonlinear models, emphasising population growth and resource harvesting. Master analytical and numerical solutions for first-order equations, conduct parameter studies, assess persistence against extinction, and produce detailed reports that effectively convey model outcomes and insights.
Elevify advantages
Develop skills
- Model nonlinear populations by constructing and evaluating logistic growth with harvesting ODEs.
- Solve nonlinear ODEs efficiently using separation of variables, exact solutions, and partial fractions.
- Analyse stability through equilibrium classification, phase line diagrams, and one-dimensional bifurcations.
- Conduct numerical simulations with Euler and Runge-Kutta methods tailored for stiff population systems.
- Communicate findings with precise, rigorous reports suited for expert audiences.
Suggested summary
Before starting, you can change the chapters and workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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