Learning Outcomes

In this free course, you will learn how to:

• Recognize the role of differential equations in modeling real-world scenarios in science and engineering
• Generate custom implementations of numerical methods for solving differential equations
• Apply the Runge-Kutta Method to numerically solve ordinary differential equations
• Solve system-level nonlinear differential equations using the Runge-Kutta method
• Discuss the theoretical foundations of the Runge-Kutta method for numerical solutions of ordinary differential equations
• Evaluate and compare results obtained from implementing the Runge-Kutta method in Python and MATLAB
• Explain the importance of numerical methods, particularly Runge-Kutta, in computational applications
• Assess the accuracy and efficiency of Runge-Kutta implementations in solving specific problems
• Relate Python and MATLAB programming skills to numerical computation in the context of differential equations
• Outline the steps involved in implementing the Runge-Kutta method for various differential equation problems
• Describe the process of implementing the Runge-Kutta 4th order algorithm in both Python and MATLAB
• Analyze and simulate a Lotka-Volterra (Predator-Prey) system's dynamics through numerical solutions