Modelling Real-World Problems with Differential Equations

Ever wondered how to mathematically describe phenomena like population growth, disease spread, or the trajectory of moving objects? This course equips you with the foundational knowledge and practical skills to build, analyze, and interpret mathematical models using differential equations, turning complex real-world problems into solvable systems. By the end of this course, you will be able to apply a structured modelling cycle to various scenarios, gaining a deeper understanding of how dynamic systems evolve over time. You will develop the ability to translate observations into mathematical language and use differential equations as powerful tools for prediction and analysis. What you'll learn: * Understand the fundamental concepts of ordinary differential equations (ODEs) and their classifications. * Formulate real-world scenarios into solvable mathematical models using differential equations. * Apply analytical techniques to find solutions for common types of differential equations. * Explore basic numerical methods for approximating solutions when analytical methods are complex. * Interpret and validate model solutions to draw meaningful conclusions about system behavior. * Practice the complete mathematical modelling cycle, from problem definition to solution analysis. Through clear, written explanations and practical examples, you will progress from understanding basic definitions to constructing and solving your own models, building confidence in mathematical problem-solving. This course is designed for absolute beginners with a basic understanding of algebra and calculus, eager to apply mathematical tools to real-world challenges. No prior experience with differential equations or advanced mathematics is required. Begin your journey into the powerful world of mathematical modelling today.