Episode June 28, 2025 20 min 17s

Introduction to Differential Equations Using Sage

Serves as a textbook for understanding differential equations. It covers both ordinary differential equations (ODEs) and partial differential equations (PDEs), introducing fundamental concepts such as their classification by order and linearity, and methods for finding their solutions. The book integrates the use of Sage, a free and open-source software, to illustrate examples and numerical approximation techniques like Euler's method. Practical applications are highlighted through various models, including Newtonian mechanics, RLC circuits, mixing problems, Lanchester's battle equations, and the Lotka-Volterra predator-prey system. It also explores advanced topics like power series methods, Laplace transforms, and eigenvalue methods for systems of differential equations.

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