## Course description - [**Course Description**](https://catalog.mines.edu/coursesaz/math/): Classical techniques for first and higher order equations and systems of equations. Laplace transforms. Phase-plane and stability analysis of non-linear equations and systems. Applications from physics, mechanics, electrical engineering, and environmental sciences. - **Prerequisites**: Grade of C- or better in MATH112 or MATH122. - **Corequisites**: CSCI128 or CSCI102. 3 hours lecture; 3 semester hours. ## Course Content The course is typically broken down into 40+ lectures each with their own learning objectives. Using LLM w/ vision, we have developed: - [[Archive of transcribed MATH225 lecture boards]] - [[Teaching/MATH225/Lecture Notes/MATH225 Fall 2024 | Fall 2024 transcribed lecture boards ]] with [[Teaching/MATH225/MATH225Su25/PublicShare/Lecture Materials/Fall 2024 - Lecture topics and learning objectives | generated learning objectives]] - [[MATH225 - Mentimeter slide base]] ### [[Teaching/MATH225/Video Resources/(Part 1-Videos) Definitions, terminology, theoretical questions, geometry, solution techniques, and models.| Part 1 - Definitions, terminology, theoretical questions, geometry, first-order solution techniques, and models]] ### [[Teaching/MATH225/Video Resources/(Part 2-Videos) Theory for second-order linear equations, general solutions for homogeneous equations with constant coefficients, the method of undetermined coefficients, electrical and mechanical oscillatory systems, and the Laplace transform| Part 2 - Theory for second-order linear equations, general solutions for homogeneous equations with constant coefficients, the method of undetermined coefficients, electrical and mechanical oscillatory systems, and the Laplace transform]] ### [[Teaching/MATH225/Video Resources/(Part 3-Videos) Systems of autonomous ordinary differential equations, linear equations, and linearization of nonlinear equations| Part 3 - Systems of autonomous ordinary differential equations, linear equations, and linearization of nonlinear equations]]