MATH225 - Differential Equations

# 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. # Lectures - [[MATH225F26(Day 1) - Introduction to the course, and what an ODE is]] - [[MATH225F26(Day 2) - Order, type, linearity, and what it means to solve an ODE]] - [[MATH225F26(Day 3) - Verifying solutions, explicit and implicit, and the existence-uniqueness theorem]] - [[MATH225F26(Day 4) - Initial value problems, intervals of definition, and when the theorem is silent]] - [[MATH225F26(Day 5) - Slope fields, and where uniqueness breaks]] - [[MATH225F26(Day 6) - Phase lines, classifying equilibria, and the first solution technique]] - [[MATH225F26(Day 7) - A table for the phase line, partial fractions, and which root to keep]] - [[MATH225F26(Day 8) - The integrating factor method, and the interval that comes with it]] - [[MATH225F26(Day 9) - Undetermined coefficients, and the method of the lucky guess]] - [[MATH225F26(Day 10) - The MUC table, resonance, and the Bernoulli substitution]] # Archived material ## Archived videos from the pandemic * [[Teaching/MATH225/Video Resources/(Part 1-Videos) Definitions, terminology, theoretical questions, geometry, solution techniques, and models.|(Part 1-Videos) Definitions, terminology, theoretical questions, geometry, 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-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]] * [[Teaching/MATH225/Video Resources/(Part 3-Videos) Systems of autonomous ordinary differential equations, linear equations, and linearization of nonlinear equations|(Part 3-Videos) Systems of autonomous ordinary differential equations, linear equations, and linearization of nonlinear equations]]