The MTH 912 course must clearly cover: · First-order equations - including all the following topics: existence and uniqueness of solutions, initial value problems, basic numerical methods, separable equations, linear equations, exact equations, substitution methods and applications · Higher-order equations - including all the following topics: the general solution to homogeneous linear equations, linear independence, method of undetermined coefficients, the general solution to linear non-homogeneous equations, variation of parameters, and applications. · Solutions of initial value problems by Laplace transforms, to include definition of Laplace transforms, inverse Laplace transforms and their properties, convolution, unit step function, and applications of Laplace transforms.In addition to the above, the course must cover at least one of the following in detail:1. Power series solutions,2. Partial differential equations and Fourier series,3. Systems of linear differential equations, including the use of eigenvalues and eigenvectors.4. Further numerical methods,5. Non-cursory treatment of other advanced topics. Prerequisite: MTH 902, Calculus II with a C or better.
REVISION: 11/9/2023 – Laplace transfer content moved from optional to required with elements identified. Effective Spring 2024 for new and first time ongoing review courses.
Minor Tweaks (rearranging topics for emphasis) – Spring 2020, effective Fall 2020. Previous Revision: Minor Tweaks (rearranging topics for emphasis) – Fall 2019, 11/22/2019, effective Spring 2020. Previous significant revision March 2016