Notes
This page contains the notes (by topic not necessarily by lecture) for MATH 341 Differential Equations during the Fall 2026 semester. Sections may be added or edited as the course progresses. The notes are not meant to be a substitute for the textbook (Logan 2015), but rather a supplement to it. They are also not meant to be a substitute for attending lectures. Students are encouraged to read through the relevant section of notes prior to attending lectures.
Section 1 (~75-90 minutes lecture time) introduces the basic idea of a differential equation with an emphasis on ordinary differential equations (ODEs).
Section 2 (~120–140 minutes lecture time) covers first-order ODEs including slope-fields, separable equations, linear equations, integrating factors, and applications.
Section 3 (~120–145 minutes lecture time) covers one-dimensional dynamical system including topics such as equilibrium points, stability, phase-line, and bifurcations.
Section 4 (~125–160 minutes lecture time) covers second-order linear constant-coefficient ODEs and applications.
Section 5 (~100–120 minutes lecture time) covers the method of variation of parameters for second-order linear ODEs that do not necessarily have constant coefficients.
Section 6 (~125–145 minutes lecture time) covers the definition and basic properties of Laplace Transforms.
Section 7 (~120–140 minutes lecture time) covers the application of Laplace Transforms to solve ODEs.
Section 8 (~125–145 minutes lecture time) covers the convolution property of Laplace Transforms and impulse forces.
Section 9 (~125–145 minutes lecture time) covers systems of first-order linear ODEs and applications. Includes a discussion of matrices.
Section 10 (~125–145 minutes lecture time) covers the eigenvalue problem for linear systems of ODEs and applications for solving linear systems.
Section 11 (~120–140 minutes lecture time) covers phase plane analysis for linear systems of ODEs, nonhomogeneous linear systems, and applications.
Section 12 (~125–145 minutes lecture time) introduces phase plane analysis for nonlinear systems of ODEs.
Section 13 (~120–140 minutes lecture time) introduces applications of phase plane analysis for nonlinear systems of ODEs.
Section 14 (~120–140 minutes lecture time) introduces numerical methods and computation of solutions for initial value problems for ODEs.