A Differential Equations class focuses on mathematical equations involving derivatives, emphasizing how quantities change and applying this understanding to real-world phenomena. Students learn to classify and solve ordinary differential equations using analytical methods, such as separation of variables and integrating factors. The course covers theoretical concepts like existence and uniqueness theorems, stability analysis, and qualitative methods, with advanced topics including systems of equations and nonlinear dynamics. Emphasis is placed on mathematical reasoning and problem-solving, equipping students to analyze and solve dynamic systems across various disciplines.
Note 1 (Sec 1.1 - 1.2): First-Order Equations / Antiderivatives (Post)
Note 6 (Sec 2.2): Equations with Constant Coefficients (Post)
Note 8 (Sec 2.4): Equations with Variable Coefficients (Post)
Note 9 (Sec 3.1): Definition of Laplace Transforms and Their Basic Properties (Post)
Note 13 (Sec 4.1): Linear Systems vs. Second-Order Equations
Note 14 (Sec 4.2): Matrices and Linear Systems
Note 15 (Sec 4.2 - 4.3): Differential Equations and Equilibria / The Eigenvalue Problem
Note 16 (Sec 4.4): Solving Linear Systems; Real Unequal Eigenvalues
Note 17 (Sec 4.4): Solving Linear Systems; Complex Eigenvalues / Real, Equal Eigenvalues
Note 18 (Sec 4.5): Phase Plane Analysis
Note 19 (Sec 4.6): Nonhomogeneous Systems
Note 20 (Sec 5.1): Nonlinear Systems and Linearization