Differential Equations

Syllabus

• Separable ordinary differential equations and basic examples.
• First-order linear ordinary differential equations and applications.
• Second-order linear ordinary differential equations; harmonic oscillation.
• First-order ordinary differential equations: existence and uniqueness of solutions.
• First-order linear systems of ordinary differential equations; fundamental systems of solutions.
• Autonomous differential equations, phase portraits, stability, and dynamical systems.
• Partial differential equations: basic concepts and special classes.
• First-order partial differential equations and representative examples.
• The heat equation and initial value problems.
• The wave equation and initial value problems.
• The Laplace and Poisson equations; boundary value problems; maximum and minimum principles.
• Mixed problems solved by Fourier methods.