Differential Equations

Learn to classify and solve first-order ordinary differential equations using separable, linear, and exact methods

• ○Introduction & Classification of ODEs14m
• ○Separable Equations16m
• ○First-Order Linear Equations & Integrating Factors18m
• ○Exact Equations16m
• ○Applications: Mixing, Growth & Cooling14m
• ?First-Order ODEs Quiz14m
• ?First-Order ODEs: Problem Set20m

Solve second-order linear ODEs with constant coefficients using characteristic equations, undetermined coefficients, and variation of parameters

• ○Homogeneous Equations with Constant Coefficients18m
• ○Nonhomogeneous Equations: Undetermined Coefficients18m
• ○Variation of Parameters16m
• ○Mechanical Vibrations16m
• ?Second-Order ODEs Quiz14m
• ?Second-Order ODEs: Problem Set20m

Use Laplace transforms to convert differential equations into algebraic equations for efficient solving

• ○Definition & Basic Transforms18m
• ○Transforms of Derivatives & Solving IVPs18m
• ○Step Functions, Shifts & Convolution18m
• ○Impulse Functions & the Dirac Delta14m
• ?Laplace Transforms Quiz14m
• ?Laplace Transforms: Problem Set20m

Analyze systems of coupled ODEs using matrix methods and eigenvalue techniques

• ○Introduction to Systems of ODEs16m
• ○The Eigenvalue Method: Real Eigenvalues18m
• ○Complex Eigenvalues & Spiral Behavior16m
• ○Nonhomogeneous Systems & Applications14m
• ?Systems of ODEs Quiz14m
• ?Systems of ODEs: Problem Set20m

Construct power series solutions to ODEs and encounter important special functions

• ○Power Series Review & Ordinary Points16m
• ○Regular Singular Points & the Frobenius Method18m
• ○Bessel & Legendre Equations16m
• ?Series Solutions Quiz12m
• ?Series Solutions: Problem Set20m

Apply differential equations to model population dynamics, electrical circuits, mechanical oscillations, and other real-world systems

• ○Population Dynamics & Epidemiology16m
• ○Electrical Circuits: RLC Circuits16m
• ○Mechanical Oscillations & the Pendulum14m
• ○Diffusion & Heat Transfer Models14m
• ?Applications & Modeling Quiz14m
• ?Applications & Modeling: Problem Set20m
• ⚒Capstone Project: Modeling a Damped Spring-Mass System60m

A 20-question assessment covering first-order ODEs, second-order linear ODEs, Laplace transforms, systems, series solutions, and applications

• ?Comprehensive Final Exam45m