Separation of Variables: Spatial Problems

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Diffusion Equations in Spherical Coordinates

Explores solving diffusion equations in steady state conditions for concentric spheres with fixed concentration and flux, emphasizing the importance of linearity and homogeneity.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Heterogeneous Reactions: Transport Effects

Explores transport effects in heterogeneous catalysis, including molecular diffusion and Knudsen diffusion in different types of pores.

Law of Hooke Applications: Spring Problems

Explores the application of the law of Hooke to spring problems and solving equations of motion for block-spring systems.

Sturm-Liouville Problem: Legendre Equation

Explores the Sturm-Liouville problem linked to the Legendre equation and its significance in physics.

Buckling of Beams: Moment-Curvature Relation

Explores beam buckling, moment-curvature relation, deflection, and fundamental beam solutions in structural mechanics.

Numerical Methods: Boundary Value Problems

Explores boundary value problems, finite difference method, and Joule heating examples in 1D.

Heat Transfer Applications

Explores the applications of the Fourier equation in heat transfer phenomena.

Parametric Continuation of Invariant Solutions

Explores parametric continuation of invariant solutions and influence matrix in differential equations.

Separable Differential Equations

Covers separable differential equations of order 1, defining separable equations and providing examples.