Applied Mathematics: A Contemporary Approach

TLDR: In this paper, the Buckingham Pi Theorem Scaling was used to scale up the Buckingham pi scaling method for dimensionality analysis in the context of multidimensional analysis of continuous systems, and the Laplace Equation Hyperbolic Equations Index.

Abstract: DIMENSIONAL ANALYSIS AND SCALING: Dimensional Analysis The Buckingham Pi Theorem Scaling PERTURBATION METHODS: Regular Perturbation Singular Perturbation Boundary Layer Analysis Two Applications CALCULUS OF VARIATIONS: Variational Problems Necessary Conditions for Extrema The Simplest Problem Generalizations Hamiltonian Theory Isoperimetric Problems EQUATIONS OF APPLIED MATHEMATICS: Partial Differential Equations The Diffusion Equation Classical Techniques Integral Equations WAVE PHENOMENA IN CONTINUOUS SYSTEMS: Wave Propagation Mathematical Models of Continua The Wave Equation Gasdynamics Fluid Motions in R3 STABILITY AND BIFURCATION: Intuitive Ideas One Dimensional Problems Two Dimensional Problems Hydrodynamic Stability SIMILARITY METHODS Invariant Variational Problems Invariant Partial Differential Equations The General Similarity Method DIFFERENCE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS: Finite Difference Methods The Diffusion Equation The Laplace Equation Hyperbolic Equations Index.