Applied Mathematics

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.