Applied Mathematics: A Contemporary Approach
Presents current topics in applied mathematics such as singular perturbation, nonlinear wave propagation, bifurcation, similarity methods, and the numerical solution of partial differential equations. It emphasizes the interdependency of mathematics and its application to physical phenomena, and is written in a style accessible to readers with a wide range of interests and backgrounds. There is also coverage of scaling and dimensional analysis, calculus of variations, Fourier and transform methods for partial differential equations, and integral equations.
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DIMENSIONAL ANALYSIS AND SCALING
Scaling Known Functions
6 other sections not shown
analysis applied approximation arbitrary assume becomes boundary conditions calculation called characteristic coefficients compute conservation Consider constant continuous convergence coordinates critical curve defined denotes depends derivative determine difference diffusion dimensional direction eigenvalues energy equilibrium Example Exercise exists Figure Find fixed flow fluid force function given gives governing heat Hence holds independent initial initial condition integral interval invariant known linear mass material mathematical matrix method motion nonlinear norm obtain occurs ordinary origin parameter partial differential equation path perturbation physical physical law positive proof Prove quantities region represents respectively result satisfy scale scheme shown similar solution solved space stability Substituting surface temperature theorem transformation unit value problem variables variations vector wave write zero