These two volumes give comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems. They cover a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus rarer material such as Green’s function, integrodifferential equations, asymptotic expansion and perturbation, calculus of variations, variational principles, finite difference method. And then a very broad range of problems, including beams and columns, plates, shells, structural dynamics, catenary and cable suspension bridge, nonlinear buckling, transports and waves in fluids, geophysical fluid flows, nonlinear waves and solitons, Maxwell equations, Schrodinger equations, celestial mechanics and fracture mechanics and dynamics. The focus is on the mathematical technique for solving the differential equations involved.
Book 1 Theory. Mathematical Preliminaries. Introduction to Differential Equations. Ordinary Differential Equations. Series Solutions of 2nd Order ODE. System of First Order Differential Equations. First Order Partial Differential Equations. Higher Order Partial Differential Equations. Green’s Function. Wave, Diffusion and Potential Equations. Eigenfunction Expansions. Integral and Integro-Differential Equations. Asymptotic Expansion and Perturbation. Calculus of Variations. Variational Principles. Finite Difference Method. Appendices. Book 2 Applications. Theory of Beams and Columns. Theory of Plates. Theory of Shells. Structural Dynamics. Catenary and Cable Suspension Bridges. Nonlinear Buckling. Transports and Waves in Fluids. Geophysical Fluid Flows. Nonlinear Waves and Solitons. Mathematical Theory for Maxwell Equations. Quantum Mechanics and Schrodinger Equation. Celestial Mechanics. Fracture Mechanics and Dynamics.