Introduction 1 Basic Theory of ODE and Vector Fields Introduction 1 The derivative 2 Fundamental local existence theorem for ODE 3 Inverse function and implicit function theorems 4 Constant-coefficient linear systems; exponentiation of matrices 5 Variable-coefficient linear systems of ODE： Duhamel＇s principle 6 Dependence of solutions on initial data and on other parameters 7 Flows and vector fields 8 Lie brackets 9 Commuting flows; Frobenius＇s theorem 10 Hamiltonian systems 11 Geodesics 12 Variational problems and the stationary action principle 13 Differential forms 14 The symplectic form and canonical transformations 15 First-order， scalar， nonlinear PDE
鄂公網(wǎng)安備 42010302001612號(hào) 