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Ordinary Differential Equations and Sturm–Liouville Theory
Ordinary Differential Equations and Sturm–Liouville Theory
foundations +9 more results +66 more equations +19 more depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) depends_on (declared) step_from (declared) definition 9.1: Ordinary differential equation 9.1 Ordinary differe… definition 9.2: Linear equation; homogeneity 9.2 Linear equation;… definition 9.4: Lipschitz condition 9.4 Lipschitz condit… definition 9.14: Wronskian 9.14 Wronskian definition 9.21: Matrix exponential 9.21 Matrix exponenti… definition 9.30: Hyperbolic equilibrium 9.30 Hyperbolic equil… definition 9.37: Fundamental matrix 9.37 Fundamental matr… definition 9.45: Orthonormal set of functions 9.45 Orthonormal set… definition 9.47: Orthonormal series expansion 9.47 Orthonormal seri… definition 9.49: Structure constants of an orthonormal set 9.49 Structure consta… definition 9.54: Sturm–Liouville differential operator 9.54 Sturm–Liouville… definition 9.64: Reduced de Broglie wavelength 9.64 Reduced de Brogl… definition 9.68: Airy functions 9.68 Airy functions lemma 9.6: Weierstrass M-test; uniform limits are continuous 9.6 Weierstrass M-te… theorem 9.8: Picard–Lindelöf 9.8 Picard–Lindelöf corollary 9.9: Linear equations: existence on the whole interval 9.9 Linear equations… lemma 9.10: Grönwall's inequality 9.10 Grönwall's inequ… proposition 9.11: Continuous dependence on the initial data 9.11 Continuous depen… theorem 9.13: Dimension of the solution space 9.13 Dimension of the… proposition 9.15: Abel's identity 9.15 Abel's identity proposition 9.16: Wronskian test for independence 9.16 Wronskian test f… proposition 9.18: The linear equation: integrating factor 9.18 The linear equat… proposition 9.19: Separation of variables 9.19 Separation of va… proposition 9.22: The exponential and its derivative 9.22 The exponential… theorem 9.23: Solution of a constant-coefficient system 9.23 Solution of a co… corollary 9.25: Normal modes of a diagonalizable system 9.25 Normal modes of… equation 9.3: eq:slt-ode-system eq. (9.3) equation 9.4: eq:slt-lipschitz eq. (9.4) equation 9.7: eq:slt-picard-integral eq. (9.7) equation 9.42: eq:slt-mathieu eq. (9.42) equation 9.55: eq:slt-eigenproblem eq. (9.55) equation 9.59: eq:slt-wkb-schrodinger eq. (9.59) equation 9.60: eq:slt-wkb-normal-form eq. (9.60) equation 9.61: eq:slt-wkb-kappa eq. (9.61) equation 9.62: eq:slt-wkb-ansatz eq. (9.62) equation 9.64: eq:slt-wkb-series eq. (9.64) equation 9.74: eq:slt-wkb-airy-scale eq. (9.74) equation 9.75: eq:slt-wkb-linearised eq. (9.75) equation 9.76: eq:slt-wkb-airy-equation eq. (9.76) The chain of Ordinary Differential Equations and Sturm–Liouville Theory: 39 of 133 objects, read left to right from what the chapter assumes to what tests it. Solid lines are declared logical edges, dashed ones were inferred from the structure of the source. Click any node to open its own chain.