Partial Differential Equations 2 Separation of variables weihuangATmail
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![Partial Differential Equations § 2 Separation of variables weihuang[AT]mail. Spring 2018, Hefei UST©-math-phys ust©](https://slidetodoc.com/presentation_image_h2/017482a0bcaca79182adda6c78759caf/image-1.jpg "Partial Differential Equations § 2 Separation of variables weihuang[AT]mail. Spring 2018, Hefei UST©-math-phys ust©")
Partial Differential Equations § 2 Separation of variables weihuang[AT]mail. Spring 2018, Hefei UST©-math-phys ust© spring 2018 § 2 分离变量法
ust© spring 2018 § 2 分离变量法
ust© spring 2018 § 2 分离变量法
Separation of variables 理� (Sturm-Liouville定理) 本征值的非负性 λn I I II X(b)=0 X’(b)=0 >0 实例 弦振动 III 自然 >0 >0 ≥ 0 >0 >0 X(a)=0 II 右I 左 I X’(a)=0 III 左 II 自然 >0 ust© spring 2018 ≥ 0 >0 ≥ 0 § 2 分离变量法 右II
左I 右I n=1, 2… 齐次b. c. 左II 右II n=0, 1, 2… Tn(t)Xn(x) ust© spring 2018
左I 右II ust© spring 2018 n=1, 2… 左II 右I § 2 分离变量法 n=1, 2…
Sturm-Liouville theory: orthogonal? 正交 Inner product ust© spring 2018
Sturm-Liouville theory: completeness? 完备 ust© spring 2018
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