List of Figures
1.1 Alternativesolutionsexample................... 5
1.2 Solutionofthebrachistochroneproblem ............. 17
1.3 Trajectoryofparticle........................ 22
2.1 Maximum area under curves . . . . . . . . . . . . . . . . . . . . 31
2.2 Thecatenarycurve......................... 34
3.1 Saddlesurface............................ 42
3.2 Catenoidsurface .......................... 44
5.1 EigensolutionsofLegendresequation .............. 66
7.1 AccuracyoftheRitzsolution ................... 94
7.2 Domain with overlapping circular regions . . . . . . . . . . . . 100
7.3 SolutionofPoissonsequation...................102
8.1 Geodesiccurveofacylinder....................118
9.1 Naturalsplineapproximation ...................128
9.2 SmoothB-splineapproximation..................133
9.3 PointconstrainedB-spline.....................136
9.4 TangentconstrainedB-spline ...................139
11.1Normalmodesofelasticstring ..................161
11.2Vibrationofelasticmembrane...................167
11.3Beamcross-section.........................170
11.4 Beam profile under its weight . . . . . . . . . . . . . . . . . . . 174
12.1Delaunaytriangularization.....................190
12.2 Parametric coordinates of triangular element . . . . . . . . . . 193
211

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