I'm interested in seeing real-world applications of OpenOpt and understanding how FuncDesigner works. Please navigate to the 'Applications' page and list two distinct examples or areas where OpenOpt is applied. Then, go to the 'FuncDesignerDoc' page and identify its primary purpose and one specific capability it offers beyond just building functions.
Navigate to the OpenOpt homepage (openopt.org). Click on the 'Applications' link (ID 26). Identify and list two distinct application examples or areas mentioned on the 'Applications' page. Navigate back to the homepage. Click on the 'FuncDesignerDoc' link (ID 91). Identify the primary purpose of FuncDesigner. Identify one specific capability of FuncDesigner beyond building functions (e.g., integration, interpolation, uncertainty analysis, interval analysis, solving equations, eigenvalue problems). Synthesize the collected information into a concise answer.
Successfully navigate to the 'Applications' page. List two distinct application examples or areas from the 'Applications' page. Successfully navigate to the 'FuncDesignerDoc' page. State the primary purpose of FuncDesigner as a 'tool to rapidly build functions over variables/arrays and get their dense/sparse derivatives via automatic differentiation'. State one specific capability of FuncDesigner beyond building functions, such as 'integration', 'interpolation', 'uncertainty analysis', 'interval analysis', 'EIG (Eigenvalue problems)', or 'solve systems of linear/nonlinear/ODE equations'.