I'm exploring OpenOpt for advanced numerical problem-solving. Can you provide two distinct real-world or academic applications of OpenOpt from its 'Applications' page? Additionally, navigate to the 'FuncDesignerDoc' and identify two specific types of advanced mathematical problems (beyond basic function building or differentiation) that FuncDesigner is capable of solving, providing the exact section titles from its documentation.
Navigate to the OpenOpt homepage (openopt.org). Click on the 'Applications' link. Identify and list two distinct application examples or areas mentioned on the 'Applications' page. Navigate back to the homepage. Click on the 'FuncDesignerDoc' link. From the 'Contents' section of the 'FuncDesignerDoc' page, identify two distinct section titles that describe FuncDesigner's capability to solve advanced mathematical problems (e.g., specific types of equations, analysis methods, or numerical procedures) beyond just creating functions or performing automatic differentiation. Synthesize the collected information into a concise answer.
The agent successfully navigates to the 'Applications' page. The agent lists two distinct application examples or areas from the 'Applications' page (e.g., 'Small Aerial Vehicle Trajectory Planning' and 'Pycel: Compiling Excel spreadsheets to Python'). The agent successfully navigates to the 'FuncDesignerDoc' page. The agent identifies and states two specific section titles from the 'FuncDesignerDoc' page that represent advanced mathematical problem-solving capabilities of FuncDesigner, such as 'Solving systems of linear equations', 'Solving systems of nonlinear equations', 'Eigenvalue analysis', 'Integration', 'Uncertainty analysis', 'Interval analysis', or 'Solving ODE'.