Add comprehensive API documentation and restructure docs organization

## Summary This PR comprehensively transforms FiniteDiff.jl documentation by adding detailed docstrings to all functions and completely restructuring the documentation organization for optimal usability. ### Comprehensive Documentation Added **Main API Functions:** - Enhanced `finite_difference_jacobian` with mathematical background and usage examples - Complete `finite_difference_gradient` documentation covering both vector→scalar and scalar→vector cases - Detailed `finite_difference_hessian` with mathematical formulation and complexity analysis - Complete `finite_difference_jvp` documentation explaining Jacobian-vector products - All corresponding in-place (`!`) versions with comprehensive usage notes **Cache Constructors:** - Full documentation for `JVPCache`, `GradientCache`, `HessianCache`, `DerivativeCache` - Both allocating and non-allocating constructor variants documented - Clear guidance on when to use each approach for optimal performance **Internal Functions:** - Complete documentation for epsilon computation functions (`compute_epsilon`) - Detailed `default_relstep` with mathematical justification for step size choices - Documentation for sparse Jacobian utilities (`_make_Ji`, `_colorediteration!`) - Array utility functions (`_vec`, `_mat`, `setindex` overloads) with clear purpose statements ### Documentation Structure Reorganization **New Page Organization:** - **Home**: Package overview from README (clean, no API clutter) - **Tutorials**: Existing tutorial content - **Derivatives**: Single/multi-point scalar function derivatives - **Gradients**: Vector→scalar and scalar→vector gradient computation - **Jacobians**: Vector→vector functions with comprehensive sparse Jacobian guide - **Hessians**: Scalar→matrix second derivatives with mathematical background - **Jacobian-Vector Products**: Efficient directional derivatives without full Jacobians - **Step Size Selection**: Mathematical theory and algorithms for optimal epsilon selection - **Internal Utilities**: Complete coverage of internal functions for advanced users **Improved Content Organization:** - **Explanations first**: Each page provides context and theory before technical details - **Logical flow**: Mathematical background → Performance notes → Function documentation - **Focused content**: Each page concentrates on one functional area - **Educational value**: Theory explanations help users understand when and how to use functions ### Documentation Features **Mathematical Rigor:** - Error analysis for truncation vs round-off errors - Optimal step size derivations for each finite difference method - Complexity analysis (e.g., "O(n) function evaluations, O(h²) accuracy") - Mathematical formulations for Hessian approximations **Practical Guidance:** - Comprehensive parameter descriptions with types and purpose - Usage examples with working code snippets - Performance characteristics and trade-offs - Cache management best practices - Sparse Jacobian computation guidelines **Professional Quality:** - Consistent Julia docstring formatting - Mathematical notation using LaTeX-style formatting - Cross-references between related functions - SciMLStyle code formatting applied throughout ## Technical Implementation **Code Quality:** - Applied JuliaFormatter with SciMLStyle to all modified files - No breaking changes to existing API - All existing tests continue to pass - Added 40+ comprehensive docstrings following Julia conventions **Documentation Build System:** - Restructured `docs/pages.jl` for flat, intuitive navigation - Updated `docs/make.jl` to generate clean index page from README - Created 8 focused category pages replacing complex nested structure - Documentation builds cleanly with proper cross-references ## Impact and Benefits ### For New Users - **Accessible entry point**: Clear explanations of finite difference theory - **Learning progression**: From basic concepts to advanced implementation details - **Practical examples**: Working code snippets for all major functions - **Method selection guidance**: When to use forward vs central vs complex step ### For Experienced Users - **Complete reference**: Detailed parameter documentation for all functions - **Performance optimization**: Complexity analysis and cache usage guidelines - **Advanced features**: Sparse Jacobian computation and JVP efficiency - **Internal understanding**: Documentation of algorithms and design decisions ### For Package Quality - **Professional appearance**: Documentation quality now matches other top-tier Julia packages - **Educational value**: Users learn finite difference theory alongside API usage - **Maintainability**: Well-organized structure makes future updates easier - **Accessibility**: Clear organization helps users find what they need quickly ## Before vs After **Before**: Minimal docstrings like "Cache-less." **After**: Comprehensive documentation with mathematical background, examples, performance analysis, and clear usage guidance. This transformation makes FiniteDiff.jl significantly more accessible while preserving its performance-focused nature and adding educational value for users learning numerical differentiation. 🤖 Generated with [Claude Code](https://claude.ai/code)