respositorio-fundamentals

Expert Tutor in Electromagnetism and Circuits (FIS1533) that integrates rigorous analytical and physical methods with practical problem-solving strategies. Specialized in electrostatics, electric dipoles, dielectrics, Gauss in material media, current, resistance, Ohm's law, DC circuits, Kirchhoff's laws, and RC transients. Focuses on physical models, geometry, and systematic equation solving.

Orchestrator skill that reads exercise images, solves them, and generates a LaTeX document. Use when user asks to "resuelve los ejercicios en", "desarrolla las soluciones de las imágenes", "escribe la solución en LaTeX para los ejercicios de", or "procesar imágenes de certámenes".

Compiles a .tex file to PDF using latexmk, then deletes all auxiliary files (log, aux, out, fls, fdb_latexmk, synctex.gz). Called automatically after latex-writer finishes, or manually when the user asks to compile/render a LaTeX file.

LaTeX document generator called by exercise-solver and other skills. Receives structured content and writes a clean, simple .tex file that looks like a student solution, not a typeset textbook. Delegates image embedding to latex-illustrator.

Estándar rector de estilo, flujo semántico en español y desarrollo continuo para todos los resolvedores. Use when user asks to "verificar estilo de las soluciones", "aplicar el estilo matemático", "auditar conectores en español", "revisar formato de resolución", or "validar flujo semántico de matemáticas".

Generates diagrams (probability trees, flowcharts, sequence diagrams) using Mermaid CLI (mmdc), exports them as PNG, and returns the relative path for embedding in LaTeX via latex-illustrator. Use whenever a diagram would be cleaner as a Mermaid chart than as raw TikZ.

Expert tutor in Probability and Statistics for probability axioms, inference, and regression. Use when user asks to "calcular probabilidad", "función de distribución conjunta", "estimación de máxima verosimilitud", "prueba de hipótesis", "regresión lineal simple", or "intervalo de confianza".

Expert skill for retrieving and integrating formulas from the NCEES FE Reference Handbook (10.1) into LaTeX documents. Provides full-text search via content_raw and image references for every page. Maps printed pages to PDF indices across three offset zones.

Skill for seamlessly integrating images into LaTeX documents. Handles graphicx package management, figure environments, captioning, labeling, and ensuring correct relative paths for assets generated by other skills (like r-plotter).

Skill for modeling and rendering mathematical functions and data visualizations using R. Generates R scripts to create high-quality, appropriately scaled images for LaTeX documents. Handles directory management for image assets.

Expert Tutor in Ordinary Differential Equations (MAT1640) that integrates rigorous analytical methods with practical problem-solving strategies. Specialized in first-order equations (linear, exact, separable, Bernoulli), second-order linear equations, and Laplace transforms. Focuses on identifying the structure of the equation and applying the precise algorithmic method.

Automates committing and pushing PDF changes to the repository with descriptive messages.

Expert assistant in Calculus I (MAT1610) that integrates the theoretical rigor of Spivak's text with the graphical and practical methodology of Stewart. Use for proofs, function analysis, and derivative resolution.

Advanced Tutor for Calculus II (MAT1620) that integrates Stewart's geometric and physical intuition with Spivak's analytical rigor. Specialized in integration techniques, topology of infinite series, and vector geometry in R3.

Expert Tutor in Multivariable Calculus (MAT1630). Masterfully handles the transition from single-variable calculus to vector fields, multiple integration, and vector analysis theorems. Combines Stewart's 3D visualization capabilities with Spivak-style rigorous analysis of differentiability and topology in R^n.