Books

• Linear Algebra and Optimization for Economists, 2025 - Published by Fondo Editorial PUCP
  Jorge Chávez and Marcelo Gallardo. Foreword by Professor Cesar Martinelli.
  Summary | Book page

  The book covers topics such as vector spaces, linear systems, topology in real vector normed spaces, convex sets (Farkas Lemma), convex functions, unconstrained and constrained optimization, smooth comparative statics and economic applications (such as pure exchange economies).
• Dynamical Systems and Optimal Control for Economists, 2026 - Under review at Springer Verlag
  Jorge Chávez and Marcelo Gallardo.
  Summary | Index| Book Excerpt

  Dynamical Systems and Optimal Control in Continuous Time for Economists. Topics include linear differential equations, nonlinear dynamical systems, limit cycles, calculus of variations, optimal control theory, and economic models.
• Fundamentals of Econometric Theory, 2025 - Published at Decon PUCP
  Juan Leon Jara-Almonte and Marcelo Gallardo.
  Summary | Book

  These lecture notes offer a deep dive into econometrics, structured around key themes from matrix algebra basics to statistical models. The content begins with foundational matrix operations and their relevance to econometrics, advancing to multivariate models with a focus on linear models and optimization issues. It also addresses qualitative variables, sampling methods, and experimental designs. Crucial econometric challenges such as multicollinearity, parameter stability, heteroscedasticity, and serial autocorrelation are thoroughly examined, alongside detection and correction techniques. The notes culminate in discussions on more advanced topics like instrumental variables, maximum likelihood estimation, basic time series analysis, and an appendix on probability theory, equipping readers with a broad understanding of econometric analysis and application.