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This lecture discusses the importance of optimizing energy consumption in buildings by utilizing solar energy through the installation of PV panels on roofs and facades. The instructor emphasizes the benefits of directly using the electricity generated on-site, particularly in EPFL. The lecture covers the process of solving nonlinear equations to calculate heat loads and optimize energy supply. Various methods, including Taylor expansion and numerical solving methodologies, are explored to find solutions efficiently. The importance of defining convergence criteria, selecting appropriate starting points, and scaling variables for accurate results is highlighted. Practical examples and strategies for improving building energy efficiency are also provided.