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This lecture covers the formulation of problems with Newtonian physics, the introduction of constraints and Lagrange multipliers, and the application of Lagrange's equations to solve problems with constraints. It also discusses the concept of generalized coordinates and the role of forces in constrained motion. The instructor explains how to express constraints mathematically, the significance of Lagrange multipliers, and the process of reducing degrees of freedom in a system. The lecture concludes with examples illustrating the application of constraints and Lagrange's equations in physics.