Explore the derivation and equilibrium solution of the Heat Equation in one dimension, also known as Laplace's equation, in this comprehensive lecture from the Engineering Mathematics course at the University of Washington. Delve into key concepts such as heat energy, temperature, and Fourier's Law. Examine the step-by-step derivation of the Heat Equation and discuss its implications. Investigate common boundary conditions, including insulated boundaries, to gain a thorough understanding of this fundamental concept in engineering mathematics. Access accompanying lecture notes and the course website for additional resources and in-depth study materials.