Section 5.1 revises some preliminaries from Multivariable Calculus needed for the derivation of the three-dimensional heat equation and uniqueness theorems.



Section 5.2 revises a derivation of the three-dimensional heat equation from Multivariable Calculus.



Section 5.3 describes the reduction to Poisson’s equation and Laplace’s equations for three-dimensional steady heat conduction.



Section 5.4 describes the reduction to Poisson’s equation and Laplace’s equations for two-dimensional steady heat conduction, as well as common boundary conditions.



Section 5.5 illustrates the application of Fourier’s method to solve a boundary value problem for Laplace’s equation in cartesian coordinates.



Section 5.6 illustrates the application of Fourier’s method to solve a boundary value problem for Laplace’s equation in polar coordinates.



Section 5.7 describes the derivation of Poisson’s integral formula.



Section 5.8 revises two Uniqueness Theorems from Multivariable Calculus and discusses briefly their implications for the application of Fourier’s methods.



The Wrap Up video contains a number of closing remarks including adverts for the optional sections of the lecture notes and follow on courses.