This discussion focuses on the concept of particular integrals in partial differential equations (PDEs) as outlined in the 2006 edition of "Mathematical Methods for Physics and Engineering" by Riley, Hobson, and Bence. Key points include the importance of understanding that a function of a single variable with a zero derivative is constant, and a function of two variables with a zero derivative with respect to one variable depends solely on the other variable. Additionally, exploring counterexamples can enhance comprehension of these principles.
PREREQUISITESThis discussion is beneficial for students and professionals in mathematics, physics, and engineering, particularly those studying partial differential equations and seeking to deepen their understanding of integration techniques and mathematical proofs.
If you have a function of a single variable whose derivative is zero, then that function must be a constant. If you have a function of two variables whose derivative is zero with respect to one of the variables, then it must be a function only of the other variable.vgarg said:TL;DR Summary: Partial integration
Can someone please explain the steps for the integrations in red circles on the attached page? This a page from Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 2006 edition.
Thank you.