Vector Calculus

This chapter gives a non-technical overview of differential equations from across mathematical physics, with particular attention to those used in the book. It is a common trend in physics and nature, or perhaps just the way numbers and calculus come together, that, to describe the evolution of things, most theories use a differential equation of low order. This chapter is useful for those with no prior knowledge of the differential equations and explains the concepts required for a basic exposition of classical mechanics. It discusses separable differential equations, boundary conditions and initial value problems, as well as particular solutions, complete solutions, series solutions and general solutions. It also discusses the Cauchy–Lipschitz theorem, flow and the Fourier method, as well as first integrals, complete integrals and integral curves.