This chapter is an introduction to exact differential equations. It begins with the observation that every differential equation \(y' = f(x,y)\) can always be written in the form \(\displaystyle M(x,y) + N(x,y)\frac {dy}{dx} = 0 \qquad \hbox{(1)} \) and that sometimes there is a function F such that \(\displaystyle \frac {d}{dx}F(x,y) = M(x,y) + N(x,y)\frac {dy}{dx} \qquad \hbox{(2)} \) at every point \((x,y)\) belonging to some open rectangular region \(\mathcal {R}\) . When this is the case, solutions of (1) are given implicitly by \(\displaystyle F(x,y) = C, \qquad \hbox{(3)} \) where C is an arbitrary constant. It is shown that the criterion for the existence of such a function is that \(\displaystyle \frac {\partial M}{\partial y} = \frac {\partial N}{\partial x} \qquad \hbox{(4)} \) at each point of \(\mathcal {R}\) . Employing (4) to ascertain whether or not a given Eq. (1) is exact and then finding a function F if it is exact requires a basic understanding of first- and second-order partial derivatives. However, students with only two semesters of calculus under their belt probably have never heard of a partial derivative, much less know what to do with one. Since this book is written for such students, whatever they need to know about partial derivatives in order to understand this chapter is gently introduced in Chap. 1 and then covered more extensively in the first four sections of this chapter. Two types of non-exact differential equations that can be converted into exact equations by means of integrating factors are covered in the last section. Exact differential equations are important for enrollees in engineering and physical science courses. For instance, in electrostatics, these equations define equipotential surfaces. In thermodynamics, equations of state for ideal and real gases involve exact and non-exact differentials and integrating factors. In a multivariable calculus course, Green’s theorem can be used to prove that a line integral \(\int _{C} M\,dx + N\,dy\) is equal to zero if C is a closed path in an open simply-connected region and M and N satisfy condition (4) in that region.