It is assumed that the reader is familiar with calculus and linear algebra. For the same equations expressed using tensor calculus or differential forms, see alternative formulations. Partial derivatives are used in vector calculus and differential geometry. The latter definition is consistent with its uses in higher mathematics such as calculus. This is useful in many areas such as integral calculus and differential equations. Lagrange equations also follow from the calculus of variations. This leads to such mathematical machinery as the exterior calculus. This is another formulation of the fundamental theorem of calculus. This is the crux of the Fundamental Theorem of Calculus. She excelled in chemistry, calculus, biology, and physics. Barrow provided the first proof of the fundamental theorem of calculus. The following are important identities involving derivatives and integrals in vector calculus. Analytic geometry continues to be a mainstay of pre-calculus and calculus curriculum. The calculus of finite differences is related to the umbral calculus of combinatorics. The orthoptic article contains another proof, without differential calculus and trigonometric formulae.