Derivatives and Integrals of Multivariable Functions This work provides a systematic examination of derivatives and integrals of multivariable functions. The approach taken here is similar to that of the author’s previous text Continuous Functions of Vector Variables : specifically elementary results from single variable calculus are extended to functions in several variable Euclidean space. Topics encompass differentiability partial derivatives directional derivatives and the gradient; curves surfaces and vector fields; the inverse and implicit function theorems; integrability and properties of integrals; and the theorems of Fubini Stokes and Gauss. Prerequisites include background in linear algebra one variable calculus and some acquaintance with continuous functions and the topology of the real line. Written in a definition theorem proof format the book is replete with historical comments questions and discussions about strategy difficulties and alternate paths. Derivatives and Integrals of Multivariable Functions is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry