Vector and complex calculus : a textbook for students of the physical sciences

Abstract

Vector and complex calculus are essential for applications to electromagnetism, fluid and solid mechanics, and the differential geometry of surfaces. The standard multivariable calculus courses are largely limited to 'xyz' calculus, but vector calculus is about geometric concepts invariant under coordinate transformations. This textbook takes the students from the geometry and algebra of vectors, to the key concepts and tools of vector calculus, including differential geometry of curves and surfaces, curvilinear coordinates, and capping off with a study of the essential elements of the calculus of functions of one complex variable.